Control of quantum thermodynamic behaviour of a charged magneto oscillator with momentum dissipation

In this work, we expose the role of environment, confinement and external magnetic field ($B$) in determining the low temperature thermodynamic behaviour in the context of cyclotron motion of a charged oscillator with anomalous dissipative coupling involving the momentum instead of the much studied coordinate coupling. Explicit expressions for different quantum thermodynamic functions (QTF) are obtained at low temperatures for different quantum heat bath characterized by spectral density function, $\mu(\omega)$. The power law fall of different QTF are in conformity with third law of thermodynamics. But, the sensitiveness of decay i.e. the power of the power law decay explicitly depends on $\mu(\omega)$. We also separately discuss the influence of confinement and magnetic field on the low temperature behavior of different QTF. In this process we demonstrate how to control low temperature behaviour of anomalous dissipative quantum systems by varying confining length $a$, $B$ and the temperature $T$. Momentum dissipation reduces effective mass of the system and we also discuss its effect on different QTF at low temperatures.