On the standard quantum Brownian equation and an associated class of non-autonomous master equations

TL;DR

This paper investigates the limitations of the standard quantum Brownian equation in maintaining positivity over time and proposes exact solutions for a class of non-autonomous master equations to ensure physical consistency.

Contribution

It introduces exact operator solutions for non-autonomous master equations and derives conditions to preserve positivity, addressing issues in the standard quantum Brownian equation.

Findings

Standard QBE can violate positivity at high frequencies and long times.

Exact solutions help identify conditions for positivity.

Improves understanding of non-autonomous quantum master equations.

Abstract

It is shown that the standard quantum Brownian equation (QBE) can violate positivity not only past the thermal correlation time, but at arbitrarily long times at high system frequencies. In an effort to improve the standard QBE, exact operator solutions are provided for a class of non-autonomous master equations. These exact solutions are used to derive sufficient positivity conditions for the coefficients of the master equations.