In this Brief Report we show how the low-temperature thermodynamics of the dissipative motion of an electron in a magnetic field is sensitive to the nature of the spectral density function, $J\left(\omega \right)$, of the quantum heat bath. In all cases of couplings considered here the free energy and the entropy of the cyclotron motion of the electron fall off to zero as power law in conformity with the third law of thermodynamics. The power of the power law however depends on the nature of $J\left(\omega \right)$. We also separately discuss the influence of confinement.

• Received 7 May 2009

DOI:https://doi.org/10.1103/PhysRevE.81.042102