Related papers: Memory corrections to Markovian Langevin dynamics
This work develops a comprehensive mathematical theory for a class of stochastic processes whose local regularity adapts dynamically in response to their own state. We first introduce and rigorously analyze a time-varying fractional…
We analyze non-Markovian memory effects displayed by the quantum Brownian motion modelled as quantum harmonic oscillators coupled to a bath consisting of harmonic oscillators. We study the time evolution of fidelity, Petz-R\'enyi relative…
Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics.…
Stochastic models of varying complexity have been proposed to describe the dispersion of particles in turbulent flows, from simple Brownian motion to complex temporally and spatially correlated models. A method is needed to compare…
We investigate continuous quantum error correction, comparing performance under a Markovian error model to two distinct non-Markovian models. The first non-Markovian model involves an interaction Hamiltonian between the system and an…
Investigations of quantum and mesoscopic thermodynamics force one to answer two fundamental questions associated with the foundations of statistical mechanics: (i) how does macroscopic irreversibility emerge from microscopic reversibility?…
We derive a non-Markovian theory for waiting time distributions of consecutive single electron transfer events. The presented microscopic Pauli rate equation formalism couples the open electrodes to the many-body system, allowing to take…
We statistically examine long time sequences of Brownian motion for a nonequilibrium version of the Rayleigh piston model and confirm that the third cumulant of a long-time displacement for the nonequilibrium Brownian motion linearly…
Realistic quantum mechanical systems are always exposed to an external environment. The presence of the environment often gives rise to a Markovian process in which the system loses information to its surroundings. However, many quantum…
Brownian dynamics is a popular fine-grained method for simulating systems of interacting particles, such as chemical reactions. Though the method is simple to simulate, it is generally assumed that the dynamics is impossible to solve…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
Subdiffusion is a hallmark of complex systems, ranging from protein folding to transport in viscoelastic media. However, despite its pervasiveness, the mechanistic origins of subdiffusion remain contested. Here, we analyze both Markovian…
Simple, controllable models play an important role to learn how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class…
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex…
Brownian motion is the only random process which is Gaussian, stationary and Markovian. Dropping the Markovian property, i.e. allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst…
Recent work has addressed the problem of inferring Langevin dynamics from data. In this work, we address the problem of relating terms in the Langevin equation to statistical properties, such as moments of the probability density function…
We introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig projection techniques and use it to derive a Generalized Langevin Equation (GLE) for a general interacting many-body system. The resulting…
Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. However, recent technological advances mean we have control over systems at scales where memory effects…
We explore in a rigorous manner the intuitive connection between the non-Markovianity of the evolution of an open quantum system and the performance of the system as a quantum memory. Using the paradigmatic case of a two-level open quantum…
The presence of pairing correlations within the time-dependent density functional theory (TDDFT) extension to superfluid systems, is tantamount to the presence of a quantum collision integral in the evolution equations, which leads to an…