Positive Quantum Brownian Evolution

TL;DR

This paper derives a quantum Brownian evolution equation for a system coupled to an environment, ensuring positivity under certain initial conditions, and applicable to arbitrary potentials.

Contribution

It introduces a non-Lindblad quantum Brownian equation that maintains positivity for a broad class of initial states with arbitrary system potentials.

Findings

Equation preserves positivity for specific initial states

Applicable to arbitrary system potentials

Not of Lindblad form but still physically consistent

Abstract

Using the independent oscillator model with an arbitrary system potential, we derive a quantum Brownian equation assuming a correlated total initial state. Although not of Lindblad form, the equation preserves positivity of the density operator on a restricted set of initial states.