Quantum mechanics from stochastic processes

Stochastic Processes and Quantum Mechanics

Exotic Stochastic Processes from Complex Quantum Environments

Stochastic processes are shown to emerge from the time evolution of complex quantum systems. Using parametric, banded random matrix ensembles to describe a quantum chaotic environment, we show that the dynamical evolution of a particle coupled to such environments displays a variety of stochastic behaviors, ranging from turbulent diffusion to Lévy processes and Brownian motion. Dissipation and ...

Momentum in stochastic quantum mechanics

Momentum is analyzed as a random variable in stochastic quantum mechanics. Arbitrary potential energy functions are considered. The oscillator is presented as an example.

Contribution from stochastic electrodynamics to the understanding of quantum mechanics

During the last decades there has been a relatively extensive attempt to develop the theory of stochastic electrodynamics (sed) with a view to establishing it as the foundation for quantum mechanics. The theory had several important successes, but failed when applied to the study of particles subject to nonlinear forces. An analysis of the failure showed that its reasons are not to be ascribed ...

Quantum Statistical Mechanics. II. Stochastic Schrödinger Equation

The stochastic dissipative Schrödinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the density matrix, which is an explicit, stochastic form of the Lindblad master equation. A quantum fluctuation-dissipation theorem is also derived. The time co...