A probability-conserving dissipative Schr\"odinger equation

TL;DR

This paper introduces a modified Schrödinger equation that accounts for dissipation while conserving probability, simplifying calculations for systems with decay processes like electronic decay and phonon damping.

Contribution

It presents a novel probability-conserving dissipative Schrödinger equation that reduces computational effort compared to traditional density matrix methods.

Findings

Successfully models electronic decay and phonon damping.

Conserves probability despite energy dissipation.

Reduces computational complexity in dissipative quantum systems.

Abstract

Dissipative effects on a microscopic level are included in the Schr\"odinger equation. When the decay between different local levels as a result of the coupling to a bath, the Schr\"odinger equation no longer conserves energy, but the probability of the states is conserved. The procedure is illustrated with several examples that include direct electronic decay and damping of local phonons (vibrational levels). This method significantly reduces the calculational effort compared to conventional density matrix techniques.