Colloquium
Interconnection in magnonic networks: functional building blocks for an alternative controllable way of spin-wave and quantum computation
13 December in 11:30
Alexandr Sadovnikov (Saratov State University)
The content of the talk is devoted to the possible integration of magnonic devices and interconnection between them with the use of magnonics, straintronics, spin-orbitronics. In recent years much research has been directed towards the use of spin waves for signal processing at microwave and subterahertz frequencies due to the possibility to carry the information signal without the transmission of a charge current. Recent theoretical and experimental studies suggest that strain can be used to engineer energy-efficient complicated 2D and 3D material and heterostructures. The main topic of the talk will be focused on the application of the magnonic unit for signal processing and interconnection routes in the magnonic networks. The part of the talk will be devoted to the the experimental observations of the strain-mediated spin-wave coupling phenomena in different magnonic structures based on the asymmetric adjacent magnonic crystals, adjacent magnetic yttrium iron garnet stripes and array of magnetic stripes, which demonstrates the collective spin-wave phenomena such as the discrete soliton formation. The voltage-controlled spin-wave transport along bilateral magnonic stripes was demonstrated. The model describing the spin-wave transmission response and predicting its value is proposed based on the self-consistent equations. It was shown that the strain-mediated spin-wave channels can be used to route the magnonic information signal and thus the composite magnon-straintronic structure could be used to fabricate magnonic platforms for energy-efficient signal processing. The obtained results open new perspectives for the future-generation electronics using integrated magnonic networks.
Oceanic Eddy-Induced Transport: Full-Tensor Approach
15 November in 11:30
Pavel S. Berloff (Imperial College London)
In geophysical turbulence effects of small-scale motions on the large-scale ones are often formulated in terms of turbulent (eddy) diffusion characterized by the eddy diffusivity coefficient. Within this context we focused on passive-tracer transport induced by mesoscale oceanic eddies and applied brute-force approach, without any simplifications and extra assumptions. The uncovered new levels of complexity of the corresponding full-tensor eddy diffusivity coefficient, referred to as the "transport tensor", call for reconsideration of how the eddy diffusion and corresponding scale interactions are treated in observations, general circulation models and theory.
Impact of lattice reconstruction on electronic properties of twistronic heterostructures hosting long-period moiré superlattice
1 March in 11:30
Vladimir Enaldiev (Abrikosov Centre of Theoretical Physics, MIPT)
In the talk I describe a multiscale approach to lattice relaxation of long-period moiré superlattice in marginally twisted bilayers [1,2]. Based on that I introduce a concept of interface ferroelectricity emerging as an array of polar domains with alternating out-of-plane polarization in twistronic heterostructures consisting of 2D material’s layers lacking of inversion symmetry [3]. For the structures based on twisted transition metal dichaIcogenides bilayers I present a domain wall network model which predicts a universal scaling of polar domain structure in external out-of-plane electric field [4]. Second part of my talk will be devoted to modelling of graphene-based twistronic heterostructures using hybrid kp-tight-binding Hamiltonians [5]. In particular, I will describe electronic properties of AB/BA domain wall in bilayer graphene [6] and show that single-element structures such as few-layer rhombohedral graphite stacks with twin boundary plane can host weak ferroelectricity [7].
[1] V.V. Enaldiev, V. Zolyomi, C. Yelgel et al, Phys. Rev. Letters 124, 206101 (2020).
[2] A. Weston, Y. Zou, V. Enaldiev et al, Nature Nanotechnology 15, 592 (2020).
[3] A. Weston, E.G. Castanon, V. Enaldiev et al, Nature Nanotechnology 17, 390 (2022).
[4] V.V. Enaldiev, F. Fereira, V.I. Fal’ko, Nano Letters 22, 1534 (2022).
[5] A. Garcia-Ruiz, H. Deng, V. Enaldiev, V. Falko, Phys Rev B 104, 085402 (2021).
[6] V. Enaldiev, C. Moulsdale, A.K. Geim, V.I. Falko, arXiv:2307.12848.
[7] A.Garcia-Ruiz, V. Enaldiev, A. McEllstrim, V. Falko, Nano Lett. 23, 4120 (2023).
[1] V.V. Enaldiev, V. Zolyomi, C. Yelgel et al, Phys. Rev. Letters 124, 206101 (2020).
[2] A. Weston, Y. Zou, V. Enaldiev et al, Nature Nanotechnology 15, 592 (2020).
[3] A. Weston, E.G. Castanon, V. Enaldiev et al, Nature Nanotechnology 17, 390 (2022).
[4] V.V. Enaldiev, F. Fereira, V.I. Fal’ko, Nano Letters 22, 1534 (2022).
[5] A. Garcia-Ruiz, H. Deng, V. Enaldiev, V. Falko, Phys Rev B 104, 085402 (2021).
[6] V. Enaldiev, C. Moulsdale, A.K. Geim, V.I. Falko, arXiv:2307.12848.
[7] A.Garcia-Ruiz, V. Enaldiev, A. McEllstrim, V. Falko, Nano Lett. 23, 4120 (2023).
Quantum chaos in two-dimensional gravity
1 December 2023 in 11:30
Alexander Altland (University of Cologne, DE)
Two-dimensional gravity defines a toy paradigm in which the physics of gravitational systems is reduced to a bare minimum (essentially topology and symmetry). Its simplicity makes it an ideal testbed for holographic principles, a concrete realization of which was proposed by Kitaev in terms of his now famous SYK model. The SYK model is approximately dual to a two-dimensional bulk known as Jackiw-Teitelboim (JT) gravity. Intriguingly, we have come to understand that a third player (next to symmetry and topology) essential to the construction of that holographic correspondence is quantum chaos. In this seminar, I will try to review these developments. Starting from a quick review of the SYK model and JT gravity, we will discuss two conceptually independent bridges between these systems. In particular, we will discuss how concepts developed in the era of mesoscopics in the 90s in condensed matter physics are now becoming key in gravity. If time permits, we will also discuss how the Efetov supersymmetric sigma model (derived as a student at the Landau institute) now appears as a natural generalization of the above duality to string theory.
