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Monday, 06 September 2021
Time Speaker Title Resources
13:15 to 13:30 Rajesh Gopakumar (ICTS, India) Welcome remarks
13:30 to 14:40 Jacopo De Nardis (Cergy Paris Université, France) Dynamics close to Integrability: A Hydrodynamics Prospective
14:50 to 16:00 Tomaz Prosen (University of Ljubljana, Slovenia) Exact results on dynamics of dual unitary circuits and their perturbations

I will review the recent results on the proof of random matrix spectral form factor and explicit computation of correlation functions of local observables in the so-called dual-unitary brickwork circuits (including integrable, non-ergodic, ergodic and chaotic cases). Further I will show how these results can be extended to another quantum-circuit platform, specifically to unitary interactions round-a-face (IRF). I will argue that correlation functions of these models are generally perturbatively stable with respect to breaking dual-unitarity, and describe a simple rigorous result within this framework.

17:00 to 18:10 Sriram Ganeshan (City College of New York, USA) Hamiltonian structure of 2D fluid dynamics with broken parity

Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. In this talk, I will discuss conditions on transport coefficients that correspond to dissipationless and separately to Hamiltonian fluid dynamics. The restriction on the transport coefficients will help identify what kind of hydrodynamics can be obtained by coarse-graining a microscopic Hamiltonian system. Interestingly, not all parity-breaking transport coefficients lead to energy conservation and, generally, the fluid dynamics is energy conserving but not Hamiltonian. I will outline how this dynamics can be realized by imposing a nonholonomic constraint on the Hamiltonian system.

18:20 to 19:30 Joel Moore (UC Berkeley, USA) Integrable and near-integrable spin chains in theory and reality

Considerable progress has taken place in the past few years in developing the hydrodynamic theory of quantum integrable models.  A surprising result of those developments was the understanding that the Heisenberg point of the spin-half chain, along with some other integrable isotropic models, shows superdiffusive dynamics even in ordinary spin correlation functions and even at high temperatures.  We review the physical picture that underlies why integrable models have special hydrodynamics with a focus on the XXZ spin chain, and show stringent tests of the validity of this theory for the ballistic easy-plane regime.  We then turn to the Heisenberg point and discuss when KPZ behavior occurs, how it connects to previously studied low-temperature limits, and how this behavior is manifested in experiments.  We close with a discussion of how integrability-breaking perturbations appear in real systems but still allow superdiffusive behavior.

Tuesday, 07 September 2021
Time Speaker Title Resources
13:30 to 14:40 Stefano Olla (Université Paris Dauphine, France) Quasi-static hydrodynamic limits

The quasi-static scaling limit corresponds to changes of the boundary conditions (boundary tension, temperature heat bath, density of particle reservoirs) on a time scale that is slower (i.e. larger) than the equilibrium relaxation scale of the dynamics in the bulk. In this very large time scale, the system is always very close to the global stationary state corresponding to the (time varying) tension, temperatures or densities applied at the boundaries. These quasi-static evolutions are usually presented as idealization of real thermodynamic transformations. On the other hand they are necessary concepts in order to construct thermodynamic potentials, for example to define thermodynamic entropy from Carnot cycles. The existence of the quasi-static transformations can be seen as another thermodynamic principle that needs to be derived from the microscopic dynamics under a proper space-time scaling that we call quasi-static hydrodynamic limit. We are particularly interested in studying quasi-static transformations among non-equilibrium stationary states (NESS).
I will expose some results concerning quasi-static hydrodynamic limits for dynamics with diffusive behavior (like symmetric simple exclusion) and hyperbolic/ballistic behavior (like the asymmetric simple exclusion).
Oscillators chains in contact with heat bath in the bulk and tension at the boundary are also studied.
The large deviations from these quasi-static limits and the relation with the large deviations in the corresponding NESS are investigated. Works in collaboration with Anna de Masi, Lu Xu, Stefano Marchesani.

14:50 to 16:00 Boris N Narozhny (Karlsruhe Institute of Technology, Germany) Hydrodynamic approach to electronic transport

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.

17:00 to 18:10 Romain Vasseur (UMass Amherst, USA) Superdiffusive hydrodynamics in isotropic quantum spin chains

Abstract: Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. In this talk, I will review the numerical and experimental evidence for this surprising anomalous transport property, and propose a kinetic theory in terms of “giant”, soft quasiparticles stabilized by integrability. I will discuss the stability of this phenomenon against integrability-breaking perturbations, and argue that it is remarkably robust to perturbations preserving non-abelian symmetries.

