Using tensor network states for multi-particle Brownian ratchets

Abstract

The study of Brownian ratchets has taught how time-periodic driving supports a time-periodic steady state that generates nonequilibrium transport. When a single particle is transported in one dimension, it is possible to rationalize the current in terms of the potential, but experimental efforts have ventured beyond that single-body case to systems with many interacting carriers. Working with a lattice model of volume-excluding particles in one dimension, we analyze the impact of interactions on a flashing ratchet's current. To surmount the many-body problem, we employ the time-dependent variational principle with a binary tree tensor network, methods discussed at length in a companion paper. Rather than propagating individual trajectories, the tensor network approach propagates a distribution over many-body configurations via a controllable variational approximation. The calculations, which reproduce Gillespie trajectory sampling, identify and explain a shift in the frequency of maximum current to higher driving frequency as the lattice occupancy increases.

arXiv comment6 pages, 3 figures

References in corpus (42)

• The density-matrix renormalization group in the age of matrix product states
• Brownian motors: noisy transport far from equilibrium
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• The ITensor Software Library for Tensor Network Calculations
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Time-evolution methods for matrix-product states
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• A modified Next Reaction Method for simulating chemical systems with time dependent propensities and delays
• Thermodynamic formalism for systems with Markov dynamics
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Inferring dissipation from current fluctuations
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Collective dynamics of molecular motors pulling on fluid membranes
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
• Efficient Matrix Product State Method for periodic boundary conditions
• Efficiency at maximum power of interacting molecular machines
• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• Time Dependent Variational Principle for Tree Tensor Networks
• Relaxation times in the ASEP model using a DMRG method
• Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem
• Dynamical simulations of classical stochastic systems using matrix product states
• Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
• Efficiency fluctuations of stochastic machines undergoing a phase transition
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• Movements of molecular motors: Ratchets, random walks and traffic phenomena
• Mechanical coupling in flashing ratchets
• Three and four current reversals versus temperature in correlation ratchets with a simple sawtooh potential
• Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks
• Validity of the additivity principle in the weakly asymmetric exclusion process with open boundaries
• Studying dynamics in two-dimensional quantum lattices using tree tensor network states
• Finite time large deviations via matrix product states
• Dynamical Transition in the Open-boundary Totally Asymmetric Exclusion Process
• Optimal sampling of dynamical large deviations via matrix product states
• Stochastic Matrix Product States
• Finite size scaling of current fluctuations in the totally asymmetric exclusion process
• Superfluid to Mott transition in a Bose-Hubbard ring: Persistent currents and defect formation
• Stochastic thermodynamics in many-particle systems
• Capturing exponential variance using polynomial resources: applying tensor networks to non-equilibrium stochastic processes
• Computing time-periodic steady-state currents via the time evolution of tensor network states
• Current inversion in a periodically driven two-dimensional Brownian ratchet

Cited by in corpus (5)

• Optimal sampling of dynamical large deviations in two dimensions via tensor networks
• Quantifying Rare Events in Stochastic Reaction-Diffusion Dynamics Using Tensor Networks
• Computing time-periodic steady-state currents via the time evolution of tensor network states
• Stochastic thermodynamic bounds on logical circuit operation
• Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System