Moat-band physics and emergent excitonic topological order in correlated electron-hole bilayers
24 November 2023 in 16:00
Tigran Sedrakyan (University of Massachusetts, Amherst)
The role of the particle-particle interaction becomes increasingly important if the spectral band structure of a free system has increasing degeneracy. Ultimately, it will be the role of interactions to choose the state of the system. Examples include the systems with the lowest band having a degenerate minimum along a closed contour in the reciprocal space -- the Moat. A weak perturbation can set a new energy scale describing the state with qualitatively different properties in such a limit of infinite degeneracy. In this talk, I will discuss the general principles behind the universal properties of correlated bosons on moat bands, which host topological order with long-range quantum entanglement. In particular, I will discuss moat-band phenomena in shallowly inverted InAs/GaSb quantum wells, where we observe an unconventional time-reversal-symmetry breaking excitonic ground state under imbalanced electron and hole densities. I will show that the strong frustration of the system leads to a moat band for excitons, resulting in a time-reversal-symmetry breaking excitonic topological order, which explains all our experimental observations.
Understanding quantum and classical chaos in Hamiltonian systems through adiabatic transformations
2 December 2022 in 16:00
A. Polkovnikov (Boston University, USA)
Chaos is synonymous to unpredictability. In the case of classical systems this unpredictability is expressed through exponential sensitivity of trajectories to tiny fluctuations of the Hamiltonian or to the initial conditions. It is well known that chaos is closely related to ergodicity or emergence of statistical mechanics at long times, but the precise relations between them are still debated. In quantum systems the situation is even more controversial with trajectories being ill-defined. A standard approach to defining quantum chaos is through emergence of the random matrix theory. However, as I will argue, this approach is rather related to the eigenstate thermalization hypothesis and ergodicity than to chaps. In this talk I will suggest that one can use fidelity susceptibility of equivalently geometric tensor and quantum Fisher information as a definition of chaos, which applies both to quantum and classical systems and which is related to long time tails of the auto-correlation functions of local perturbations. Through this approach we can establish of existence of the intermediate chaotic but non-ergodic regime separating integrable and ergodic phases, which have maximally sensitive eigenstates. I will discuss how this measure is also closely related to recently proposed definition of chaos through the Krylov complexity or the operator growth and that there is very interesting and still unexplained duality between short and long time behavior of chaotic and integrable systems As a specific example of this approach I will apply these ideas to interacting disordered systems and show that (many-body) localization is unstable in thermodynamic limit irrespective of the disorder strength.
Chirality and spin in organic molecules
10 June 2022 in 11:30
Karen Michaeli (Weizmann Institute of Science)
In the late 19th century, Louis Pasteur discovered that biology shows a preference for molecules with a specific handedness. Ever since, researchers have been trying to understand the origin of life’s homochirality and its implications. For example, electron transport in organisms, an essential part of basic biological processes such as respiration and photosynthesis, is realized via insulating helical molecules. Recent studies further found that the transmission probability of electrons through such molecules is strongly spin-dependent, with the preferred spin direction set by the chirality. This direct connection between spin and chirality raises numerous fundamental questions. It thus opens a new arena of research at the interface between biology and quantum physics. In my talk, I will review the most important experimental findings and describe a theoretical model that explains the origin of spin-dependent transport: The helical geometry induces robust spin filtering accompanied by, and intimately related to, strongly enhanced overall transmission through chiral molecules. In particular, I will focus on spin-selectivity in the chiral system with strong electron-phonon interactions. Finally, I will present some ideas for integrating organic molecules into solid-state devices for various applications.
Plethora of Many-Body Ground States in Magic Angle Twisted Bilayer Graphene
1 April 2022 in 10:00
Dmitri K. Efetov (LMU Munich, Germany)
Twist-angle engineering of 2D materials has led to the recent discoveries of novel many-body ground states in moiré systems such as correlated insulators, unconventional superconductivity, strange metals, orbital magnetism and topologically nontrivial phases. These systems are clean and tuneable, where all phases can coexist in a single device, which opens up enormous possibilities to address key questions about the nature of correlation induced superconductivity and topology, and allows to create entirely novel quantum phases with enhanced interactions. In this talk we will introduce some of the main concepts underlying these systems, concentrating on magic angle twisted bilayer graphene (MATBG) and show how symmetry-broken states emerge at all integer electron fillings [1]. We further will discuss recent experiments including screened interactions [2], Chern insulators [4], magnetic Josephson junctions [4], quantum criticality [5], re-entrant correlated insulators at high magnetic fields [6] and discuss some of the avenues for novel quantum sensing applications [7].
[1] Nature, 574, 653 (2019).
[2] Nature, 583, 375–378 (2020).
[3] Nature Physics, 17, 710 (2021).
[4] arXiv:2110.01067 (2021).
[5] arXiv:2108.07753 (2021).
[6] arXiv:2201.09260 (2021).
[7] arXiv:2111.08735 (2021).
[1] Nature, 574, 653 (2019).
[2] Nature, 583, 375–378 (2020).
[3] Nature Physics, 17, 710 (2021).
[4] arXiv:2110.01067 (2021).
[5] arXiv:2108.07753 (2021).
[6] arXiv:2201.09260 (2021).
[7] arXiv:2111.08735 (2021).
Many-body delocalisation as symmetry breaking
12 November 2021 in 11:30
John Chalker (Physics Department, University of Oxford)
I will start this talk with an overview of recent work on quantum dynamics in many body systems far from equilibrium. This work has led to an understanding from the
perspective of quantum information, of how a such systems may approach an
equilibrium state at long times, in which initial conditions are effectively forgotten. It
has also led to an appreciation that there are classes of system in which an
equilibrium state is not reached at long times. One of these classes is made up of
many-body localised systems, in which randomness in the Hamiltonian is
responsible for a long-lived memory of the initial state of a system. By varying the
strength of randomness, a transition can be induced between localised and ergodic
phases, which seems very different from conventional symmetry-breaking phase
transitions.
In the second part of the talk I will discuss minimal models for quantum chaos and many-body localisation. The models are Floquet quantum circuits for lattice spin systems, in which time evolution is generated by unitary gates that couple neighbouring sites. In particular, I will examine the circumstances in which a version of the so-called diagonal approximation (originally developed for the semiclassical limit in low-dimensional chaotic systems) can be applied to these systems. Within this framework I will show that the many-body delocalisation transition can be seen as a form of symmetry breaking transition, having many of the features generally associated with conventional phase transitions in classical statistical mechanical models.
