Integrable dissipative exclusion process: Correlation functions and physical properties

Abstract

We study a one-parameter generalization of the symmetric simple exclusion process on a one dimensional lattice. In addition to the usual dynamics (where particles can hop with equal rates to the left or to the right with an exclusion constraint), annihilation and creation of pairs can occur. The system is driven out of equilibrium by two reservoirs at the boundaries. In this setting the model is still integrable: it is related to the open XXZ spin chain through a gauge transformation. This allows us to compute the full spectrum of the Markov matrix using Bethe equations. Then, we derive the spectral gap in the thermodynamical limit. We also show that the stationary state can be expressed in a matrix product form permitting to compute the multi-points correlation functions as well as the mean value of the lattice current and of the creation-annihilation current. Finally the variance of the lattice current is exactly computed for a finite size system. In the thermodynamical limit, it matches perfectly the value obtained from the associated macroscopic fluctuation theory. It provides a confirmation of the macroscopic fluctuation theory for dissipative system from a microscopic point of view.

31 pages, 7 figures ; introduction expanded, typos corrected and title changed

References in corpus (12)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
• Matrix representation of the stationary measure for the multispecies TASEP
• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Energy distribution and effective temperatures in a driven dissipative model
• Injected Power Fluctuations in 1D Dissipative Systems
• An exactly solvable dissipative transport model
• Relaxation dynamics of the asymmetric simple exclusion process with Langmuir kinetics on a ring
• Correlation and response in a driven dissipative model
• Correlation functions in conformal invariant stochastic processes

Cited by in corpus (12)

• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units
• Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state
• Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions
• Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
• Matrix Product representation of the stationary state of the open Zero Range Process
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
• Integrability in out-of-equilibrium systems
• Lattice SUSY for the DiSSEP at ${\lambda }^2=1$ (and ${\lambda }^2=-3$)
• A stochastic model solvable without integrability