Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLarge deviations in the symmetric simple exclusion process with slow boundaries
84
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We obtain the exact large deviation functions of the density profile and of the current, in the non-equilibrium steady state of a one dimensional symmetric simple exclusion process coupled to boundary reservoirs with slow rates. Compared to earlier results, where rates at the boundaries are comparable to the bulk ones, we show how macroscopic fluctuations are modified when the boundary rates are slower by an order of inverse of the system length.
rate research
Read More
We study the probability distribution of entanglement in the Quantum Symmetric Simple Exclusion Process, a model of fermions hopping with random Brownian amplitudes between neighboring sites. We consider a protocol where the system is initialized in a pure product state of $M$ particles, and focus on the late-time distribution of Renyi-$q$ entropies for a subsystem of size $ell$. By means of a Coulomb gas approach from Random Matrix Theory, we compute analytically the large-deviation function of the entropy in the thermodynamic limit. For $q>1$, we show that, depending on the value of the ratio $ell/M$, the entropy distribution displays either two or three distinct regimes, ranging from low- to high-entanglement. These are connected by points where the probability density features singularities in its third derivative, which can be understood in terms of a transition in the corresponding charge density of the Coulomb gas. Our analytic results are supported by numerical Monte Carlo simulations.
We study mixing times of the symmetric and asymmetric simple exclusion process on the segment where particles are allowed to enter and exit at the endpoints. We consider different regimes depending on the entering and exiting rates as well as on the rates in the bulk, and show that the process exhibits pre-cutoff and in some cases cutoff. Our main contribution is to study mixing times for the asymmetric simple exclusion process with open boundaries. We show that the order of the mixing time can be linear or exponential in the size of the segment depending on the choice of the boundary parameters, proving a strikingly different (and richer) behavior for the simple exclusion process with open boundaries than for the process on the closed segment. Our arguments combine coupling, second class particle and censoring techniques with current estimates. A novel idea is the use of multi-species particle arguments, where the particles only obey a partial ordering.
For diffusive many-particle systems such as the SSEP (symmetric simple exclusion process) or independent particles coupled with reservoirs at the boundaries, we analyze the density fluctuations conditioned on current integrated over a large time. We determine the conditioned large deviation function of density by a microscopic calculation. We then show that it can be expressed in terms of the solutions of Hamilton-Jacobi equations, which can be written for general diffusive systems using a fluctuating hydrodynamics description.
We consider the dynamics of fluctuations in the quantum asymmetric simple exclusion process (Q-ASEP) with periodic boundary conditions. The Q-ASEP describes a chain of spinless fermions with random hoppings that are induced by a Markovian environment. We show that fluctuations of the fermionic degrees of freedom obey evolution equations of Lindblad type, and derive the corresponding Lindbladians. We identify the underlying algebraic structure by mapping them to non-Hermitian spin chains and demonstrate that the operator space fragments into exponentially many (in system size) sectors that are invariant under time evolution. At the level of quadratic fluctuations we consider the Lindbladian on the sectors that determine the late time dynamics for the particular case of the quantum symmetric simple exclusion process (Q-SSEP). We show that the corresponding blocks in some cases correspond to known Yang-Baxter integrable models and investigate the level-spacing statistics in others. We carry out a detailed analysis of the steady states and slow modes that govern the late time behaviour and show that the dynamics of fluctuations of observables is described in terms of closed sets of coupled linear differential-difference equations. The behaviour of the solutions to these equations is essentially diffusive but with relevant deviations, that at sufficiently late times and large distances can be described in terms of a continuum scaling limit which we construct. We numerically check the validity of this scaling limit over a significant range of time and space scales. These results are then applied to the study of operator spreading at large scales, focusing on out-of-time ordered correlators and operator entanglement.
We consider the asymmetric simple exclusion process (ASEP) on the one-dimensional lattice. The particles can be created/annihilated at the boundaries with time-dependent rate. These boundary dynamics are properly accelerated. We prove the hydrodynamic limit of the particle density profile, under the hyperbolic space-time rescaling, evolves with the entropy solution to Burgers equation with Dirichlet boundary conditions. The boundary conditions are characterised by boundary entropy flux pair.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