Joint work with Sam Garratt: Phys. Rev. X 11, 021051 (2021) and Phys. Rev. Lett. 127, 026802 (2021)
In the second part of the talk I will discuss minimal models for quantum chaos and many-body localisation. The models are Floquet quantum circuits for lattice spin systems, in which time evolution is generated by unitary gates that couple neighbouring sites. In particular, I will examine the circumstances in which a version of the so-called diagonal approximation (originally developed for the semiclassical limit in low-dimensional chaotic systems) can be applied to these systems. Within this framework I will show that the many-body delocalisation transition can be seen as a form of symmetry breaking transition, having many of the features generally associated with conventional phase transitions in classical statistical mechanical models.
Joint work with Sam Garratt: Phys. Rev. X 11, 021051 (2021) and Phys. Rev. Lett. 127, 026802 (2021)
Limit shape phase transitions. A merger of Arctic circles
29 October 2021 in 15:30
Alexander Abanov (SUNY Stony Brook)
A limit shape phenomenon in statistical mechanics is the appearance of a most probable macroscopic state. This state is usually characterized by a well-defined boundary separating frozen and liquid spatial regions. The earliest studies related to this phenomenon in the context of crystal shapes are in works by Pokrovsky and Talapov [1]. We will review a few examples of the models leading to the appearance of limit shapes. Then we consider a class of topological phase transitions in the limit shape problem of statistical mechanics. The problem considered is generally known as the Arctic circle problem. The considered transition can be visualized as the merging of two melted regions (Arctic circles). We establish the mapping, which identifies the transition as the transition known in lattice QCD and random matrix problems [2,3]. The transition is a continuous phase transition of the third order. We identify universal features of the limiting shape close to the transition using the hydrodynamic description.
[1] V. L. Pokrovsky and A. L. Talapov, Phys. Rev. Lett. 42, 65 (1979). "Ground State, Spectrum, and Phase Diagram of Two-Dimensional Incommensurate Crystals."
[2] D. J. Gross and E. Witten, Phys. Rev. D, 21 (2): 446, (1980). "Possible third-order phase transition in the large-n lattice gauge theory"; S. R. Wadia, Phys. Lett. B 93, 403 (1980). "$N=\infty$ phase transition in a class of exactly soluble model lattice gauge theories."
[3] M. R. Douglas and V. A. Kazakov. Phys. Lett. B, 319 (1-3): 219–230, 1993. "Large n phase transition in continuum QCD2."
[1] V. L. Pokrovsky and A. L. Talapov, Phys. Rev. Lett. 42, 65 (1979). "Ground State, Spectrum, and Phase Diagram of Two-Dimensional Incommensurate Crystals."
[2] D. J. Gross and E. Witten, Phys. Rev. D, 21 (2): 446, (1980). "Possible third-order phase transition in the large-n lattice gauge theory"; S. R. Wadia, Phys. Lett. B 93, 403 (1980). "$N=\infty$ phase transition in a class of exactly soluble model lattice gauge theories."
[3] M. R. Douglas and V. A. Kazakov. Phys. Lett. B, 319 (1-3): 219–230, 1993. "Large n phase transition in continuum QCD2."
The Riemann Hypothesis and Quantum Physics
1 October 2021 in 11:30
Jon Keating (Oxford)
The Riemann Hypothesis concerns the positions of the zeros of the Riemann zeta-function. It has been one of the central unsolved problems in mathematics for over 150 years. Surprisingly, there appear to be deep connections between the theory of the Riemann zeta-function and quantum physics, and these have stimulated close collaborations between the two areas. In particular, analogies with quantum chaos and random matrix theory have been the focus of considerable attention. In this colloquium I will review some of these ideas and their implications.
Tetraquarks in the spotlight of recent LHCb data
17 September 2021 in 11:30
A.V. Nefediev (LPI)
Recently the LHCb Collaboration announced intriguing results in the spectroscopy of hadrons with charmed quarks. I discuss a theoretical approach to the analysis of these and similar experimental data, interpretation of the results obtained and a possible connection with the tetraquark states which are widely discussed in the literature in this respect.
Topology protection–unprotection transition: Example from multiterminal superconducting nanostructures
21 May 2021 in 11:30
Xiao-Li Huang and Yuli V. Nazarov (TU Delft)
We show theoretically that in the superconducting nanostructures the gapped states of different topology are not always protected by separating gapless states. Depending on the structure design parameters, they can be either protected or not, with a protection–unprotection transition separating these two distinct situations. We build up a general theoretical description of the transition vicinity in the spirit of Landau theory. We speculate that similar protection–unprotection transitions may also occur for other realizations of topological protection in condensed matter systems.
The hydrodynamics of many-body integrable systems
19 March 2021 in 11:30
Benjamin Doyon (King's College London)
Hydrodynamics is a powerful theory for the emergent behaviour at large wavelengths and low frequencies in many-body systems. The theory says that only few degrees of freedom are sufficient in order to describe what is observed at large scales of space and time, and it provides equations for the dynamics of these degrees of freedom. It is strongly based on the presence of microscopic conservation laws in the many-body model, such as conservation of energy, momentum and mass. But the standard equations of hydrodynamics fail to describe cold atom experiments in low dimensions. It is now understood that this is because the model accurately describing these experiments, the Lieb-Liniger model, is integrable. Integrable systems admit an extensive number of conservation laws, which must be taken into account in the emergent hydrodynamic theory. Recently this hydrodynamic theory, dubbed ``generalised hydrodynamics”, has been developed. In this colloquium, I will review fundamental aspects of hydrodynamics and the main idea and equations of generalised hydrodynamics, with the simple example of the quantum Lieb-Liniger model. I will discuss recent cold-atom experiments that confirm the theory, and some of the exact results that can be obtained with this formalism, such as exact nonequilibrium steady states and exact asymptotic of correlation functions at large space-time separations in Gibbs and generalised Gibbs states.
Probabilistic Liouville Theory
19 February 2021 in 11:30
Antti Kupiainen (University of Helsinki)
A. Polyakov introduced Liouville Conformal Field theory (LCFT) in 1981 as a way to put a natural measure on the set of Riemannian metrics over a two dimensional
manifold. Ever since, the work of Polyakov has echoed in various branches of physics
and mathematics, ranging from string theory to probability theory and geometry.
