arXiv subjects

Andrew Urilyon

Publications and source records attributed to Andrew Urilyon.

4 recordsLinked to original sources

arXiv2026

Anomalous Diffusion and Superdiffusion in Integrable Spin Chains via a Soliton Gas Mapping

We introduce a multi-species soliton gas in which each species has a distinct effective scattering length, and the repulsive scattering shift is set by the smaller of the two colliding particles. We argue that this model shares key quasiparticle and scattering features with the XXZ spin chain. We show that fixing only the functional decay of bare velocities with particle size is sufficient to reproduce the XXZ spin-transport phase diagram: diffusion (with anomalous fluctuations) in the anisotropic regime and superdiffusion at the isotropic point. We then demonstrate that the statistics of charge transfer differs qualitatively from that of \textit{particle trajectories}. For large particles, trajectories are Gaussian in the diffusive regime and appear to exhibit KPZ statistics at the isotropic point, providing a direct microscopic signature of KPZ physics in integrable quasiparticle motion. In contrast, charge-transfer fluctuations are anomalous in the anisotropic regime, while they cross over to Gaussian statistics at late times at the isotropic point, reconciling non-Gaussian trajectory fluctuations with Gaussian charge-transfer statistics. Our results establish this soliton gas as a minimal framework for anomalous spin and charge transport in integrable systems, and offer new insight into the origin of KPZ fluctuations in isotropic integrable models.

cond-mat.str-el↗

arXiv2025

Simulating generalised fluids via interacting wave packets evolution

One-dimensional integrable and quasi-integrable systems display, on macroscopic scales, a universal form of transport known as Generalized Hydrodynamics (GHD). In its standard Euler-scale formulation, GHD mirrors the equations of a two-dimensional compressible fluid but ignores fluctuations and becomes numerically unwieldy as soon as integrability-breaking perturbations are introduced. We show that GHD can be efficiently simulated as a gas of semiclassical wave packets - a natural generalisation of hard-rod particles - whose trajectories are efficiently mapped onto those of point particles. This representation (i) provides a transparent route to incorporate integrability-breaking terms, and (ii) automatically embeds the exact fluctuating-hydrodynamics extension of GHD. The resulting framework enables fast, large-scale simulations of quasi-integrable systems even in the presence of complicated integrability-breaking perturbations. It also manifest the pivotal role of two-point correlations in systems confined by external potentials: we demonstrate that situations where local one-point observables appear thermalised can nevertheless sustain long-lived, far-from-equilibrium long-range correlations for arbitrarily long times, signaling that, differently from what previously stated, true thermalisation is not reached at diffusive time-scales.

cond-mat.stat-mech↗

arXiv2025

Ballistic macroscopic fluctuation theory via mapping to point particles

Ballistic Macroscopic Fluctuation Theory (BMFT) captures the evolution of fluctuations and correlations in systems where transport is strictly ballistic. We show that, for \emph{generic integrable models}, BMFT can be constructed through a direct mapping onto ensembles of classical or quantum point particles. This mapping generalises the well-known correspondence between hard spheres and point particles: the two-body \emph{scattering shift} now plays the role of an effective rod length for arbitrary interactions. Within this framework, we re-derive both the full-counting statistics and the long-range correlation functions previously obtained by other means, thereby providing a unified derivation. Our results corroborate the general picture that all late-time fluctuations and correlations stem from the initial noise, subsequently convected by Euler-scale hydrodynamics.

cond-mat.stat-mech↗

arXiv2024

Quantum fluctuating theory for one-dimensional shock waves

We study the formation and the subsequent dynamics of shock waves in repulsive one-dimensional Bose gases during the free expansion of a density hump. By building coherent Fermi states for interacting Bethe fermions, we define a quantum fluctuating initial state expressed in terms of universal quantities, namely the density and the Luttinger parameter. In the integrable case, this fluctuating state is then evolved by generalized hydrodynamics (GHD) and, differently from non-fluctuating initial states, it develops density ripples on top of the hydrodynamic mean value. Our analysis gives a general theory of quantum ripples and wave breaking in integrable and quasi-integrable one-dimensional liquids and clarifies the role of the interaction strength. In particular, for strongly/intermediately interacting bosons, we find quantum ripples originating from low-energy modes at the Fermi surface interfering when transported by GHD. In the low coupling limit, near the quasicondensate regime, we find instead that density ripples have a semi-classical nature, and their description requires information on the curvature of the Fermi surface.

cond-mat.stat-mech↗