ICTS

In this talk, I will explore how measurements shape an observer’s description of transport in diffusive classical systems. I will present a framework for incorporating continuous monitoring into Macroscopic Fluctuation Theory and show how the cumulants of the current scale with measurement strength, revealing an interesting behaviour at particular boundary densities. Finally, I will discuss how measurements can play a role on the properties of dynamical phase transitions.

Chaotic quantum systems at finite energy density are expected to act as their own heat baths, rapidly dephasing local quantum superpositions. We argue that in fact this dephasing is subexponential for chaotic dynamics with conservation laws in one spatial dimension: all local correlation functions decay as stretched exponentials or slower. The stretched exponential bound is saturated for operators that are orthogonal to all hydrodynamic modes. This anomalous decay is a quantum coherent effect, which lies beyond standard fluctuating hydrodynamics; it vanishes in the presence of extrinsic dephasing. Our arguments are general, subject principally to the assumption that there exist zero-entropy charge sectors (such as the particle vacuum) with no nontrivial dynamics: slow relaxation is due to the persistence of regions resembling these inert vacua, which we term "voids". In systems with energy conservation, this assumption is automatically satisfied because of the third law of thermodynamics.

We consider quantum and classical many-body Hamiltonian systems that combine integrable contact interactions with generic two-body long-range potentials. We show that the time evolution of local observables can be formulated as a generalized Bogoliubov–Born–Green–Kirkwood–Yvon
(gBBGKY) hierarchy, built on the quasiparticle densities of the underlying integrable model and their correlations. Starting from an ansatz for the state at time t, which we denote the correlated fluid cell ensemble, we derive this hierarchy and demonstrate that it exactly reproduces the dynamics of one- and multi-point correlation functions in perturbed integrable models at all times. These predictions are validated against microscopic molecular-dynamics simulations with perfect agreement. In the late-time regime, approach to the Gibbs ensemble is mediated by a Boltzmann-style scattering integral featuring a complex interplay of contact integrable and long-range collision processes. In the specific case of dipolar gases—where the relevant matrix elements are known—we verify that our collision integral exactly recovers the Fermi’s golden rule result and provide a full theoretical characterization of the experimental observations of [Tang et al. Phys. Rev. X 8, 021030 2018]. Our framework thus demonstrates how the BBGKY approach can be systematically extended to include strong local interactions, making it applicable to a broad class of experimentally relevant systems, from one-dimensional dipolar cold-atom gases to Lennard-Jones interacting molecules.

I will discuss charge current fluctuations in a family of stochastic charged cellular automata away from the deterministic single-file limit, and obtain the exact typical charge probability distributions, known to be anomalous, using hydrodynamics. The cellular automata considered here are examples of linearly degenerate systems where two distinct mechanisms of diffusion, namely normal and convective diffusion, coexist. Our formalism, based on macroscopic fluctuation theory, allows us to describe current fluctuations stemming from these two diffusive processes, and we expect it to be applicable to generic linearly degenerate systems.

Thermalization of isolated and open quantum systems has been studied extensively. However, being the subject of investigation by different scientific communities and being analysed using different mathematical tools, the connection between the isolated (IQS) and open (OQS) approaches to thermalization has remained opaque. Here we demonstrate that the fundamental difference between the two paradigms is the order in which the long time and the thermodynamic limits are taken. This difference implies that they describe physics on widely different time and length scales. Our analysis is carried out numerically for the case of a double quantum dot (DQD) coupled to a fermionic lead, also known as the interacting resonant level model in quantum impurity physics. We show how both OQS and IQS thermalization can be explored in this model on equal footing, allowing a fair comparison between the two. We find that while the quadratically coupled (free) DQD experiences no isolated thermalization, it of course does experience open thermalization. For the non-linearly interacting DQD coupled to a fermionic lead, the many-body interaction in the DQD breaks the integrability of the whole system. We find that this system shows strong evidence of both OQS and IQS thermalization in the same dynamics, but at widely different time scales, consistent with reversing the order of the long time and the thermodynamic limits.