In the context of 2D quantum gravity models, LCFT is related through the work of Knizhnik, Polyakov and Zamolodchikov to the scaling limit of Random Planar Maps and through the Alday-Gaiotto- Tachikava correspondence LCFT is conjecturally related to certain 4D Yang-Mills theories. Through the work of Dorn,Otto, Zamolodchikov and Zamolodchikov and Teschner LCFT was argued to be to a certain extent integrable.
I will review a probabilistic construction of LCFT developed together with David, Rhodes and Vargas and recent proofs concerning the integrability of LCFT.
References
Francois David, Antti Kupiainen, Remi Rhodes, Vincent Vargas, Liouville quantum gravity on the Riemann sphere, Commun. Math. Phys. 342 (3), 869-907 (2016)
Antti Kupiainen, Remi Rhodes, Vincent Vargas, The DOZZ formula from the path integral, Journal of High Energy Physics May 2018, 2018:94
Antti Kupiainen, Remi Rhodes, Vincent Vargas, Integrability of Liouville Theory: Proof of the DOZZ Formula, Annals of Mathematics 191, 81-166, (2020)
Colin Guillarmou, Antti Kupiainen, Remi Rhodes, Vincent Vargas, Conformal bootstrap in Liouville Theory, arXiv:2005.11530
I will review a probabilistic construction of LCFT developed together with David, Rhodes and Vargas and recent proofs concerning the integrability of LCFT.
References
Francois David, Antti Kupiainen, Remi Rhodes, Vincent Vargas, Liouville quantum gravity on the Riemann sphere, Commun. Math. Phys. 342 (3), 869-907 (2016)
Antti Kupiainen, Remi Rhodes, Vincent Vargas, The DOZZ formula from the path integral, Journal of High Energy Physics May 2018, 2018:94
Antti Kupiainen, Remi Rhodes, Vincent Vargas, Integrability of Liouville Theory: Proof of the DOZZ Formula, Annals of Mathematics 191, 81-166, (2020)
Colin Guillarmou, Antti Kupiainen, Remi Rhodes, Vincent Vargas, Conformal bootstrap in Liouville Theory, arXiv:2005.11530
First principle models of human memory
15 January 2021 in 11:30
Prof. Michail Tsodyks (Weizmann Institute of Science, Rehovot; and Institute for Advanced Study, Princeton)
Human memory is a multi-staged phenomenon of extreme complexity, which results in highly unpredictable behavior in real-life situations. Psychologists developed classical paradigms for studying memory in the lab, which produce easily quantifiable measures of performance at the cost of using artificial content, such as lists of randomly assembled words. I will introduce a set of simple mathematical models describing how information is maintained and recalled in these experiments. Surprisingly, they provide a very good description of experimental data obtained with internet-based memory experiments on a large number of human subjects. Moreover, more detailed mathematical analysis of the models leads to some interesting ideas for future experiments with potentially very surprising results.
Photon-assisted tunneling at the atomic scale: Probing resonant Andreev reflections from Yu-Shiba-Rusinov states
4 December 2020 in 16:00
Katharina Franke (Free University Berlin, Germany)
Exchange coupling of magnetic adsorbates to a superconducting substrate leads to Yu-Shiba-Rusinov (YSR) states within the superconducting energy gap. These can be probed by scanning tunneling spectroscopy as a pair of resonances at positive and negative bias voltage and over a wide range of tunnel conductances. At low tunneling rates, the current is carried by single-electron processes, where each excitation is sufficiently quickly followed by a relaxation into the energetic continuum. Upon increasing the junction conductance, the relaxation rates suppress single-electron tunneling and resonant Andreev processes start to dominate the transport process. The cross-over of these processes is expressed in the variation of the ratio of YSR peak height at positive and negative bias voltage [1].
Here, we investigate these transport processes by photon-assisted tunneling. While applying highfrequency radiation to the tunneling junction, we record the differential conductance spectra in the low and high-conductance regime. At low conductance, the YSR states exhibit symmetrically spaced sidebands with their spacing directly evidencing single-electron tunneling. Surprisingly, at large junction conductance, the spacing remains the same while the patterns become asymmetric. We show that this asymmetry is direct evidence of a resonant Andreev reflection with tunneling threshold conditions imposed on its electron and hole component [2]. We suggest that photon-assisted tunneling can be a powerful tool for the determination of the nature of the charge carriers in a single tunneling event.
References
[1] M. Ruby, F. Pientka, Y. Peng, F. von Oppen, B.W. Heinrich, and K.J. Franke, "Tunneling Processes into Localized Subgap States in Superconductors", Phys. Rev. Lett. 115, 087001 (2015).
[2] O. Peters, N. Bogdanoff, S. Acero González, L. Melischek, J. Rika Simon, Gaël Reecht, C.B. Winkelmann, Felix von Oppen & K.J. Franke, "Resonant Andreev reflections probed by photon-assisted tunnelling at the atomic scale", Nat. Phys. (2020). https://doi.org/10.1038/s41567-020-0972-z; arXiv:2001.09534
References
[1] M. Ruby, F. Pientka, Y. Peng, F. von Oppen, B.W. Heinrich, and K.J. Franke, "Tunneling Processes into Localized Subgap States in Superconductors", Phys. Rev. Lett. 115, 087001 (2015).
[2] O. Peters, N. Bogdanoff, S. Acero González, L. Melischek, J. Rika Simon, Gaël Reecht, C.B. Winkelmann, Felix von Oppen & K.J. Franke, "Resonant Andreev reflections probed by photon-assisted tunnelling at the atomic scale", Nat. Phys. (2020). https://doi.org/10.1038/s41567-020-0972-z; arXiv:2001.09534
Mòire Samples: The twisted bilayer graphene scenario
20 November 2020 in 16:00
Andrei Bernevig (Princeton University, USA)
We present a full theory of the interacting insulating phases of twisted bilayer graphene around the first magic angle where the bandwidth of the “active” bands becomes very small. We show that the single particle Hamiltonian is fully anomalous: it contains stable topology for every set of bands. Furthermore, we analyze the Coulomb interaction and obtain exact insulating ground states as well as the full excitation spectrum in certain limits.
Higher-order topological insulators and superconductors
15 May 2020 in 11:30
Piet Brouwer (Free University Berlin, Germany)
Topological insulators combine an insulating bulk with gapless states at their surfaces. This talk introduces "higher-order topological insulators", which are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at corners or at edges of the crystal. I'll show that such "higher-order boundary states" are a generic boundary manifestation of the nontrivial bulk topology, if the bulk topology relies on a crystalline symmetry for its protection.
