相关论文: Stochastic Quantisation and Non-Equilibrium Statis…

The quantum mechanical transition amplitudes are calculated perturbatively on the basis of the stochastic quantization method of Parisi and Wu. It is shown that the stochastic scheme reproduces the ordinary result for the amplitude and…

We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…

We study strictly parabolic stochastic partial differential equations on $\R^d$, $d\ge 1$, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give…

We present a new approach to stochastic quantization \`a la Parisi-Wu with a discrete fictitious time. The noise average is modified by weights, which results in the equivalence in the large time limit to the correlation function of the…

The concept of stochastic resonance in nonlinear dynamics is applied to interpret the capacity of noisy quantum channels. The two-Pauli channel is used to illustrate the idea. The fidelity of the channel is also considered. Noise…

We have analyzed the phenomenon of stochastic resonance in a system driven by non Gaussian noises. We have considered both white and colored noises. In the latter case we have obtained a consistent Markovian approximation that enables us to…

A white noise quantum stochastic calculus is developped using classical measure theory as mathematical tool. Wick's and Ito's theorems have been established. The simplest quantum stochastic differential equation has been solved, unicity and…

The stochastic quantization scheme proposed by Parisi and Wu in 1981 is known to have differences from conventional quantum field theory in higher orders. It has been suggested that some of these new features might give rise to a mechanism…

The numerical stochastic perturbation method based on Parisi-Wu quantisation is applied to a suite of simple models to test its validity at high orders. Large deviations from normal distribution for the basic estimators are systematically…

In the chaotic quantization approach one replaces the Gaussian white noise of the Parisi-Wu approach of stochastic quantization by a deterministic chaotic process on a very small scale. We consider suitable coupled chaotic noise processes…

A parameter estimation problem is considered for a one-dimensional stochastic wave equation driven by additive space-time Gaussian white noise. The estimator is of spectral type and utilizes a finite number of the spatial Fourier…

In many applications, the common assumption that a driving noise process affecting a system is independent or Markovian may not be realistic, but the noise process may be assumed to be stationary. To study such problems, this paper…

This paper considers uncertainty quantification in systems perturbed by stochastic disturbances, in particular, Gaussian white noise. The main focus of this work is on describing the time evolution of statistical moments of certain…

We show that a basic quantum white noise process formally reproduces quantum stochastic calculus when the appropriate normal / chronological orderings are prescribed. By normal ordering techniques for integral equations and a generalization…

We extend the stochastic quantization method recently developed by Haba and Kleinert to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization…

Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical…

As commonly understood, the noise spectroscopy problem---characterizing the statistical properties of a noise process affecting a quantum system by measuring its response---is ill-posed. Ad-hoc solutions assume implicit structure which is…

The basic aspects of the Hudson-Parthasarathy quantum stochastic calculus and of the Accardi-Fagnola-Quaegebeur representation free stochastic calculus are presented. The basic features of the stochastic calculus for the square of white…

This brief paper proposes an uncertainty quantification method for the periodic steady-state (PSS) analysis with both Gaussian and non-Gaussian variations. Our stochastic testing formulation for the PSS problem provides superior efficiency…

Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state…