Hydrodynamics of low-dimensional interacting systems: Advances, challenges, and future directions

Contribution List

29. Opening remarks

Hisao Hayakawa

6/2/25, 1:30 PM

1. Lectures: Generalized hydrodynamics of the Toda fluid

Herbert Spohn

6/2/25, 1:45 PM

The hydrodynamics of integrable many-body systems has accomplished spectacular advances. In my lectures, I will use the famous Toda chain to illustrate the main features of generalized hydrodynamics. Key items are generalized Gibbs ensembles, their connection to random matrix theory, average charges and currents,TBA equations, and scattering coordinates as yielding large deviations.

2. Lectures: Generalized hydrodynamics of the Toda fluid

Herbert Spohn

6/3/25, 9:30 AM

The hydrodynamics of integrable many-body systems has accomplished spectacular advances. In my lectures, I will use the famous Toda chain to illustrate the main features of generalized hydrodynamics. Key items are generalized Gibbs ensembles, their connection to random matrix theory, average charges and currents, TBA equations, and scattering coordinates as yielding large deviations.

3. Energy diffusion in the long-range interacting spin systems

Hideaki Nishikawa

6/3/25, 11:30 AM

We investigate energy diffusion in long-range interacting spin systems, where the interaction decays algebraically as $V(r) \propto r^{-\alpha}$ with the distance $r$ between the sites. We consider prototypical spin systems, the transverse Ising model, and the XYZ model in the $D$-dimensional lattice with a finite exponent $\alpha >D$ which guarantees the thermodynamic extensivity. In one...

5. The Kardar-Parisi-Zhang universality class for driven interfaces and... integrable spin chains?

Kazumasa Takeuchi

6/4/25, 9:30 AM

The Kardar-Parisi-Zhang (KPZ) universality class, originally formulated to describe driven systems such as growing interfaces, has undergone several paradigm shifts. One major breakthrough was the discovery of exact solutions for the 1D KPZ class, achieved thanks to its underlying integrability [1]. However, more recently, the KPZ framework appears to be entering a new phase, extending...

6. From integrable spin chains to coupled KPZ equations

Abhishek Dhar

6/4/25, 11:30 AM

Surprising signatures of anomalous spin transport have been reported in the spin-half Heisenberg spin chain at the isotropic point, in a number of recent works. The talk will discuss: (i) analogous results for classical integrable spin chains and (ii) properties of coupled Burgers equations that have been proposed as effective hydrodynamic descriptions of integrable spin chains.

26. Efimov effect at the Kardar-Parisi-Zhang roughening transition

Yu Nakayama

6/4/25, 2:30 PM

I would like to give a short talk on my personal interest in the roughening transition of the KPZ system in relation to the Efimov effect (discrete scale invariance).

7. Quantum dynamics and entanglement in open systems

Manas Kulkarni

6/5/25, 9:30 AM

I will discuss Page-curve entanglement dynamics between a system and its environment under various scenarios. In particular, I will discuss an analytically tractable model of a gas of noninteracting fermions on a lattice that is released from a box into the vacuum [1]. I will then discuss the dynamics of entanglement in a one-dimensional XXZ spin-1/2 chain [2], with and without...

9. Speed limits and optimal transport: General bounds and maximal speed of particle transport

Tan Van Vu

6/5/25, 11:30 AM

8. Coherent transport: Thermodynamic uncertainty relations and large deviation analysis

Keiji Saito

6/5/25, 2:15 PM

We derive a universal thermodynamic uncertainty relation for Fermionic coherent transport, which bounds the total rate of entropy production in terms of the mean and fluctuations of a single particle current. This bound holds for any multi-terminal geometry and arbitrary chemical and thermal biases, as long as no external magnetic fields are applied. It can further be saturated in two-terminal...