Towards an analytic description of periodic anomalous waves in nature via the focusing NLS model (joint work with P. G. Grinevich)
7 May 2020 in 11:30
Paolo Maria Santini (Dept. of Physics, University of Roma "La Sapienza")
The focusing NLS equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, and MI is considered the main physical mechanism for the appearence of anomalous (rogue) waves (AWs) in nature. We first show how the finite gap method adapts to the NLS Cauchy problem for a generic periodic initial perturbation of the unstable background solution, in the case of a finite number N of unstable modes, allowing one to construct the solution, to leading order, in terms of elementary functions of the initial data. In particular, if N=1, one obtains the analytic quantitative description of a Fermi-Pasta-Ulam recurrence of AWs already observed in real (water wave and nonlinear optics) and numerical experiments. Then we present the analytic description of the O(1) effect of a small loss or gain on the dynamics of periodic AWs, in full agreements with recent water wave and numerical experiments. If time remains, we shall discuss analogies and differences with AWs in other contexts: on the Ablowitz-Ladik lattice and in the massive Thirring model relativistic field theory (with F. Coppini).
Charge and entropy transport in strontium titanate
17 April 2020 in 11:30
Kamran Behnia (CNRS/ESPCI, PSL Research University, Paris, France)
The ferroelectric instability in pristine strontium titanate is aborted by quantum fluctuations. Therefore, the static electric permittivity saturates to an extremely large value at low temperature and the effective Bohr radius approaches a micron. In this context, removing a tiny fraction of oxygen atoms turns the system to a dilute metal with a sharp Fermi surface and a superconducting instability. The focus of this talk will be charge and entropy transport by electrons in this dilute metal and their general implications.
The temperature dependence of the resistivity of this dilute metal at low-temperature implies that electron-electron scattering can generate a T-square resistivity even in absence of Umklapp scattering with a single Fermi pocket. The magnitude of resistivity at a low temperature would imply a mean-free-path too short to be physically plausible. Combined with the temperature dependence of the Seebeck coefficient, this implies that non-degenerate electrons become heavier with warming. We will see that these observations cannot be explained by available polaronic theories. There is a whole family of dilute metals emerging from doped quantum paraelectrics with similar properties.
The temperature dependence of the resistivity of this dilute metal at low-temperature implies that electron-electron scattering can generate a T-square resistivity even in absence of Umklapp scattering with a single Fermi pocket. The magnitude of resistivity at a low temperature would imply a mean-free-path too short to be physically plausible. Combined with the temperature dependence of the Seebeck coefficient, this implies that non-degenerate electrons become heavier with warming. We will see that these observations cannot be explained by available polaronic theories. There is a whole family of dilute metals emerging from doped quantum paraelectrics with similar properties.
Effective function theory on Riemann surfaces and applications.
21 February 2020 in 11:30
Bogatyrev A.B. (INM RAS)
Many model physical and engineering problems admit closed form solutions in terms of function-theoretic objects on Riemann surfaces or spaces of their moduli. We consider issues of effective and robust calculation of such objects (Abelian integrals,
their periods, linear and quadratic differentials, meromorphic functions ...) for surfaces of a high genus (greater than one).
Examples of solving several problems will be given.
Electric dipole moment searches using storage rings
24 January 2020 in 11:30
Frank Rathmann (Institut f. Kernphysik, Forschungszentrum Juelich, Germany)
The Standard Model (SM) of Particle Physics is not capable to account for the apparent matter-antimatter asymmetry of our Universe. Physics beyond the SM is required and is either probed by employing highest energies (e.g., at LHC), or by striving for ultimate precision and sensitivity (e.g., in the search for electric dipole moments). Permanent electric dipole moments (EDMs) of particles violate both time reversal (T) and parity (P) invariance, and are via the CPT-theorem also CP-violating. Finding an EDM would be a strong indication for physics beyond the SM, and pushing upper limits further provides crucial tests for any corresponding theoretical model, e.g., SUSY.
Up to now, EDM searches focused on neutral systems (neutrons, atoms, and molecules). Storage rings, however, offer the possibility to measure EDMs of charged particles by observing the influence of the EDM on the spin motion in the ring. Direct searches of proton and deuteron EDMs, however, bear the potential to reach sensitivities beyond 10−29 e⋅cm. Since the Cooler Synchrotron COSY at the Forschungszentrum Jülich provides polarized protons and deuterons up to momenta of 3.7 GeV/c, it constitutes an ideal testing ground and starting point for such an experimental program. Besides the discussion of the achievements of the JEDI collaboration, and the description of an effort to perform a first direct deuteron EDM measurement at COSY, the talk will highlight in addition future technical developments that will pave the way toward EDM searches in dedicated rings. A recent advancement that grew out of the successful work performed by JEDI is the formation of the CPEDM Collaboration, which aims at the design of an EDM prototype ring that could be hosted either at CERN or at COSY, will be discussed as well.
Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape
20 December 2019 in 15:00
Vadim Smelyanskiy (Google, Los Angeles)
We will review the advances and challenges in the field of quantum combinatorial optimization and closely related problem of low-energy eigenstates and coherent dynamics in transverse field quantum spin glass models. We will discuss the role of collective spin tunneling that gives rise to bands of delocalized non-ergodic quantum states providing the coherent pathway for the population transfer (PT) algorithm: the quantum evolution under a constant transverse field that starts at a low-energy spin configuration and ends up in a superposition of spin configurations inside a narrow energy window. We study the transverse field induced quantum dynamics of the following spin model: zero energy of all spin configurations except for a small fraction of spin configuration that form a narrow band at large negative energy. We use the cavity method for heavy-tailed random matrices to obtain the statistical properties of the low-energy eigenstates in an explicit analytical form. In a broad interval of transverse fields, they are non-ergodic, albeit extended giving rise to a qualitatively new type of quantum dynamics. For large transverse fields »1 the typical runtime of PT algorithm $\sim \sqrt{2^n / \Omega e^r}$ scales with n and Ω as that of the Grover’s quantum search, except for the small correction to the exponent θ ≈ 1/(2). The model we consider is non-integrable. As a result, our PT protocol does not require any fine-tuning of and may be initialized in a computational basis state. We argue that our approach can be applied to study PT protocol in other optimization problems with the potential quantum advantage over classical algorithms.
