Quantum Dynamics of Complex Hamiltonians

TL;DR

This paper introduces a method using time-dependent normalization states to simplify the analysis of dissipative quantum systems with complex Hamiltonians, demonstrated through damped oscillators and leaky cavities.

Contribution

It presents a novel approach for analyzing non-Hermitian Hamiltonians by employing time-dependent normalization states, enhancing understanding of dissipative quantum dynamics.

Findings

Simplified description of dissipative systems using time-dependent normalization.

Application to damped harmonic oscillator dynamics.

Analysis of radiation in leaky cavity systems.

Abstract

Non hermitian Hamiltonians play an important role in the study of dissipative quantum systems. We show that using states with time dependent normalization can simplify the description of such systems especially in the context of the classical limit. We apply this prescription to study the damped harmonic oscillator system. This is then used to study the problem of radiation in leaky cavity.