Ajay Mohan - Phase space hydrodynamics of C = 1 matrix model and the lowest Landau level

Rushikesh Suresh Suroshe - 2D or not 2D : The holographic dictionary of LLL

Pushkar Soni - Hydrodynamics in the Carrollian regime

Shuvayu Roy - Field Redefinitions and Stable-Causal Theories of Relativistic Hydrodynamics

Arpit Das - Hydrodynamic EFT for chiral MHD

We study a coupled driven system where two different species of particles, along with some vacancies or holes, move on a landscape whose shape fluctuates with time. The movement of the particles is guided by the local shape of the landscape, and this shape is also affected by the presence of different particle species. The nature of this coupling plays a crucial role in formation of long range order in the system. In absence of vacancies, the system reduces to previously studied LH model for which different kinds of ordered and disordered phases were observed upon tuning the coupling between the particles and landscape dynamics. We show here that although the vacancies do not bias the landscape dynamics, their presence significantly affects the phase diagram. In particular, a novel kind of ordered phase is observed where one particle species phase-separates and shapes the
landscape beneath it in the form of a plateau. For a system of size N , the height of the plateau scales √ as N , in sharp contrast with earlier-observed landscape structures which were macroscopic. This ordered part coexists with a disordered part where the second particle species forms a homogeneous mixture with the vacancies, and this mixture occupies a disordered segment of the landscape. We call this new kind of ordered phase ‘vacancy induced phase separation’. We analytically calculate the phase boundaries within mean field approximation.

We introduce a discrete space-time dynamics of charged particles with stochastic particle scattering. By mapping the dynamics to a "vacany-dressed" bistochastic six-vertex model we derive the exact anomalous distribution of the charge current that interpolates between the charged single-file class in the limit of pure reflection and free dynamics in the limit of pure transmission. Non-Gaussianity is related to dynamical criticality by Lee-Yang analysis of the cumulant generating function. Building on macroscopic fluctuation theory, we give a hydrodynamic description of the model's anomalous fluctuations. Linear degeneracy, arising from charge inertness, allows for combined contributions from convective and normal diffusion.

Similar phenomenology of dynamical criticality is observed in equilibrium spin current fluctuations in the easy-axis and isotropic regimes of the XXZ spin chain. The easy-axis regime supports the non-Gaussian distribution of the charged single-file class despite not manifestly satisfying a single-file constraint. We show that anomalous fluctuations instead arise due to linear degeneracy of the vacuum polarization in the quasi-particle description. The dynamical spin structure factor at the isotropic point matches that of the Kardar-Parisi-Zhang (KPZ) universality class while spin fluctuations are anomalous but distinct from those of the KPZ class.

The symmetric exclusion process (SEP) occupies a central place in the study of interacting particle systems, underpinning major developments such as the matrix product ansatz and macroscopic fluctuation theory (MFT). It is well known that the SEP arises from a stochastic representation of the spin-1/2 XXX chain.

By moving to non-compact spins, one obtains a broad family of stochastic processes generated by the XXX chain, encompassing both non-integrable models—such as the inclusion process, the KMP process, and the Kac process—and recently introduced integrable ones [1], including the harmonic process and an integrable model of heat conduction. Owing to the underlying su(1,1) symmetry, all these processes admit a natural dual formulation.

In this talk, after reviewing the definitions of these models and their non-equilibrium steady state, I will discuss their large-deviation properties. In particular, I will present a new method for analysing path-space large deviations without passing to a continuum space limit, thereby retaining the lattice structure [2]. This approach corresponds to studying the XXX chain in a large-spin limit and yields a discrete analogue of macroscopic fluctuation theory.

For the harmonic process, the integrability of the classical Ishimori chain, together with its mapping to the Ablowitz–Ladik model, enables an explicit closed-form computation of the current large-deviation function [3].

[1] R. Frassek, C. Giardinà, J. Kurchan, Non-compact quantum spin chains as integrable stochastic particle processes, J. Stat. Phys. 180, 135-171 (2020)
[2] C. Giardinà, T. Sasamoto, Large spin and large deviations for interacting particle systems [work in progress].
[3] C. Giardinà, K. Mallick, T. Sasamoto, H. Suda, Exact solution of discrete macroscopic fluctuation theory for an integrable spin system [work in progress].

Integrable systems feature an infinite number of conserved charges and on hydrodynamic scales are described by generalised hydrodynamics (GHD). This description breaks down when the integrability is weakly broken and sufficiently large space-time-scales are probed. The emergent hydrodynamics depends then on the charges conserved by the perturbation.

In my contribution I will focus on nearly-integrable Galilean-invariant systems with conserved particle number, momentum and energy. Basing on the Boltzmann approach to integrability -breaking we describe dynamics of the system with GHD equation supplemented with a collision term. Employing Chapman-Enskog formalism and nonlinear fluctuating hydrodynamics I will show that depending on the length scales, one can expect three hydrodynamic regimes: generalised hydrodynamics, Navier-Stokes (NS) regime and Kardar-Parisi-Zhang (KPZ) superdiffusion known to occur in generic 1d non-integrable fluids. Moreover, I will show how we can compute transport coefficients characterising the fluid in NS and KPZ regimes.

I will explain the fundamental principles for the emergence of the hydrodynamic theory for large-scale behaviours in many-body systems. I will then apply these to generalised hydrodynamics, the hydrodynamic theory of integrable systems, describing its main equations and structures.