Ordered fluctuations: about vestigial order in quantum materials
20 December 2019 in 11:30
Joerg Schmalian (Karlsruhe Institute of Technology)
A hallmark of the phase diagrams of quantum materials is the existence of multiple electronic ordered states. In many cases those are not independent, competing phases, but instead display a complex intertwinement. In this talk, we focus on a realization of intertwined orders with a fluctuation-driven vestigial phase characterized by a composite order parameter. In other words, we are investigating the condensation of fluctuations.
We demonstrate that this concept naturally explains the nematic state in iron-based superconductors and nematic superconductivity in doped topological insulators. In addition we propose a natural mechanism for charge 4e superconductivity with half flux quanta. We present a formalism that provides a framework to understand the complexity of quantum materials based on symmetry, largely without resorting to microscopic models.
We demonstrate that this concept naturally explains the nematic state in iron-based superconductors and nematic superconductivity in doped topological insulators. In addition we propose a natural mechanism for charge 4e superconductivity with half flux quanta. We present a formalism that provides a framework to understand the complexity of quantum materials based on symmetry, largely without resorting to microscopic models.
Physics at the Edge of a QHE setting
25 October 2019 in 11:30
Yuval Gefen (Weizmann Institute of Science, Israel)
The structure of the edge of a QHE edge is constrained, but not dictated, by the topology of the bulk. Particularly interesting is the class of hole-conjugate fractional QH states. For such states the edge hosts counter-propagating modes that are responsible for quantized electrical and thermal conductance. In the coherent quantum limit renormalized edge modes emerge, which may involve neutral modes with non-trivial exchange statistics. I will discuss the behavior of topology-influenced transport coefficient both in the coherent and the fully equilibrated regimes, topological classification of non-equilibrium shot noise, and the relation to recent experiments.
Dynamical Glass - en route from KAM and FPUT to MBL
6 September 2019 in 11:30
Sergej Flach (Institute for Basic Science, Republic of Korea)
Classical many body interacting systems are typically chaotic (nonzero Lyapunov exponents) and their microcanonical dynamics ensures that time averages and phase space averages are identical (ergodic hypothesis). In proximity to an integrable limit the long- or short-range properties of the network of nonintegrable action space perturbations define the finite time relaxation properties of the system towards Gibbs equilibrium. I will touch upon few analytical results including the KAM theorem, and review a number of computational studies which originate from the pioneering work of Enrico Fermi, John Pasta, Stanislaw Ulam and Mary Tsingou. I will then focus on short range networks which lead to a dynamical glass (DG), using a classical Josephson junction chain in the limit of large energy densities or small Josephson energies. Close to these limits the Josephson coupling between the superconducting grains induces a short-range nonintegrable network in the corresponding action space. I will introduce a set of quantitative measures which lead to the Lyapunov time TΛ, the ergodization time TE, and to a diffusion constant D. In the DG the system fragments into large patches of nonresonant ’integrable’ grains of size l separated by triplets of resonant chaotic patches, all surviving over large times. TE sets the time scale for chaotic dynamics in the triplets. Contrary, TE ≈ l2/D is the much larger time scale of slow diffusion of chaotic triplets. The DG is a generic feature of weakly non-integrable systems with a short range coupling network in action space, and expected to be related to nonergodic quantum metallic states of quantum many-body systems in proximity to a many-body localization phase.
Two-fluid phenomena in one-dimensional quantum liquids
21 June 2019 in 11:30
Anton Andreev
One-dimensional quantum liquids are commonly treated using the Luttinger liquid theory, which neglects elementary excitations with high energies. In this approximation, in addition to the number of particles, energy, and momentum the liquid possesses another conserved quantity - J, which may be interpreted as the difference between the numbers of right- and left- moving particles. Beyond the Luttinger liquid approximation J is no longer conserved, but its relaxation time is exponentially long at low temperatures.
I will show that as a result, one-dimensional quantum liquids exhibit two-fluid behavior. In particular in a wide frequency interval they support two sound modes that are similar to the first and second sound in superfluid He.
Minimal excitations states: From time resolved single particle fermionic states for Electron Quantum Optics to Digital communication and music.
24 May 2019 in 11:30
D. Christian Glattli (Nanoelectronics Group, Service de Physique de l’Etat Condensé, CEA Saclay, France)
In the 90’s, an impressive series of works by theoreticians from the Landau Institute on electrons shot noise in quantum conductors [1] and on the statistics of transfer of electrons [2] has leaded to the emergence of the beautiful concept of minimal excitation states [3-5]. These minimal excitation states can be generated by applying voltage pulses on the contact of a conductor to inject short single electron pulses. These states show minimal noise and provide a convenient and clean single electron source for electron optics whose aim is to perform quantum optics tasks with electrons instead of photons. The minimal excitations states, now called levitons, have been produced in recent experiments [6] and have triggered a large number of theoretical works. They have enabled Hong Ou Mandel like experiments [6] with electrons and single electron quantum Tomography [7]. Extension to fractionally charged anyons is possible.
At the root of the minimal excitation property is a specific single side band modulation of the electron wave by the Lorentzian voltage pulse. This property can be applied to classical electromagnetic or acoustic waves for applications in digital communication [8] or in music sound synthesis.
[1] G. B. Lesovik, JETP Letters, 49 (9), 592-594 (1989).
[2] L.S. Levitov, G.B. Lesovik, Charge-transport statistics in quantum conductors, JETP Lett., 55 (9), 555-559 (1992).
[3] A. Ivanov, H.W. Lee, L.S. Levitov, Coherent states of alternating current, Phys. Rev. B 56(11), 6839-6850 (1997); cond-mat/9501040
[4] L.S. Levitov, H. Lee, G.B. Lesovik, Electron Counting Statistics and Coherent States of Electric Current, J. Math. Phys., 37(10), 4845-4866 (1996); cond-mat/9607137.
[5] J. Keeling, I. Klich, and L. S. Levitov, Minimal Excitation States of Electrons in One-Dimensional Wires, Phys. Rev. Lett. 97, 116403 (2006).
[6] Minimal-excitation states for electron quantum optics using levitons, J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegscheider, P. Roulleau & D. C. Glattli, Nature, 502, 659–663 (2013).
