Name: Hydrodynamics of low-dimensional interacting systems: Advances, challenges, and future directions
Start: 2025-06-02T09:30:00+09:00
End: 2025-06-13T18:00:00+09:00
Location: Yukawa Institute for Theoretical Physics, Kyoto University

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

from Monday, June 2, 2025 (9:30 AM) to Friday, June 13, 2025 (6:00 PM)

Monday, June 2, 2025
1:30 PM Opening remarks - Hisao Hayakawa
Opening remarks
- Hisao Hayakawa
1:30 PM - 1:40 PM
Room: Panasonic Auditorium, Yukawa Hall
1:45 PM Lectures: Generalized hydrodynamics of the Toda fluid - Herbert Spohn
Lectures: Generalized hydrodynamics of the Toda fluid
- Herbert Spohn
1:45 PM - 3:15 PM
Room: Panasonic Auditorium, Yukawa Hall 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.
3:15 PM Coffee break
Coffee break
3:15 PM - 3:45 PM
Room: Panasonic Auditorium, Yukawa Hall
Tuesday, June 3, 2025
9:30 AM Lectures: Generalized hydrodynamics of the Toda fluid - Herbert Spohn
Lectures: Generalized hydrodynamics of the Toda fluid
- Herbert Spohn
9:30 AM - 11:00 AM
Room: Panasonic Auditorium, Yukawa Hall 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.
11:00 AM Coffee break
Coffee break
11:00 AM - 11:30 AM
Room: Panasonic Auditorium, Yukawa Hall
11:30 AM Energy diffusion in the long-range interacting spin systems - Hideaki Nishikawa
Energy diffusion in the long-range interacting spin systems
- Hideaki Nishikawa
11:30 AM - 12:15 PM
Room: Panasonic Auditorium, Yukawa Hall 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 dimension, both normal and anomalous diffusion are observed, where the anomalous diffusion is attributed to anomalous enhancement of the amplitude of the equilibrium current correlation. We prove the power-law clustering property of arbitrary orders of joint cumulants in general dimensions. Applying this theorem to equal-time current correlations, we further prove several theorems leading to the statement that the sufficient condition for normal diffusion in one dimension is $\alpha > 3/2$ regardless of the models. The fluctuating hydrodynamics approach consistently explains L\'{e}vy diffusion for $\alpha < 3/2$, which implies the condition is optimal. In higher dimensions of $D \geq 2$, normal diffusion is indicated as long as $\alpha > D$. [1] [1] HN and K.Saito, arXiv:2502:10139
12:15 PM Lunch break
Lunch break
12:15 PM - 2:30 PM
Room: Panasonic Auditorium, Yukawa Hall

