Spectral signatures of symmetry-breaking dynamical phase transitions

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 $\mathbb{Z}_n$ 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

Symmetries in Fluctuations Far from Equilibrium

Fluctuations arise universally in Nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. In order to sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation which links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulae. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.Comment: 8 pages, 4 figure

Estudi de la inserció laboral dels graduats en Comptabilitat i Finances de la Universitat Autònoma de Barcelona

En aquest treball s'explica en quina situació laboral es troben els antics alumnes de la facultat d'Economia i Empresa de la Universitat Autònoma de Barcelona, graduats en Comptabilitat i Finances. L'anàlisi s'ha realitzat a través de les dades obtingudes d'una enquesta dirigida als graduats de les promocions que va haver-hi entre els anys 2010-2014 i 2013-2017. Amb tota la informació que s'ha extret, s'han pogut analitzar les variables que influeixen en la situació laboral, i també s'ha realitzat una comparativa de les dades més significatives amb el grau d'Administració i Direcció d'Empreses de la Universitat Autònoma de Barcelona, per així poder analitzar quines són les diferències més significatives al món laboral. Per finalitzar aquest treball, s'ha realitzat un anàlisi discriminant per poder veure quines són les variables que més poden influenciar al sou i al temps d'inserció, i amb aquestes dades poder rebutjar o no les hipòtesis formulades al principi del trebal

Herbivores, saprovores and natural enemies respond differently to within-field plant characteristics of wheat fields

Understanding ecosystem functioning in a farmland context by considering the variety of ecological strategies employed by arthropods is a core challenge in ecology and conservation science. We adopted a functional approach in an assessment of the relationship between three functional plant groups (grasses, broad-leaves and legumes) and the arthropod community in winter wheat fields in a Mediterranean dryland context. We sampled the arthropod community as thoroughly as possible with a combination of suction catching and flight-interception trapping. All specimens were identified to the appropriate taxonomic level (family, genus or species) and classified according to their form of feeding: chewing-herbivores, sucking-herbivores, flower-consumers, omnivores, saprovores, parasitoids or predators. We found, a richer plant community favoured a greater diversity of herbivores and, in turn, a richness of herbivores and saprovores enhanced the communities of their natural enemies, which supports the classical trophic structure hypothesis. Grass cover had a positive effect on sucking-herbivores, saprovores and their natural enemies and is probably due to grasses' ability provide, either directly or indirectly, alternative resources or simply by offering better environmental conditions. By including legumes in agroecosystems we can improve the conservation of beneficial arthropods like predators or parasitoids, and enhance the provision of ecosystem services such as natural pest control

Sampling rare events across dynamical phase transitions

Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. In some cases, this leads to symmetry-broken space-time trajectories which enhance the probability of such events due to the emergence of ordered structures. Despite their conceptual and practical importance, these dynamical phase transitions (DPTs) at the trajectory level are difficult to characterize due to the low probability of their occurrence. However, during the last decade, advanced computational techniques have been developed to measure rare events in simulations of many-particle systems that allow the direct observation and characterization of these DPTs. Here we review the application of a particular rare-event simulation technique, based on cloning Monte Carlo methods, to characterize DPTs in paradigmatic stochastic lattice gases. In particular, we describe in detail some tricks and tips of the trade, paying special attention to the measurement of order parameters capturing the physics of the different DPTs, as well as to the finite-size effects (both in the system size and in the number of clones) that affect the measurements. Overall, we provide a consistent picture of the phenomenology associated with DPTs and their measurement.Ministerio Español MINECO proyecto (No. FIS2017-84256-P). Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía and European Regional Development Fund (ERDF), ref. SOMM17/6105/UGR. C.P.E. acknowledges the funding received from the European Union’s Horizon 2020 re-search and innovation programme under the Marie Sklodowska-Curie Cofund Programme Athenea3I GrantAgreement No. 754446