[7] Quantum tomography of an electron, T. Jullien, P. Roulleau, B. Roche, A. Cavanna, Y. Jin & D. C. Glattli, Nature, 514, 603–607 (2014).
[8] Power Spectrum Density of Single Side Band CPM Using Lorenztian Frequency Pulses, Haïfa Farès, D. Christian Glattli, Yves Louet, Jacques Palicot, Preden Roulleau, and Christophe Moy, IEEE Wireless Communications Letters, 6 (6), 786-789, (2017).
At the root of the minimal excitation property is a specific single side band modulation of the electron wave by the Lorentzian voltage pulse. This property can be applied to classical electromagnetic or acoustic waves for applications in digital communication [8] or in music sound synthesis.
[1] G. B. Lesovik, JETP Letters, 49 (9), 592-594 (1989).
[2] L.S. Levitov, G.B. Lesovik, Charge-transport statistics in quantum conductors, JETP Lett., 55 (9), 555-559 (1992).
[3] A. Ivanov, H.W. Lee, L.S. Levitov, Coherent states of alternating current, Phys. Rev. B 56(11), 6839-6850 (1997); cond-mat/9501040
[4] L.S. Levitov, H. Lee, G.B. Lesovik, Electron Counting Statistics and Coherent States of Electric Current, J. Math. Phys., 37(10), 4845-4866 (1996); cond-mat/9607137.
[5] J. Keeling, I. Klich, and L. S. Levitov, Minimal Excitation States of Electrons in One-Dimensional Wires, Phys. Rev. Lett. 97, 116403 (2006).
[6] Minimal-excitation states for electron quantum optics using levitons, J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegscheider, P. Roulleau & D. C. Glattli, Nature, 502, 659–663 (2013).
[7] Quantum tomography of an electron, T. Jullien, P. Roulleau, B. Roche, A. Cavanna, Y. Jin & D. C. Glattli, Nature, 514, 603–607 (2014).
[8] Power Spectrum Density of Single Side Band CPM Using Lorenztian Frequency Pulses, Haïfa Farès, D. Christian Glattli, Yves Louet, Jacques Palicot, Preden Roulleau, and Christophe Moy, IEEE Wireless Communications Letters, 6 (6), 786-789, (2017).
Hydrodynamic approach to electronic transport
26 April 2019 in 11:30
Boris Narozhny (KIT)
The last few years have seen an explosion of interest in hydrodynamic effects in interacting electron systems in ultra-pure materials. One such material, graphene, is not only an excellent platform for the experimental realization of the hydrodynamic flow of electrons, but also allows for a controlled derivation of the hydrodynamic equations on the basis of kinetic theory. The resulting hydrodynamic theory of electronic transport in graphene yields quantitative predictions for experimentally relevant quantities, e.g. viscosity, electrical conductivity, etc. In this talk I will review recent theoretical advances in the field, compare the hydrodynamic theory of charge carriers in graphene with relativistic hydrodynamics and recent experiments, and discuss applications of hydrodynamic approach to novel materials beyond graphene.
Видео (в связи с ошибкой видео записано не до конца)
On reconstructing nonlinearly encrypted signals corrupted by noise.
12 April 2019 in 11:30
Yan V. Fyodorov (King's College London)
I consider the problem of reconstructing a source vector from its encrypted image corrupted by an additive Gaussian noise.
Assuming encryption to be given by a random Gaussian mapping, the reconstruction problem in the framework of the Least Square Scheme turns out to be equivalent to finding the configuration of minimal energy in a certain version of spherical spin glass model.
As a measure of the quality of the signal reconstruction one can use the mean overlap between the original signal and its recovered image.
Thi overlap is analysed in the framework of Parisi scheme of Replica Symmetry Breaking. If the mapping is quadratic, there exists a threshold in the noise-to-signal ratio beyond which the reconstruction is impossible. The behaviour close to the threshold is controlled by the replica symmetry breaking mechanism and is characterized by a nontrivial exponent 3/4.
Correlation-induced localization
5 April 2019 in 11:30
Vladimir Kravtsov
Conventional Anderson localization is due to destructive interference of
matter waves described by local random Hamiltonians. Correlations in
random diagonal elements of such a Hamiltonian are known to favor
delocalization. Recently systems with non-local Hamiltonians become
experimentally accessible. We consider two families of such random
matrix Hamiltonians with correlations in the long-range hopping terms
and demonstrate that localization is enhanced and the wave function
ergodicity is progressively degrading as the correlations become stronger.
We review the localization/delocalization criteria of Mott and Anderson
and show that the former is the sufficient criterion of weak ergodicity
and the latter is the sufficient criterion of localization. The fact
that these two criteria are not complimentary is the reason why the
non-ergodic extended (multifractal) states may exist when neither the
Mott, nor the Anderson criterion is fulfilled.
We suggest a new class of random matrix models (Toeplitz RMT) with translation-invariant hopping integrals and identify the character of eigenfunction and eigenvalue statistics in them. We formulate the principles of level statistics if the type of eigenfunction statistics is known both in the coordinate and in the momentum basis and demonstrate that for the Toeplitz RMT the ergodic delocalization in the coordinate space may coexist with the Poisson level statistics.
Finally, we suggest a matrix-inversion trick that allows to identify uniquely the type of eigenfunction statistics and prove the absence of delocalized states in the bulk of spectrum of long-range Hamiltonians with deterministic (fully correlated) hopping.
We suggest a new class of random matrix models (Toeplitz RMT) with translation-invariant hopping integrals and identify the character of eigenfunction and eigenvalue statistics in them. We formulate the principles of level statistics if the type of eigenfunction statistics is known both in the coordinate and in the momentum basis and demonstrate that for the Toeplitz RMT the ergodic delocalization in the coordinate space may coexist with the Poisson level statistics.
Finally, we suggest a matrix-inversion trick that allows to identify uniquely the type of eigenfunction statistics and prove the absence of delocalized states in the bulk of spectrum of long-range Hamiltonians with deterministic (fully correlated) hopping.
Recent theoretical developments in the integer quantum Hall effects
22 February 2019 in 11:30
Ferdinand Evers (Regensburg University)
The quantum Hall effects belong to the most striking phenomena in condensed matter physics. Despite of intensive theoretical efforts over the last three decades, important aspects of the quantum Hall transitions are still not fully understood. In particular, there is still no consensus concerning the critical field theory and the corresponding scaling properties of the observables near and at the plateau transition.