18:20 to 19:30 Andrew Lucas (University of Colorado, USA) Breakdown of hydrodynamics below four dimensions in a fracton fluid

I will describe a new universality class of non-equilibrium dynamics that arises in a chaotic many-body system with conserved charge, dipole and momentum.   This universality class arises out of the instability of a constrained quantum fluid, similar to the emergence of KPZ physics in a conventional 1d fluid; however, due to dipole conservation, the upper critical dimension gets pushed up to 4.   I will outline both the theory of such a constrained fluid, and the theory/numerics which suggest its instability.  Our construction opens up a pathway to discovering infinitely many new universality classes of (hydro)dynamics.

Wednesday, 08 September 2021
Time Speaker Title Resources
13:30 to 14:40 Cedric Bernardin (Nice University) Localization effects on transport properties in chains of oscillators

In this talk we will present recent results about the transport properties of chains of harmonic oscillators with random defects such as random masses or random charges.

14:50 to 16:00 Vir Bulchandani (Princeton University, USA) Semiclassical kinetic theory of integrable systems

We show how the semiclassical limit of thermodynamic Bethe ansatz can be used to obtain the kinetic theory of various canonical classical integrable systems, such as the Toda lattice and Calogero family of models. We discuss applications to situations where integrability is weakly broken by the presence of an external trapping potential.

17:00 to 18:10 Benjamin Doyon (King's College, London) Correlation functions from hydrodynamics beyond the Boltzmann-Gibbs paradigm

The Euler-scale power-law asymptotics of space-time correlation functions in many-body systems, quantum and classical, can be obtained by projecting the observables onto the hydrodynamic modes admitted by the model and state. This is the Boltzmann-Gibbs principle; it works for integrable and non-integrable models alike. However, certain observables, such as some order parameters in thermal states or GGEs, do not couple to any hydrodynamic mode: the Boltzmann-Gibbs principle gives zero. After reviewing this principle, I will explain how hydrodynamics can give the leading exponential decay of order parameter correlation functions. With the example of the quantum XX chain, I will explain how the large-deviation theory for the fluctuations of spins is related to such exponential decay, and how exact predictions are given by the ballistic fluctuation theory based on Euler hydrodynamics. This is in agreement with results obtained previously by a more involved Fredholm determinant analysis and other techniques, and even gives a new formula for a parameter regime not hitherto studied. The hydrodynamic method is widely applicable, beyond the XX model.

This is work with Giuseppe Del Vecchio Del Vecchio.

18:20 to 19:30 Pavel Krapivsky (Boston University, USA) Blast and splash in the one-dimensional cold gas

We study the response of the one-dimensional hard-point gas of particles at rest when one particle suddenly starts moving. The masses of particles are alternating allowing for relaxation in one dimension. The outcome is the flow between shock waves advancing as ±t2/3. The density, velocity, and temperature in the growing region between the shock waves approach to scaling forms predicted by Euler equations for the ideal non-dissipative compressible gas. Direct microscopic simulations show deviations from non-dissipative hydrodynamics in the core region, and we argue that this core region grows as t38/93. More rich behaviors arise in the semi-infinite setting when the left most particle suddenly starts moving to the right. A shock wave propagates to the right, and a growing number of “splatter” particles penetrate the initially empty half-line. Splatter particles asymptotically carry 100% of energy, and their total momentum diverges in the long time limit. The precise asymptotic for the position of the shock wave, the total energy in the initially occupied half-line, etc., are algebraic and expressible through a single exponent that is a non-linear eigenvalue found from a scaling solution of Euler’s equations.

Thursday, 09 September 2021
Time Speaker Title Resources
13:30 to 14:40 Enej Ilievski (University of Ljubljana, Slovenia) Superuniversality of superdiffusion: transport in quantum and classical integrable systems with high-rank symmetries

Inspired by the recent discovery of superdiffusive spin transport in the isotropic Heisenberg chain, we shall systematically examine the role of global nonabelian symmetries of higher rank for all the semi-simple Lie algebras and their unitary representations. By extracting the quasiparticle spectra with aid of the Algebraic Bethe Ansatz and subsequently taking advantage of the kinetic theory scaling analysis, we find that spin/charge superdiffusion is remarkably robust, provided integrability and nonabelian symmetry remain unbroken. The observed 'superuniversal' behavior of superdiffusive charge transport takes place in quantum spin chains, in integrable quantum field theories and likewise in completely integrable partial differential equations on compact manifolds, including lattice discretizations thereof dubbed as the matrix models. In addition, we shall provide convincing numerical evidence for the KPZ scaling behavior.

14:50 to 16:00 Takato Yoshimura (Tokyo Institute of Technology, Japan) Macroscopic fluctuation theory for integrable systems

Macroscopic fluctuation theory (MFT) has served as a powerful and universal framework to compute the large deviations of current and density fluctuations in many-body systems. While MFT has been particularly successful in studying large deviations in diffusive systems, its application to ballistic transport has been rather limited. In this talk I shall illustrate how the idea of MFT can be applied to integrable systems by extensively exploiting the results from generalised hydrodynamics. It turns out that MFT provides new insights into large deviation in integrable systems as well as reproduces known results, such as cumulants of the current generating function.

