相关论文: Star-unitary transformations. From dynamics to irr…

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us…

This paper is concerned with the Fokker-Planck (FP) description of classical stochastic systems with discrete time delay. The non-Markovian character of the corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy of…

This thesis is dedicated to the study of stochastic processes; non-deterministic physical phenomena that can be well described by classical physics. The stochastic processes we are interested in are akin to Brownian Motion and can be…

The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of…

We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…

Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…

We consider a simple model of lossless interaction between a two-level single atom and a standing-wave single-mode laser field which creates a one-dimensional optical lattice. Internal dynamics of the atom is governed by the laser field…

Infinitesimal volumes stretch and contract as they coevolve with classical phase space trajectories according to linearized dynamics. Unless these tangent-space dynamics are modified, chaotic evolution causes the volume spanned by evolving…

A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of…

We compute the particle creation of a harmonic oscillator using the classical stochastic method. This recently constructed method reproduces all the vacuum expectation values in quantum theory. We prepare the vacuum state at the initial…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

For the Langevin model of the dynamics of a Brownian particle with perturbations orthogonal to its current velocity, in a regime when the particle velocity modulus becomes constant, an equation for the characteristic function $\psi…

We present a numerical method to compute non-equilibrium memory kernels based on experimental data or molecular dynamics simulations. The procedure uses a recasting of the non-stationary generalized Langevin equation, in which we expand the…

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon…

Particles and fields are standard components in numerical simulations like transport simulations in nuclear physics and have very well understood dynamics. Still, a common problem is the interaction between particles and fields due to their…

We consider stochastic differential equations, obtained by adding weak Gaussian white noise to ordinary differential equations admitting $N$ asymptotically stable periodic orbits. We construct a discrete-time, continuous-space Markov chain,…

We consider a model of Non-Brownian self-propelled particles with anti-alignment interactions where particles try to avoid each other by attempting to turn into opposite directions. The particles undergo apparent Brownian motion, even…

We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for…

A number of random processes in various fields of science is described by phenomenological equations containing a stochastic force, the best known example being the Langevin equation (LE) for the Brownian motion (BM) of particles. Long ago…

We study a fairly general class of time-homogeneous stochastic evolutions driven by noises that are not white in time. As a consequence, the resulting processes do not have the Markov property. In this setting, we obtain constructive…