Effective Description of the Quantum Damped Harmonic Oscillator: Revisiting the Bateman Dual System

TL;DR

This paper introduces a novel quantization approach for the damped harmonic oscillator using momentous quantum mechanics, providing a robust framework that aligns with Lindblad dynamics and advances the understanding of open quantum systems.

Contribution

It presents a new semiclassical quantization scheme based on an extended Hamiltonian and phase-space variables, enhancing the description of dissipation in quantum mechanics.

Findings

The method aligns well with Lindblad master equations.

It offers a versatile tool for modeling open quantum systems.

The approach demonstrates robustness across different scenarios.

Abstract

In this work, we present a quantization scheme for the damped harmonic oscillator (QDHO) using a framework known as momentous quantum mechanics. Our method relies on a semiclassical dynamical system derived from an extended classical Hamiltonian, where the phase-space variables are given by expectation values of observables and quantum dispersions. The significance of our study lies in its potential to serve as a foundational basis for the effective description of open quantum systems (OQS), and the description of dissipation in quantum mechanics. By employing the Bateman's dual model as the initial classical framework, and undergoing quantization, we demonstrate that our description aligns exceptionally well with the well-established Lindblad master equation. Furthermore, our approach exhibits robustness and broad applicability in the context of OQS, rendering it a versatile and powerful tool for studying various phenomena. We intend to contribute to the advancement of quantum physics by providing an effective means of quantizing the damped harmonic oscillator and shedding light on the behavior of open quantum systems.