Conformal invariance in driven diffusive systems at high currents

Abstract

We consider space-time correlations in driven diffusive systems which undergo a fluctuation into a regime with an atypically large current or dynamical activity. For a single conserved mass we show that the spatio-temporal density correlations in one space dimension are given by conformally invariant field theories with central charge $c=1$, corresponding to a ballistic universality class with dynamical exponent $z=1$. We derive a phase diagram for atypical behaviour that besides the conformally invariant regime exhibits a regime of phase separation for atypically low current or activity. On the phase transition line, corresponding to typical behaviour, the dynamics belongs to the Kardar-Parisi-Zhang universality class with dynamical exponent $z=3/2$, except for a diffusive point with $z=2$. We demonstrate the validity of the theory for the one-dimensional asymmetric simple exclusion process with both periodic and open boundaries by exact results for the dynamical structure in the limit of maximal current.

arXiv comment5 pages, 2 figures. Revision with typo in Eq. (1) corrected and some cosmetic changes

References in corpus (16)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Macroscopic fluctuation theory
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Nonequilibrium Markov processes conditioned on large deviations
• Distribution of current in non-equilibrium diffusive systems and phase transitions
• Universal cumulants of the current in diffusive systems on a ring
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Fibonacci family of dynamical universality classes
• Effective interactions and large deviations in stochastic processes
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Current large deviations for Asymmetric Exclusion Processes with open boundaries
• Dynamical phase transition for current statistics in a simple driven diffusive system
• Transition probabilities and dynamic structure factor in the ASEP conditioned on strong flux
• Inactive dynamical phase of a symmetric exclusion process on a ring
• Critical Behaviour of Mixed Heisenberg Chains
• Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory

Cited by in corpus (34)

• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• Large deviations and dynamical phase transitions in stochastic chemical networks
• Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains
• Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Dynamical phase transitions in the current distribution of driven diffusive channels
• Building continuous time crystals from rare events
• Order and symmetry-breaking in the fluctuations of driven systems
• Sampling rare events across dynamical phase transitions
• Current fluctuations in boundary-driven quantum spin chains
• Finite time large deviations via matrix product states
• Phases of quantum dimers from ensembles of classical stochastic trajectories
• Optimal sampling of dynamical large deviations in two dimensions via tensor networks
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Non-equilibrium dynamic hyperuniform states
• Catching and reversing quantum jumps and thermodynamics of quantum trajectories
• Rare-Event Properties of the Nagel-Schreckenberg Model
• The kinetic exclusion process: a tale of two fields
• Coupled activity-current fluctuations in open quantum systems under strong symmetries
• Dynamical criticality in open systems: non-perturbative physics, microscopic origin and direct observation
• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
• Current large deviations for partially asymmetric particle systems on a ring
• Lower current large deviations for zero-range processes on a ring
• Exact solution of the Rule 150 reversible cellular automaton
• A lattice gas model for generic one-dimensional Hamiltonian Systems
• KPZ fluctuations in finite volume
• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions
• Hyperuniformity in mass transport processes with center-of-mass conservation: Some exact results
• Non-local meta-conformal invariance in diffusion-limited erosion
• Infinite family of universal profiles for heat current statistics in Fourier's law
• Current fluctuations in a stochastic system of classical particles with next-nearest-neighbor interactions
• Quest for the golden ratio universality class
• Effective dynamics of a conditioned generalized linear Glauber model