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.

6 pages, 3 figures

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
• Dynamical simulations of classical stochastic systems using matrix product states
• Movements of molecular motors: Ratchets, random walks and traffic phenomena
• Mechanical coupling in flashing ratchets
• Finite time large deviations via matrix product states
• Optimal sampling of dynamical large deviations via matrix product states
• 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

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