Notwithstanding this status, the last ten years have seen considerable progress in understanding basic properties of scaling near localization-delocalization transitions that have implications also for the quantum Hall transition. These concern, e.g., the important topic of corrections to scaling, the wavefunction statistics and higher-order multifractality. A brief review of these developments will be offered in the first part of the talk.
The second part of the talk will be devoted to the spin quantum Hall effect, which is a variant of the integer quantum Hall effect (class A) taking place in the Altland-Zirnbauer class C. For this transition several critical exponents are known analytically and can serve as reference points. Therefore, this transition provides an ideal testbed for the qualitative predictions made by analytical theories. Analytical predictions will be confronted with most recent numerical results.
Notwithstanding this status, the last ten years have seen considerable progress in understanding basic properties of scaling near localization-delocalization transitions that have implications also for the quantum Hall transition. These concern, e.g., the important topic of corrections to scaling, the wavefunction statistics and higher-order multifractality. A brief review of these developments will be offered in the first part of the talk.
The second part of the talk will be devoted to the spin quantum Hall effect, which is a variant of the integer quantum Hall effect (class A) taking place in the Altland-Zirnbauer class C. For this transition several critical exponents are known analytically and can serve as reference points. Therefore, this transition provides an ideal testbed for the qualitative predictions made by analytical theories. Analytical predictions will be confronted with most recent numerical results.
Noisy quantum measurements: just a nuisance or fundamental physics?
7 December 2018 in 11:30
Wolfgang Belzig
Weak, almost non-invasive quantum measurements differ from the standard text book example of strongly invasive, projective measurements, since they leave the measured system basically unchanged. This opens the path to measure e.g. non-commuting observables and at the same time poses several open questions: Which order of operators is measured? Can quantum tests like Bell or Leggett-Garg be reformulated? What time scales are involved in the measurement process? We will address some basic properties of weak measurements leading to surprises like apparent spontaneous time-reversal symmetry breaking or the possibility of engineered detectors to tailor the measured quantum correlations.
Wonders of viscous electronics
19 October 2018 in 11:30
Gregory Falkovich (Weizmann Institute of Science, Israel)
Quantum-critical strongly correlated systems feature universal collision-dominated collective transport. Viscous electronics is an emerging field dealing with systems in which strongly interacting electrons flow like a fluid. Such flows have some remarkable properties never seen before. I shall describe recent theoretical and experimental works devoted, in particular, to a striking macroscopic DC transport behavior: viscous friction can drive electric current against an applied field, resulting in a negative resistance, recently measured experimentally in graphene. I shall also describe conductance exceeding the fundamental quantum-ballistic limit, field-theoretical anomalies and other wonders of viscous electronics. Strongly interacting electron-hole plasma in high-mobility graphene affords a unique link between quantum-critical electron transport and the wealth of fluid mechanics phenomena.
Quantum electrodynamics of heavy ions and atoms
5 October 2018 in 11:30
Vladimir Shabaev (St. Petersburg State University)
The present status of the QED theory of heavy ions and atoms is reviewed. The theoretical predictions for the Lamb shifts, the hyperfine splittings, and the bound-electron g factors of highly charged few-electron ions are compared with available experimental data. Special attention is paid to tests of QED at strong-coupling regime and determination of fundamental constants. The current status of studying the parity nonconservation effects with heavy atoms is also reported. Recent results on the charge-transfer and pair-creation probabilities in low-energy heavy-ion collisions are presented. Prospects for tests of QED at supercritical fields are discussed.
Superconductivity that breaks time-reversal symmetry and its experimental manifestations
28 September 2018 in 11:30
Victor Yakovenko (University of Maryland)
References:
- [1] X. Gong, M. Kargarian, A. Stern, D. Yue, H. Zhou, X. Jin, V. M. Galitski, V. M. Yakovenko, and J. Xia, Science Advances 3, e1602579 (2017), arXiv:1609.08538
- [2] P. M. R. Brydon, D. S. L. Abergel, D. F. Agterberg, and V. M. Yakovenko, arXiv:1802.02280
Quantum Many-Body Physics of Qubits
22 June 2018 in 11:30
Leonid Glazman (Yale University)
Eukaryotic cell polarity and protein sorting
27 April 2018 in 11:30
Andrea Gamba, Politecnico di Torino
Chiral magnetic crystals
23 March 2018 in 11:30
Markus Garst (TU Dresden)
The weak Dzyaloshinskii-Moriya interaction in chiral cubic magnets like MnSi, FeGe or Cu2OSeO3 twists the magnetization on long length scales resulting in spatially periodic magnetic textures — magnetic crystals. There exist especially magnetic crystals with a one- and two-dimensional periodicity corresponding to the magnetic helix and the topologically non-trivial skyrmion lattice, respectively. In this talk, we provide an overview of their properties. In particular, we discuss the crystallization process of these magnetic crystals that is characterized by strongly correlated chiral paramagnons that drive the transition first-order [1,2]. This fluctuation-induced first-order transition is well described by a theory put forward by Brazovskii. We will introduce the magnon band structure and their non-reciprocal properties in the presence of a magnetic field [3,4]. For the skyrmion lattice, this band structure is topological and characterized by finite Chern numbers that can be attributed to the formation of magnon Landau levels due to an emergent orbital magnetic field [5,6,7]. Finally, we will discuss domain walls of helimagnets that share similarities with grain boundaries consisting of disclination and dislocation defects of the helimagnetic order [8].
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References:
- [1] M. Janoschek et al. Phys. Rev. B 87, 134407 (2013).
- [2] A. Bauer, M. Garst and C. Pfleiderer, Phys. Rev. Lett. 110, 177207 (2013).
- [3] M. Kugler et al. Phys. Rev. Lett. 115, 097203 (2015)
- [4] T. Weber et al. arXiv:1708.02098
- [5] C. Schütte and M. Garst, Phys. Rev. B 90, 094423 (2014).
- [6] T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer, and D. Grundler, Nat. Mater. 14, 478 (2015).
- [7] M. Garst J. Waizner, and D. Grundler, J. Phys. D: Appl. Phys. 50, 293002 (2017)
- [8] P. Schoenherr et al. Nat. Phys. in press, arXiv:1704.06288
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