R. Hurtado-Gutiérrez, P.I. Hurtado, C. Pérez-Espigares
Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. One of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While the Macroscopic Fluctuation Theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete ℤn symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. We show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate manifold. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in three paradigmatic many-body systems: (i) the 1D boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (ii) the 3 and 4-state Potts model, which displays discrete rotational symmetry-breaking DPT for energy fluctuations, and (iii) the closed WASEP which presents a continuous symmetry-breaking DPT to a time-crystal phase characterized by a rotating condensate.
P.L. Garrido, P.I. Hurtado, D. Manzano, F. de los Santos
The special issue of European Physical Journal Special Topics has been finally published. It originated at the 14th Granada Seminar on Quantum Systems in and out of equilibrium: Fundamentals, dynamics and applications, which took place in 2017, from June 20 to June 23 in Granada, Spain. This edition was sponsored by the University of Granada through the Department of Electromagnetism and Physics of the Matter and the Faculty of Sciences, the Spanish Minister of Economy, Industry and Competitiveness, and the European Physical Society. There were in this edition a total of 57 lectures and 27 poster contributions covering quantum aspects of thermalization, quantum transport, quantum effects in condensed matter, biology, quantum computation, open quantum systems, quantum fluctuations and large deviations, and quantum thermodynamics.
C. Pérez-Espigares, F. Carollo, J.P. Garrahan, P.I. Hurtado
Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on both the macroscopic large deviation properties and the microscopic origin of such spontaneous symmetry breaking in the weakly asymmetric exclusion process. By studying the joint fluctuations of the current and a collective order parameter, we uncover the full dynamical phase diagram for arbitrary boundary driving, which is reminiscent of a ℤ2 symmetry-breaking transition. The associated joint large deviation function becomes non-convex below the critical point, where a Maxwell-like violation of the additivity principle is observed. At the microscopic level, the dynamical phase transition is linked to an emerging degeneracy of the ground state of the microscopic generator, from which the optimal trajectories in the symmetry-broken phase follow. In addition, we observe this new symmetry-breaking phenomenon in extensive rare-event simulations of the microscopic dynamics.
Symmetry is a powerful concept in physics, and its recent application to understand nonequilibrium behavior is providing deep insights and groundbreaking exact results. Here we show how to harness symmetry to control transport and statistics in open quantum systems. Such control is enabled by a first-order-type dynamic phase transition in current statistics and the associated coexistence of different transport channels (or nonequilibrium steady states) classified by symmetry. Microreversibility then ensues, via the Gallavotti-Cohen fluctuation theorem, a twin dynamic phase transition for rare current fluctuations. Interestingly, the symmetry present in the initial state is spontaneously broken at the fluctuating level, where the quantum system selects the symmetry sector that maximally facilitates a given fluctuation. We illustrate these results in a qubit network model motivated by the problem of coherent energy harvesting in photosynthetic complexes, and introduce the concept of a symmetry-controlled quantum thermal switch, suggesting symmetry-based design strategies for quantum devices with controllable transport properties.
Phase transitions not allowed in equilibrium steady states may happen however at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While small fluctuations result from the sum of weakly-correlated local events, for currents above a critical threshold the system self-organizes into a coherent traveling wave which facilitates the current deviation by gathering energy in a localized packet, thus breaking translation invariance. This results in Gaussian statistics for small fluctuations but non-Gaussian tails above the critical current. Our observations, which agree with predictions derived from hydrodynamic fluctuation theory, strongly suggest that rare events are generically associated with coherent, self-organized patterns which enhance their probability.