17:00 to 18:10 Hugues Chate (CEA Saclay, France & Beijing CSRC, China) Hydrodynamics and Fluctuations in Dry Aligning Dilute Active Matter

Active matter designates systems in which energy is converted at some local scale into mechanical work. This very wide class of out-of-equilibrium systems has been under intense study for the last two decades, which has revealed a wealth of spectacular and novel collective properties at all levels.

A limit of case of historical and theoretical interest is that of dry aligning dilute active matter (DADAM), where, typically, self-propelled particles locally align their velocities in the presence of noise, as in the Vicsek model.

The seminal works of John Toner, Yuhai Tu, and Sriram Ramaswamy have focused on the generic scaling of fluctuations in the orientationally-ordered phases of hydrodynamic theories of DADAM. Since then, a lot of progress has been made.

I will first give an account of our current knowledge of DADAM. Then I will discuss the relative faithfulness to microscopic level phenomenology of the approximate hydrodynamic and kinetic theories proposed by physicists to describe DADAM systems.

18:20 to 19:30 Vincenzo Vitelli (University of Chicago, USA) Non reciprocal phase transitions: a hydrodynamics theory
Friday, 10 September 2021
Time Speaker Title Resources
13:30 to 14:40 Vincenzo Alba (University of Amsterdam, Netherlands) Entanglement dynamics and dissipation in out-of-equilibrium systems

Distinguishing genuine quantum correlation (entanglement) from spurious statistical one in out-of-equilibrium open quantum many-body systems is in general a challenging task. In this talk I will review some recent efforts to describe the entanglement dynamics in the presence of Markovian dissipation. In particular, I will focus on free-fermion and free-bosons  subjected to global linear dissipation as well as to localized one. I will show that, at least for free systems,  it is possible to incorporate the effects of dissipation in a hydrodynamic description for the entanglement spreading (quasiparticle picture).

14:50 to 16:00 Manas Kulkarni (ICTS, India) Collective behaviour of a family of power law models

I will discuss recent results on collective behaviour of N particles repelling each other via pairwise interaction potential and confined by an external harmonic trap. I will discuss the large-N field theory for all-to-all coupling [1] and the finite ranged case [2]. These family of models contain in them various well known systems of interest both in physics and mathematics such as one component plasma, Dyson's log-gas, and the integrable Calogero-Moser model to name a few. I will also present results in the presence of a barrier [3]. I will then discuss gap statistics (analogous to the well known level spacing statistics) in these family of models [4]. In the end, I will present some preliminary results that show how the derived large-N theory can be used to understand collective non-equilibrium dynamics of these interacting particles.

[1] S. Agarwal, A. Dhar, M. Kulkarni, A. Kundu, S. N. Majumdar, D. Mukamel, G. Schehr, Phys. Rev. Lett. 123, 100603 (2019), Editors' Suggestion
[2] A. Kumar, M. Kulkarni, A. Kundu, Phys. Rev. E 102, 032128 (2020)
[3] J. Kethepalli, M. Kulkarni, A. Kundu, S. N. Majumdar, D. Mukamel, G. Schehr, arXiv:2107.00524 (2021)
[4] S. Santra, J. Kethepalli, S. Agarwal, A. Dhar, M. Kulkarni, A. Kundu, S. N. Majumdar, and G. Schehr [in preparation]

17:00 to 18:10 P Wiegmann (University of Chicago, USA) Quantum Hall states as a quantum rotating superfluid

Since early days of superfluidity quantum liquids were central to understanding collective quantum matter. Apart from superconductors, two quantum liquids: superfluid Helium and (fractional) quantum Hall states are the most studied and  measured. The aim of this talk is to emphasize an intimate relation between the two. In short, the theory of  fast rotating superfluid is formally equivalent to that of FQHE under identifying the frequency of rotation of the superfluid with the Larmor frequency, vortices with electrons  and the ratio between vortices and the number of atoms in superfluid with the filling fraction in FQHE.The physical difference between the two is that the hydrodynamics of the superfluid helium is semiclassical, while that of FQH states is ultra quantum.

18:20 to 19:30 Herbert Spohn (Technical University of Munich, Germany) Hydrodynamics for the one-dimensional discrete nonlinear Schroedinger equation.

NLS in one dimension is an integrable PDE and the respective hydrodynamic description has to include all conserved fields. This goal can be achieved for the defocusing Ablowitz-Ladik discretization. We explain the construction and the resulting infinite set of coupled hyperbolic conservation laws. There is a curious connection to the circular unitary ensemble of random matrix theory, the orthogonal version being linked to the modified Korteweg-De Vries equation.