Related papers: Normalized Gaussian Path Integrals
We investigate the bifurcation phenomena for stochastic systems with multiplicative Gaussian noise, by examining qualitative changes in mean phase portraits. Starting from the Fokker-Planck equation for the probability density function of…
An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with…
The most probable transition paths of a stochastic dynamical system are the global minimizers of the Onsager-Machlup action functional and can be described by a necessary but not sufficient condition, the Euler-Lagrange equation (a…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
This paper proposes a numerical method using neural networks to solve the path integral problem in quantum mechanics for arbitrary potentials. The method is based on a radial basis function expansion of the interaction term that appears in…
We study the semiclassical Ehrenfest trajectories in open quantum systems. We first derive in explicit form the Fokker-Planck equation that governs the time evolution of the mixing measure for a Gaussian mixture. Then, we embed the…
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels…
We present a new formulation for the emergence of classical dynamics in a quantum world by considering a path integral approach that also incorporates continuous measurements. Our program is conceptually different from the decoherence…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
In this paper, we consider stochastic Schroedinger equations with two-dimensional white noise. Such equations are used to describe the evolution of an open quantum system undergoing a process of continuous measurement. Representations are…
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
After a short review of recent progresses in 2D Euler equations with random initial conditions and noise, some of the recent results are improved by exploiting a priori estimates on the associated infinite dimensional Fokker-Planck…
The existence of an observer independent minimum length scale can lead to the modification of the Heisenberg uncertainty principle to the generalized uncertainty principle. This in turn would be responsible for the modification of the…
We address the calculation of transition probabilities in multiplicative noise stochastic differential equations using a path integral approach. We show the equivalence between the conditional probability and the propagator of a quantum…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
We present a path integral formalism to compute potentials for nonequilibrium steady states, reached by a multiplicative stochastic dynamics. We develop a weak-noise expansion, which allows the explicit evaluation of the potential in…
This paper considers the Fokker-Planck equation and path integral formulation of the fractional Ornstein-Uhlenbeck process parametrized by two indices. The effective Fokker-Planck equation of this process is derived from the associated…
For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…
Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is…