Orthogonal jumps of wavefunction in white-noise potentials

TL;DR

This paper models the evolution of a quantum particle in white-noise potentials, introducing a stochastic process with orthogonal jumps in the wavefunction, and derives a related master equation.

Contribution

It presents a novel stochastic process with orthogonal jumps in the wavefunction for quantum particles in white-noise potentials, linking it to existing quantum noise theories.

Findings

Derived a master equation for the density matrix.

Proposed a nonlinear Schrödinger equation with orthogonal jumps.

Connected the model to traditional quantum noise and damping theories.

Abstract

We investigate the evolution of the quantum state for a free particle placed into a random external potential of white-noise type. The master equation for the density matrix is derived by means of path integral method. We propose an equivalent stochastic process where the wavefunction satisfies a nonlinear Schr\"odinger equation except for random moments at which it shows orthogonal jumps. The relation of our work to the usual theory of quantum noise and damping is briefly discussed.