Related papers: Universal Stochastic Equations of Monitored Quantu…
We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic…
We establish a correspondence between the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the…
We discuss the unitary quantum dynamics of the Dicke model (spin and oscillator coupled). A suitable quasiprobabilty representing the quantum state turns out to obey a Fokker-Planck equation, with drift terms representing the underlying…
We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the…
The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are analytical stochastic…
Systems out of equilibrium exhibit a net production of entropy. We study the dynamics of a stochastic system represented by a Master Equation that can be modeled by a Fokker-Planck equation in a coarse-grained, mesoscopic description. We…
Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
While accurate simulations of dense gas flows far from the equilibrium can be achieved by Direct Simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order…
Non-equilibrium stochastic dynamics of several active Brownian systems are modeled in terms of non-linear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for…
We consider three classes of linear non-symmetric Fokker-Planck equations having a unique steady state and establish exponential convergence of solutions towards the steady state with explicit (estimates of) decay rates. First,…
The Fokker-Planck (FP) equation governs the evolution of densities for stochastic dynamics of physical systems, such as the Langevin dynamics and the Lorenz system. This work simulates FP equations through a mean field control (MFC)…
We consider several observers who monitor different parts of the environment of a single quantum system and use their data to deduce its state. We derive a set of conditional stochastic master equations that describe the evolution of the…
Recent experimental and theoretical works have uncovered nontrivial quantum dynamics due to external dissipation. Using an exact numerical method and a renormalization-group-based analytical technique, we theoretically elucidate that…
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…
The Fokker-Planck equation is a partial differential equation which is a key ingredient in many models in physics. This paper aims to obtain a quantum counterpart of Fokker-Planck dynamics, as a means to describing quantum Fokker-Planck…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
We investigate the purification dynamics of a single qubit under continuous in time monitoring. By employing a collisional model framework where the system interacts sequentially with ancillary qubits, we describe the conditioned evolution…
We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response…
We obtain the equations of fluctuating hydrodynamics for many-particle systems whose microscopic units have both translational and rotational motion. The orientational dynamics of each element are studied in terms of the rotational Brownian…