Quantum Dynamics of a Dissipative and Confined Cyclotron Motion

Abstract

We study the dissipative dynamics of a charged oscillator in a magnetic field by coupling (a la Caldeira and Leggett) it to a heat bath consisting of non-interacting harmonic oscillators. We derive here the auto-correlation functions of the position and momentum and study its behavior at various limiting situations. The equilibrium (steady state) dispersions of position and momentum are obtained from their respective autocorrelation functions. We analyse the equilibrium position and momentum dispersions at low and high temperatures for both low and high magnetic field strengths. We obtain the classical diffusive behavior (at long times) as well as the equilibrium momentum dispersion of the free quantum charged particle in a magnetic field, in the limit of vanishing oscillator potential ω_0 . We establish the relations between the reduced partition function and the equilibrium dispersions of the dissipative and confined cyclotron problem.

Accepted for publication in Physica A: Statistical Mechanics and its Applications

References in corpus (3)

• Finite quantum dissipation: the challenge of obtaining specific heat
• Low temperature Thermodynamics in the Context of Dissipative Diamagnetism
• Landau-Drude Diamagnetism: Fluctuation, Dissipation and Decoherence

Cited by in corpus (4)

• Quantum Brownian motion under generalized position measurements: A converse Zeno scenario
• Thermodynamic anomalies in the presence of dissipation: from the free particle to the harmonic oscillator
• Exact solution of the position-dependent mass Schrödinger equation with the completely positive oscillator-shaped quantum well potential
• Long Time Tails in Quantum Brownian Motion of a charged particle in a magnetic field