2:30 PM Coffee break
Coffee break
2:30 PM - 3:00 PM
Room: Panasonic Auditorium, Yukawa Hall
Wednesday, June 4, 2025
9:30 AM The Kardar-Parisi-Zhang universality class for driven interfaces and... integrable spin chains? - Kazumasa Takeuchi
The Kardar-Parisi-Zhang universality class for driven interfaces and... integrable spin chains?
- Kazumasa Takeuchi
9:30 AM - 11:00 AM
Room: Panasonic Auditorium, Yukawa Hall 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 unexpectedly to integrable spin chains at thermal equilibrium [2]. Although this connection was nearly dismissed when clear discrepancy in full counting statistics was reported, the speaker and collaborators numerically found that various two-point quantities agree precisely with KPZ exact solutions [3], even though higher-order quantities remain clearly different. In my talk, I will first review some of the main outcomes of the 1D KPZ exact solutions, often referring to the corresponding experimental observations that the speaker and collaborators have reported [1]. Then I will present our recent numerical results on integrable spin chains, showing the aforementioned partial yet definite emergence of the KPZ class therein [3]. This partial emergence of the KPZ class is yet to be understood; therefore, this talk will serve as an introduction to the discussion session scheduled in the afternoon. [1] For a review, see, e.g., K. A. Takeuchi, Physica A 504, 77 (2018). [2] For reviews, see, e.g., V. B. Bulchandani et al., J. Stat. Mech. (2021), 084001; S. Gopalakrishnan and R. Vasseur, Annu. Rev. Condens. Matter Phys. 15, 159 (2024). [3] K. A. Takeuchi, et al., Phys. Rev. Lett. 134, 097104 (2025).
11:00 AM Coffee break
Coffee break
11:00 AM - 11:30 AM
Room: Panasonic Auditorium, Yukawa Hall
11:30 AM From integrable spin chains to coupled KPZ equations - Abhishek Dhar
From integrable spin chains to coupled KPZ equations
- Abhishek Dhar
11:30 AM - 1:00 PM
Room: Panasonic Auditorium, Yukawa Hall 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.
1:00 PM Lunch break
Lunch break
1:00 PM - 2:30 PM
Room: Panasonic Auditorium, Yukawa Hall
2:30 PM Efimov effect at the Kardar-Parisi-Zhang roughening transition - Yu Nakayama
Efimov effect at the Kardar-Parisi-Zhang roughening transition
- Yu Nakayama
2:30 PM - 4:00 PM
Room: Panasonic Auditorium, Yukawa Hall 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).
4:00 PM Coffee break
Coffee break
4:00 PM - 4:30 PM
Room: Panasonic Auditorium, Yukawa Hall

