Quantum Stochastic Differential Equation

TL;DR

This paper introduces a semi-classical stochastic model for quantum state collapse, deriving a new stochastic evolution that generalizes the quantum Zeno effect through Poisson-driven state transitions.

Contribution

It presents a novel non-Hamiltonian stochastic model for quantum collapse with a unitary dilation, extending the quantum Zeno effect to a stochastic framework.

Findings

Derived a stochastic evolution for unstable quantum systems.

Established a connection to the quantum Zeno effect.

Provided a unitary dilation of the stochastic dynamics.

Abstract

A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a contraction C. The counting trajectories are assumed to satisfy the Poisson law. A unitary dilation of the concractive stochastic dynamics is found. In particular, in the limit of frequent detection corresponding to the large number limit we obtain the Ito-Schroedinger stochastic unitary evolution for the pure state of unstable quantum system providing a new stochastic version of the quantum Zeno effect.