Thermodynamics of a quantum dissipative charged magneto-oscillator

Quantum dissipative effect on the thermodynamics of an electron in the combined presence of a parabolic potential and a uniform (and homogeneous) magnetic field, is investigated here. Starting from the microscopic system plus bath model, we explicitly derive the thermodynamic properties using the reduced partition function of the system which is calculated using the imaginary time path integral method. The quantum heat bath we consider here is a structured heat bath whose spectral density corresponds to a structured thermal harmonic noise. All the statistical thermodynamic functions calculated do reconcile with the requirements of the fundamental axioms of physics. In particular, the specific heat and the entropy vanishes as the temperature approaches its absolute zero value, a necessity of the third law of thermodynamics. Moreover the specific heat satisfies classical equipartition theorem at high temperatures. The coefficients of the leading temperature dependent terms of the thermodynamic quantities depend only on the damping constant but not on other parameters of the bath spectral density, which is similar to the analysis based on the Drude bath spectral density. Our study facilitates the physics of small quantum systems, which are always in contact with some environments, at very low temperatures.