Related papers: The Schroedinger Problem, Levy Processes Noise in …
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
We discuss the so-called Schr{\"o}dinger problem of deducing the microscopic (basically stochastic) evolution that is consistent with given positive boundary probability densities for a process covering a finite fixed time interval. The…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
Probabilistic solutions of the so called Schr\"{o}dinger boundary data problem provide for a unique Markovian interpolation between any two strictly positive probability densities designed to form the input-output statistics data for the…
By departing from the previous attempt (Phys. Rev. {\bf E 51}, 4114, (1995)) we give a detailed construction of conditional and perturbed Markov processes, under the assumption that the Cauchy law of probability replaces the Gaussian law…
We show that the Schr\"{o}dinger-Newton equation, which describes the nonlinear time evolution of self-gravitating quantum matter, can be made compatible with the no-signaling requirement by elevating it to a stochastic differential…
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the…
This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by L\'evy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then,…
The changes that quantum states undergo during measurement are both probabilistic and nonlocal. These two characteristics complement one another to insure compatibility with relativity and maintain conservation laws. The probabilistic…
The present contribution is based on the assumption that the probabilistic character of quantum mechanics does not originate from uncertainties caused by the process of measurement or observation, but rather reflects the presence of…
Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time…
The Schr\"odinger-Newton model describes self-gravitating quantum particles, and it is often cited to explain the gravitational collapse of the wave function and the localization of macroscopic objects. However, this model is completely…
In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
This paper investigates the long-time dynamics of solutions for an abstract nonlinear stochastic hydrodynamic-type equation driven by multiplicative L\'{e}vy noise. The framework encompasses several key hydrodynamical models, including the…
Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild…
In this thesis we consider primarily the dynamics of quantum systems subjected to continuous observation. In the Schr\"{o}dinger picture the evolution of a continuously monitored quantum system, referred to as a `quantum trajectory', may be…
We establish the existence and uniqueness of solutions to an abstract nonlinear equation driven by a multiplicative noise of L\'evy type, which covers many hydrodynamical models including 2D Navier-Stokes equations, 2D MHD equations, the 2D…
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…