4:30 PM

4:30 PM - 6:00 PM
Room: Panasonic Auditorium, Yukawa Hall
Thursday, June 5, 2025
9:30 AM TBA - Manas Kulkarni
TBA
- Manas Kulkarni
9:30 AM - 11:00 AM
Room: Panasonic Auditorium, Yukawa Hall
11:00 AM Coffee break
Coffee break
11:00 AM - 11:30 AM
Room: Panasonic Auditorium, Yukawa Hall
11:30 AM Speed limits and optimal transport: General bounds and maximal speed of particle transport - Tan Van Vu
Speed limits and optimal transport: General bounds and maximal speed of particle transport
- Tan Van Vu
11:30 AM - 12:15 PM
Room: Panasonic Auditorium, Yukawa Hall
12:15 PM Lunch break
Lunch break
12:15 PM - 2:15 PM
Room: Panasonic Auditorium, Yukawa Hall
2:15 PM Coherent transport: Thermodynamic uncertainty relations and large deviation analysis - Keiji Saito
Coherent transport: Thermodynamic uncertainty relations and large deviation analysis
- Keiji Saito
2:15 PM - 3:45 PM
Room: Panasonic Auditorium, Yukawa Hall 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 settings with boxcar-shaped transmission functions and reduces to its classical counterpart in linear response. Upon insertion of a numerical factor, our bound also extends to systems with broken time-reversal symmetry. As an application, we derive trade-off relations between the figures of merit of coherent thermoelectric heat engines and refrigerators, which show that such devices can attain ideal efficiency only at vanishing mean power or diverging power fluctuations. To illustrate our results, we work out a model of a coherent conductor consisting of a chain of quantum dots.
3:45 PM Coffee break
Coffee break
3:45 PM - 4:15 PM
Room: Panasonic Auditorium, Yukawa Hall
Friday, June 6, 2025
9:30 AM On the dynamical origin of the vorticity alignment in homogeneous and isotropic turbulence - Takeshi Matsumoto
On the dynamical origin of the vorticity alignment in homogeneous and isotropic turbulence
- Takeshi Matsumoto
9:30 AM - 10:15 AM
Room: Panasonic Auditorium, Yukawa Hall 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, making use of a three-dimensional polar representation of the equation for the velocity gradient tensor obtained before, we explore the alignment mechanism theoretically and numerically combined with the direct numerical simulation of the Navier--Stokes equations.
10:15 AM Mean-field theory becomes exact under shear flow: A dynamic renormalization group study of the O(n) model - Harukuni Ikeda
Mean-field theory becomes exact under shear flow: A dynamic renormalization group study of the O(n) model
- Harukuni Ikeda
10:15 AM - 11:00 AM
Room: Panasonic Auditorium, Yukawa Hall 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 flow and recent simulations of spin models have reported mean-field-like critical exponents even in two dimensions [1, 2]. These findings suggest that shear flow may fundamentally alter the nature of critical behavior, effectively lowering the upper critical dimension. To uncover the physical mechanism behind this phenomenon, we performed a dynamic renormalization group analysis of the O(n) model under simple shear flow [3]. A key innovation of our work is the explicit treatment of shear-induced anisotropy in the scaling analysis—an aspect neglected in earlier studies [4]. Our results reveal the existence of a novel Gaussian fixed point governed by strong anisotropy due to shear. Strikingly, we find that the upper critical dimension of this fixed point is reduced to two or lower for both conserved and non-conserved dynamics. This implies that mean-field theory becomes asymptotically exact in all dimensions except one. [1] D. Beysens, M. Gbadamassi, and L. Boyer Light-Scattering of a Critical Mixture with Shear Flow, Phys.Rev.Lett. 43 (1979) 1253 [2] H. Nakano, Y. Minami, and S. Sasa Long-Range Phase Order in Two Dimensions under Shear Flow, Phys.Rev.Lett. 126 (2021) 1606 04 [3] H. Ikeda, and H. Nakano, Dynamical renormalization group analysis of O(n) model in steady shear flow, arXiv:2412.02111 (2024) [4] A. Onuki, and K. Kawasaki, Nonequilibrium Steady State of Critical Fluids under Shear Flow: A Renormalization Group Approach, Ann. Phys. 121 (1979) 456
11:00 AM Coffee break
Coffee break
11:00 AM - 11:30 AM
Room: Panasonic Auditorium, Yukawa Hall
11:30 AM Steady velocity of entropic driven interface in shear flow - Yutaro Kado
Steady velocity of entropic driven interface in shear flow
- Yutaro Kado
11:30 AM - 12:15 PM
Room: Panasonic Auditorium, Yukawa Hall 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 Halperin(1977), a new interface driving force arises due to entropic contributions from noise and asymmetric shape of free energy density. We refer to such an interface as an "entropic driven interface". We investigate the steady-state velocity of planer entropic driven interfaces parallel to the flow by the Model A. We decompose the interface driving force into components in the bulk and at the interface, and derive the velocity formula. We also perform numerical calculations to verify the validity of the formula.
12:15 PM Kinetic theory of moderately dense dry granular particles under a simple shear: steady flows and anomalous relaxation dynamics - Hisao Hayakawa
Kinetic theory of moderately dense dry granular particles under a simple shear: steady flows and anomalous relaxation dynamics
- Hisao Hayakawa
12:15 PM - 1:00 PM
Room: Panasonic Auditorium, Yukawa Hall 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 for the volume fraction $\varphi<0.5$ except for the case of nearly elastic situations. We also get qualitatively accurate results for the steady normal stress differences for $\varphi<0.5$. By using a protocol of reversing a shear rate satisfying Newton's equation of motion, we also discuss the relaxation dynamics to reach the steady state. We observe the Kovacs effect in a wide range of parameters and Mpemba effect if the initial conditions of two copied systems are not largely deviated. This is based on the collaboration with Shunsuke Iizuka and Satoshi Takada.
1:00 PM Lunch break
Lunch break
1:00 PM - 2:30 PM
Room: Panasonic Auditorium, Yukawa Hall

2:30 PM

2:30 PM - 4:00 PM
Room: Panasonic Auditorium, Yukawa Hall

4:00 PM Coffee break
Coffee break
4:00 PM - 4:30 PM
Room: Panasonic Auditorium, Yukawa Hall

4:30 PM

4:30 PM - 6:00 PM
Room: Panasonic Auditorium, Yukawa Hall
Saturday, June 7, 2025
Sunday, June 8, 2025