Langevin Equation for a Dissipative Macroscopic Quantum System: Bohmian Theory versus Quantum Mechanics

TL;DR

This paper compares the Langevin equations derived from quantum mechanics and Bohmian theory for a macroscopic quantum oscillator coupled to an environment, highlighting their differences and conditions for equivalence.

Contribution

It analytically derives the Langevin equation from both theories for a macroscopic quantum system and compares their predictions under different vibrational frequency regimes.

Findings

Quantum and Bohmian Langevin equations differ in real conditions.

High vibrational frequency reduces Bohmian to quantum Langevin equation.

Analytical solutions for a macroscopic quantum oscillator coupled to environment.

Abstract

In this study, we solve analytically the Schrodinger equation for a macroscopic quantum oscillator as a central system coupled to a large number of environmental micro-oscillating particles. Then, the Langevin equation is obtained for the system using two approaches: Quantum Mechanics and Bohmian Theory. Our results show that the predictions of the two theories are inherently different in real conditions. Nevertheless, the Langevin equation obtained by Bohmian approach could be reduced to the quantum one, when the vibrational frequency of the central system is high enough compared to the maximum frequency of the environmental particles.