Related papers: Universal Stochastic Equations of Monitored Quantu…
We study the discrete Fokker-Planck equation associated with the mean-field dynamics of a particle system called the dispersion process. For different regimes of the average number of particles per site (denoted by $\mu > 0$), we establish…
Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin…
From the underlying Master equations we derive one-dimensional stochastic processes that describe generalized ensemble simulations as well as tempering (simulated and parallel) simulations. The representations obtained are either in the…
A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence towards equilibrium of mean-field systems due to finite-N effects. The thermalization process involves notably…
Dynamics of complex systems is often hierarchically organized on different time scales. To understand the physics of such hierarchy, here Brownian motion of a particle moving through a fluctuating medium with slowly varying temperature is…
Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference…
We study the quantum dynamics generated by a non-Hermitian Hamiltonian subject to stochastic perturbations in its anti-Hermitian part, describing fluctuating gains and losses. The dynamics averaged over the noise is described by an…
The interplay of unitary evolution and local measurements in many-body systems gives rise to a stochastic state evolution and to measurement-induced phase transitions in the pure state entanglement. In realistic settings, however, this…
In this paper, we study the numerical schemes for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion. The main challenges of the numerical schemes come from the…
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behaviour and for its possible application in near-term quantum technologies. However, understanding these…
We develop a geometric formulation of stochastic dynamics in which noise, diffusion, path probabilities, fluctuation theorems, and entropy production arise from the intrinsic geometry of an evolving manifold rather than from externally…
Results are presented for the quench dynamics of a clean and interacting electron system, where the quench involves varying the strength of the attractive interaction along arbitrary quench trajectories. The initial state before the quench…
We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective…
The phase space dynamics of dissipative quantum systems in strongly condensed phase is considered. Based on the exact path integral approach it is shown that the Wigner transform of the reduced density matrix obeys a time evolution equation…
By using a condition of average trace preservation we derive a general class of non-Markovian Gaussian diffusive unravelings [L. Diosi and L. Ferialdi, Phys. Rev. Lett. \textbf{113}, 200403 (2014)], here valid for arbitrary non-Hermitian…
At lower energies, the resonances in scattering experiments are often isolated. In quantum chaotic many-body, disordered or generically stochastic systems, the resonances overlap at larger energies. Eventually, the Ericson regime is reached…
We uncover emergent universality arising in the equilibration dynamics of multimode continuous-variable systems. Specifically, we study the ensemble of pure states supported on a small subsystem of a few modes, generated by Gaussian…
A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing…