Universal anomalous fluctuations in charged single-file systems

Abstract

Conventional classification of dynamical phenomena is based on universal hydrodynamic relaxation characterized by algebraic dynamical exponents and asymptotic scaling of the dynamical structure factor. This work uncovers a novel type of dynamical universality reflected in statistical properties of macroscopic fluctuating observables such as the transmitted charge. By considering a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore charged particles, we demonstrate that stringent dynamical constraints give rise to universal anomalous statistics of cumulative charge currents manifested both on the timescale characteristic of typical fluctuations and also in the rate function describing rare events. By computing the full counting statistics of net transferred charge between two extended subsystems, we establish a number of unorthodox dynamical properties in an analytic fashion. Most prominently, typical fluctuations in equilibrium are governed by a universal distribution that markedly deviates from the expected Gaussian statistics, whereas large fluctuations are described by an exotic large-deviation rate function featuring an exceptional triple critical point. Far from equilibrium, competition between dynamical phases leads to dynamical phase transitions of first and second order. Despite dynamical criticality, we find the large-deviation rate function of the joint particle-charge transfer obeys the fluctuation relation. Curiously, the univariate charge-current rate function experiences a spontaneous breaking of fluctuation symmetry upon varying the particle and charge densities in a nonequilibrium initial state. The rich phenomenology of the outlined dynamical universality is exemplified on an exactly solvable classical cellular automaton of charged hardcore particles. We determine the dynamical phase diagram in the framework of Lee-Yang's theory of phase transitions and exhibit a hyper-dimensional diagram of distinct dynamical regimes.

Hydrodynamic gauge fixing and higher order hydrodynamic expansion

“…In particular, the Onsager reciprocal relations hold, and entropy production is non-negative. This, we believe, is an important remark, especially in relation to some recent works investigating such aspects [52][53][54][55]. The diffusive order of hydrodynamics is sometimes broken: the Kubo formula may give infinity, implying that superdiffusion occurs instead of diffusion.…”

Matrix product symmetries and breakdown of thermalization from hard rod deformations

“…This phenomenon was already observed in a number of works dealing with similar models [17,24,36,39,40]. It induces Hilbert space fragmentation: different values of the spin pattern all correspond to different irreducible sectors in the Hilbert space.…”

“…This phenomenon underlies the existence of the exotic symmetries of all our models. Furthermore, it allows for exact solutions of real time dynamics in similar models [39][40][41][42][43].…”

“…The XXC models that appeared in our study have the special property that spin-charge separation is exact, the spin pattern is always conserved, and it does not influence the charge degrees of motion. It was argued in [40] that in such models the spin transport has anomalous fluctuations. This is believed to be true also for the folded XXZ model [30,40], although the rigorous proofs of [40] do not apply in that case.…”

“…It was argued in [40] that in such models the spin transport has anomalous fluctuations. This is believed to be true also for the folded XXZ model [30,40], although the rigorous proofs of [40] do not apply in that case. We conjecture that our family of models also displays anomalous fluctuations, in both the integrable and non-integrable cases.…”