27. On the dynamical origin of the vorticity alignment in homogeneous and isotropic turbulence

Takeshi Matsumoto

6/6/25, 9:30 AM

Since the 1980s it has been known that in incompressible homogeneous and isotropic turbulence the vorticity vector tends to align with one of the eigen-directions of the rate-of-strain tensor, specifically the one associated with its intermediate (second largest) eigenvalue. Despite extensive studies, the underlying mechanism of the preferential alignment is not fully understood. In this work,...

12. Mean-field theory becomes exact under shear flow: A dynamic renormalization group study of the O(n) model

Harukuni Ikeda

6/6/25, 10:15 AM

Mean-field theory, such as Landau theory, provides a simple yet powerful framework for understanding critical phenomena. However, in equilibrium systems, its predictions often fail in low dimensions: the upper critical dimension is typically four, and significant deviations in critical exponents are observed in two and three dimensions. Intriguingly, experiments on phase separation under shear...

14. Steady velocity of entropic driven interface in shear flow

Yutaro Kado

6/6/25, 11:30 AM

When different two phases come into contact through a flat interface, the interface moves in a certain direction, and its steady-state velocity is determined by the driving force caused by the difference in free energy between the two phases and the mobility. When describing interface phenomena using the probabilistic order parameter field model, which is Model A of Hohenberg and...

11. Kinetic theory of moderately dense dry granular particles under a simple shear: steady flows and anomalous relaxation dynamics

Hisao Hayakawa

6/6/25, 12:15 PM

We formulate the kinetic theory of dry granular particles under a simple shear based on the Enskog and Grad approximations. We get a complete set of equations for the kinetic stress and the collisional contribution to the stress within this approximation. The steady solution under this approximation reproduces the quantitatively accurate results for the shear viscosity and kinetic temperature...

15. Lectures: Generalised hydrodynamics: exact solutions, fluctuations, and all-order expansion

Benjamin Doyon

6/9/25, 9:30 AM

Hydrodynamics is more than a set of PDES. It is a framework for emergent dynamical behaviour in many-body systems. Generalised hydrodynamics (GHD), with its exact equations and rich structure, has led to a much deeper understanding of this framework.

Lecture 1: Following on from Herbert’s talk, I will explain the general features of GHD for classical and quantum systems, focusing on the...

16. Unified description of hydrodynamic and Nambu–Goldstone modes in open and closed systems

Yoshimasa Hidaka

6/9/25, 11:30 AM

I present a unified effective theory of hydrodynamic and Nambu–Goldstone (NG) modes in both closed and open systems. A central focus is the distinction between strong and weak symmetries, which clarifies how NG modes can emerge even in the absence of conserved charges, as in open systems. Using the Schwinger–Keldysh formalism, I classify NG modes and derive their dispersion relations,...

13. Looking at bare transport coefficients in fluctuating hydrodynamics

Hiroyoshi Nakano

6/9/25, 12:15 PM

It is well established that fluid motions at the macroscopic scale are governed by the celebrated Navier-Stokes equation. However, in mesoscopic regimes where fluctuations become significant, the governing equations must incorporate fluctuation terms, leading to the framework of "fluctuating hydrodynamics" [1]. A central feature of this framework is the presence of noise terms and associated...

25. Macroscopic particle transport in dissipative long-range bosonic systems

Hongchao Li

6/9/25, 2:30 PM

The speed limit for macroscopic particle transport is one of the central topics in quantum mechanics, which quantifies the minimum time required for a given number of particles to propagate to a reachable regime. Recently, there are constant progress on maximal bosonic particle transport speed in Bose-Hubbard model and long-range bosonic models. However, the existing findings are limited to...

18. Fluctuations and correlations in hard-rod gas

Anupam Kundu

6/10/25, 9:30 AM

19. Exact expression of multifractal dimension on the non-Hermitian Cayley tree

Shu Hamanaka

6/10/25, 11:30 AM

Multifractal analysis is a powerful tool for characterizing the localization properties of wave functions. Despite its utility, this tool has been predominantly applied to disordered Hermitian systems. Multifractal statistics associated with the non-Hermitian skin effect remain largely unexplored. Here, we demonstrate that the tree geometry induces multifractal statistics for the...