The Dyson exclusion process (SDEP) is a lattice gas with exclusion and long-range, Coulomb-type interactions. It emerges both as the maximal-activity limit of the symmetric exclusion process and as a discrete version of Dyson's Brownian motion on the unitary group. Exploiting an exact ground-state (Doob) transform, the stochastic generator of the SDEP maps onto the XX quantum chain. We derive a non-local hydrodynamic equation that governs the macroscopic behavior of the SDEP. Interestingly, the model displays limit shape phenomena, and its long-distance fluctuations are described by conformal field theory. The talk is based on joint work with Ali Zahra and Gunter Schütz.

We discuss various "quasiballistic" regimes that can arise in high-temperature transport. We first motivate the problem by presenting experimental and numerical evidence for long-lived and transiently ballistic regimes of spin and charge transport in strongly interacting quantum systems at a high effective temperature. We then focus on the specific example of quasiballistic spin transport in non-integrable, power-law interacting XXZ chains. We show that elementary analytical arguments based on minimizing norms of commutators suffice to reproduce the main qualitative features of this physics on accessible timescales.

Many models in active matter consist of self-propelled particles that interact, leading to phase transitions including flocking and phase separation. I will discuss some lattice models of this type, whose large-scale (hydrodynamic) behaviour is described by macroscopic fluctuation theory. This will include the entropy production rate and its fluctuations, as well as the behaviour of flocking (travelling) solutions.

Understanding thermalisation in quantum many-body systems is among the most enduring problems in modern physics. A particularly interesting question concerns the role played by quantum mechanics in this process, i.e. whether thermalisation in quantum many-body systems is fundamentally different from that in classical many-body systems and, if so, which of its features are genuinely quantum. I will discuss this question by considering minimally structured many-body systems that are only constrained to have local interactions, i.e. local random circuits. In particular, I will introduce random permutation circuits (RPCs), which are circuits comprising gates that locally permute basis states, as a counterpart to random unitary circuits (RUCs), a standard toy model for generic quantum dynamics.

In this talk, we discuss the recently developed Ballistic Macroscopic Fluctuation Theory (BMFT). It is a framework for describing how initial fluctuations in ballistic systems propagate through Euler-scale hydrodynamics and how correlations between hydrodynamic variables like conserved densities and currents evolve. We outline the main ideas of BMFT and contrast it with the Macroscopic Fluctuation Theory (MFT) used for diffusive systems. The talk focuses on applying BMFT to integrable models, whose many conserved quantities give rise to generalized hydrodynamics (GHD). Recent work shows that Euler-scale GHD can be mapped to the hydrodynamics of effectively non-interacting particles. In certain cases, such as hard rods and the Toda model, this correspondence has been proven to hold microscopically, and one expects such a mapping to hold for generic integrable models. We illustrate this mapping through classical and quantum examples and present our BMFT approach based on this effective non-interacting description. We demonstrate the method using observables such as particle currents in generic integrable models and the rank (ordering) of particle positions in the hard-rod system.

I will present examples of Limit Shapes - the most probable macroscopic shape with sharp boundaries separating frozen and fluctuating regions - which arise in a variety of classical and quantum systems. I will explain a special role played by analytic functions defining Riemann surface whose topology can be changed abruptly across phase transitions. Most of the examples are based on free fermionic models, however recently we studied a notable exception from this rule - the Polytropic Gas with a power-law equation of state. The hydrodynamic approach to Emptiness Formation Probability in Polytropic Gas will be discussed.

We consider a tight-binding chain with dephasing noise, whose time evolution is described by the  quantum master equation called the Gorini-Kossakowski-Sudarhan-Lindblad (GKSL) equation. 

By using a connection of this model to the Hubbard model with imaginary coupling [1], we study  the density profile [2] and current fluctuations [3] exactly for the model on the infinite line by writing down contour integral formulas using Bethe ansatz. 

The talk is based on collaborations with Taiki Ishiyama and Kazuya Fujimoto. 
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References

[1]M. V. Medvedyeva, F. H. L. Essler, and T. Prosen, Exact Bethe Ansatz Spectrum of a Tight-Binding Chain with Dephasing Noise, Phys. Rev. Lett. 117, 137202 (2016).

[2] T. Ishiyama, K. Fujimoto, T. Sasamoto, Exact density profile in a tight-binding chain with dephasing noise,  J. Stat. Mech. 2025, 033103 (2025)  (arXiv: 2501.07095). 

[3] T. Ishiyama, K. Fujimoto, T. Sasamoto, Exact current fluctuations in a tight-binding chain with dephasing noise arXiv: 2504.06989.