Velocity multistability vs ergodicity breaking in a biased periodic potential
arXiv:2112.03192 · doi:10.3390/e24010098
Abstract
Multistability, i.e. the coexistence of several attractors for a given set of system parameters is one of the most important phenomena occurring in dynamical systems. We consider it in velocity dynamics of a Brownian particle driven by thermal fluctuations and moving in a biased periodic potential. In doing so we focus on the impact of ergodicity - a concept which lies at the core of statistical mechanics. The latter implies that a single trajectory of the system is representative for the whole ensemble and as a consequence the initial conditions of the dynamics are fully forgotten. The ergodicity of the deterministic counterpart is strongly broken and we discuss how the velocity multistability depends on the starting position and velocity of the particle. While for non-zero temperature the ergodicity is in principle restored, in the low temperature regime the velocity dynamics is still affected by initial conditions due to weak ergodicity breaking. For moderate and high temperature the multistability is robust with respect to the choice of the starting position and velocity of the particle.
References in corpus (19)
- Artificial Brownian motors: Controlling transport on the nanoscale
- Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
- Absolute negative mobility induced by thermal equilibrium fluctuations
- Tunable transport with broken space-time symmetries
- Packets of Diffusing Particles Exhibit Universal Exponential Tails
- Observation of negative absolute resistance in a Josephson junction
- GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA
- Tunable mass separation via negative mobility
- Nonergodic Diffusion of Single Atoms in a Periodic Potential
- Coexistence of absolute negative mobility and anomalous diffusion
- Colossal Brownian yet non-Gaussian diffusion induced by nonequilibrium noise
- SQUID ratchet: Statistics of transitions in dynamical localization
- Continuous-time random walk for a particle in a periodic potential
- Diffusion in a biased washboard potential revisited
- Corrections to Einstein's relation for Brownian motion in a tilted periodic potential
- Arcsine Law and Multistable Brownian Dynamics in a Tilted Periodic Potential
- Transition of multi-diffusive states in a biased periodic potential
- Mapping the Arnold web with a GPU-supercomputer
- Negative conductance in driven Josephson junctions