Dynamics of Micro and Nanoscale Systems in the Weak-Memory Regime
arXiv:2411.12595 · doi:10.1103/PhysRevLett.134.037101
Abstract
Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. If the characteristic time scales of accessible and inaccessible degrees of freedom are sharply separated, locality can be restored through the standard Markov approximation. Here, we show that this approach can be rigorously extended to a well-defined weak-memory regime, where the relevant time scales can be of comparable order of magnitude. We derive explicit bounds on the error of the local approximation and a convergent perturbation scheme for its construction. Being applicable to any non-local time evolution equation that is autonomous and linear in the variables of interest, our theory provides a unifying framework for the systematic description of memory effects.
7 pages, 1 figure, accompanied by a longer Research Article
References in corpus (39)
- Non-Markovian dynamics in open quantum systems
- Anomalous transport in the crowded world of biological cells
- Stochastic thermodynamics under coarse-graining
- Universal Lindblad equation for open quantum systems
- Markovian and non-Markovian dynamics in quantum and classical systems
- Completely Positive Post-Markovian Master Equation via a Measurement Approach
- Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation
- Inferring broken detailed balance in the absence of observable currents
- Open quantum system dynamics and the mean force Gibbs state
- Preservation of Positivity by Dynamical Coarse-Graining
- Memory-induced transition from a persistent random walk to circular motion for achiral microswimmers
- Non-Markovianity and negative entropy production rates
- Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
- Completely positive master equation for arbitrary driving and small level spacing
- Multiple-scale stochastic processes: decimation, averaging and beyond
- Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
- Structure of completely positive quantum master equations with memory kernel
- Anisotropic memory effects in confined colloidal diffusion
- Coarse-Graining Can Beat the Rotating Wave Approximation in Quantum Markovian Master Equations
- Phenomenological memory-kernel master equations and time-dependent Markovian processes
- Emergent memory and kinetic hysteresis in strongly driven networks
- Time scales in the dynamics of an interacting quantum dot
- Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
- Post-Markov master equation for the dynamics of open quantum systems
- Systematic Perturbation Theory for Dynamical Coarse-Graining
- Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: phenomenological description and its microscopic foundation
- Manifestations of Projection-Induced Memory: General Theory and the Tilted Single File
- Violation of Local Detailed Balance Despite a Clear Time-Scale Separation
- Time local master equation connecting the Born and Markov approximations
- Nanoscale Quantum Calorimetry with Electronic Temperature Fluctuations
- Operationally Accessible Uncertainty Relations for Thermodynamically Consistent Semi-Markov Processes
- Coarse graining of biochemical systems described by discrete stochastic dynamics
- How quantum evolution with memory is generated in a time-local way
- Relaxation Dynamics of Meso-Reservoirs
- Geometric-Arithmetic Master Equation in Large and Fast Open Quantum Systems
- Stochastic thermodynamics of a quantum dot coupled to a finite-size reservoir
- The connection between time-local and time-nonlocal perturbation expansions
- On the emergence of memory in equilibrium versus non-equilibrium systems
- Dynamics of micro and nanoscale systems in the weak-memory regime: A mathematical framework beyond the Markov approximation