20. Kinetic predictions for the blast in cold gas

Umesh Kumar

6/10/25, 12:15 PM

I will present our recent (ongoing) work on understanding blast in cold gas of hard discs in two dimensions. We are able to make some theoretical estimates for quantities of interest in the hydrodynamic limit and test them using simulations.

31. Size-independent shear viscosity from equilibrium fine-grained shear stress correlations in two dimensional molecular dynamics simulations

Kazuma Yokota

6/10/25, 2:30 PM

21. Lectures: Generalised hydrodynamics: exact solutions, fluctuations, and all-order expansion

Benjamin Doyon

6/11/25, 9:30 AM

Hydrodynamics is more than a set of PDES. It is a framework for emergent dynamical behaviour in many-body systems. Generalised hydrodynamics (GHD), with its exact equations and rich structure, has led to a much deeper understanding of this framework.

Lecture 1: Following on from Herbert’s talk, I will explain the general features of GHD for classical and quantum systems, focusing on the...

22. Signatures of integrability/non-integrability in two-dimensional quantum spin systems: local conserved quantities, operator growth, and complex-time evolution

Hal Tasaki

6/11/25, 11:30 AM

In the first part of the talk, I will discuss our recent result on the absence of local conserved quantities in a wide class of standard S=1/2 quantum spin systems in two or higher dimensions. This is an extension of Shiraishi's 2019 work on spin chains. I will also discuss related observations about the absence of quasi-local conserved quantities and spectrum generating algebra.
In the...

30. Quantum dynamics in Krylov space: from tridiagonal matrices to quantum chaos

Pratik Nandy

6/11/25, 2:30 PM

The dynamics of quantum systems typically unfolds within a subspace of the state or operator space, known as the Krylov space. Krylov subspace methods provide a compact and computationally efficient description of quantum evolution and quantum chaos, which is particularly useful for describing nonequilibrium phenomena of many-body systems with a large Hilbert space. In this talk, I will...

23. Jamming of deformable foams

Kuniyasu Saitoh

6/11/25, 3:15 PM

The jamming transition of soft athermal particles has long been explored by numerical models of undeformable spheres/circles and the researchers have extensively studied the critical behavior of the particles near jamming. It is now well known that the shear modulus of undeformable particles scales as the square root of the proximity to the jamming transition density. However, the square-root...

10. Macroscopic fluctuation theory on a lattice and its connection to classical integrable systems

Tomohiro Sasamoto

6/12/25, 9:30 AM

Macroscopic fluctuation theory (MFT) is a general theory for studying large deviations of interacting particle systems. A central object in the theory is the MFT equations, whose solution gives the rate function for certain rare events. A few years ago, we have found a mapping from the MFT equations for the symmetric simple exclusion process to the AKNS system, which is a well-known classical...

24. Colloquium: Kardar-Parisi-Zhang equation: one and two components

Herbert Spohn

6/12/25, 3:30 PM

The KPZ equation was first written down in 1985 and has a rich history, reaching physical applications beyond the originally envisioned surface growth. In my lecture, I will discuss recent advances. Amongst others, they include the extension to two components and the riddle of the space-time spin-spin correlations of the Heisenberg spin chain.

28. Self-consistent method to predict trapped states in Vlasov systems

Yoshiyuki Yamaguchi

6/13/25, 9:30 AM

A Vlasov system describes dynamics of a many-body long-range interacting Hamiltonian system including self-gravitating systems and plasmas. Such a system does not go to thermal equilibrium and is trapped at a so-called quasi-stationary state. A central issue is then to predict the trapped state, which may experience a bifurcation by varying a parameter. The self-consistent method is a powerful...

32. TBU

6/13/25, 10:45 AM

33. Closing remark

Hisao Hayakawa

6/13/25, 11:30 AM