相关论文: From Stochastic Differential Equations to Quantum …
Using stochastic quantization method we derive gauge-invariant equations, connecting multilocal vacuum correlators of nonperturbative field configurations immersed into the quantum background. Three alternative methods of stochastic…
Physics in (canonical) quantum gravity needs to be manifestly diffeomorphism-invariant. Consequently, physical observables need to be formulated in terms of manifestly diffeomorphism-invariant operators, which are necessarily composite.…
A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison to…
A natural formulation of the theory of quantum measurements in continuous time is based on quantum stochastic differential equations (Hudson-Parthasarathy equations). However, such a theory was developed only in the case of…
In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has variable coefficients that may depend on the temporal and spatial…
A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…
We investigate quantum systems perturbed by noise in the form of repeated interactions between the system and the environment. As the number of interactions (aka time steps) tends to infinity, we show, following the works by Pellegrini,…
Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is…
We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the…
In this note we review recent results on existence and uniqueness of solutions of infinite-dimensional stochastic differential equations describing interacting Brownian motions on $\R^d$.
The issue of non-locality in quantum mechanics can potentially be resolved by considering relativistically covariant diffusion in four-dimensional spacetime. Stochastic particles described by the Klein-Gordon equation are shown to undergo a…
This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the…
Differential $p$-forms and $q$-vector fields with constant coefficients are studied. Differential $p$-forms of degrees $p=1,2,n-1,n$ with constant coefficients on a smooth $n$-dimensional manifold $M$ are characterized. In the contravariant…
A model-independent, locally generally covariant formulation of quantum field theory over four-dimensional, globally hyperbolic spacetimes will be given which generalizes similar, previous approaches. Here, a generally covariant quantum…
Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the large-N limit. These equations are treated both in the coordinate and momentum representations. In…
Quantum field theory (QFT) on non-stationary spacetimes is well understood from the side of the algebra of observables. The state space, however, is largely unexplored, due to the non-existence of distinguished states (vacuum, scattering…
In this report we discuss some results of non--commutative (quantum) probability theory relating the various notions of statistical independence and the associated quantum central limit theorems to different aspects of mathematics and…
We study mean field stochastic differential equations with a diffusion coefficient that depends on the distribution function of the unknown process in a discontinuous manner, which is a type of distribution dependent regime switching. To…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…