Physical review. E

Two-dimensional open quantum system in dissipative bosonic heat bath, external magnetic field, and two time-dependent electric fields

E. Kh. Alpomishev, G. G. Adamian, N. V. Antonenko

Published Apr 9, 2024• 4 citations

Abstract

Non-Markovian dynamics of a charged particle in a two-dimensional harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in an external uniform magnetic field and two perpendicular time-dependent electric fields. The analytical expressions for the time-dependent and asymptotic angular momentum are derived for the Markovian and non-Markovian dynamics. The dependence of the angular momentum on the frequency of the electric field, cyclotron frequency, collective frequency, and anisotropy of the heat bath is studied. The angular momentum (or magnetization) of a charged particle can be ruled by varying the frequency of the electric field.

DOI: 10.1103/physreve.109.044125

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Publisher

Abstract

DOI: 10.1103/physreve.109.044125

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{\mathcal{E}}_{k}

and

{\mathcal{E}}_{p}

denote the average kinetic and potential energies of individual thermostat oscillators. The net averaging is twofold; the first one is over the Gibbs canonical state for the thermostat, giving

{\mathcal{E}}_{k}

and

{\mathcal{E}}_{p}

, and the second one, denoted by $\ensuremath{\langle}\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\rangle}$, is over the frequencies $\ensuremath{\omega}$ of the bath oscillators which contribute to

{E}_{k}

and

{E}_{p}

according to probability distributions ${\mathcal{P}}_{k}(\ensuremath{\omega})$ and ${\mathcal{P}}_{p}(\ensuremath{\omega})$, respectively. The relationship of the present quantum version of the equipartition theorem with that of the fluctuation-dissipation theorem (within the linear-response theory framework) is also explored. Further, we investigate the influence of the external magnetic field and the effect of different dissipation processes through Gaussian decay and Drude and radiation bath spectral density functions on the typical properties of ${\mathcal{P}}_{k}(\ensuremath{\omega})$ and ${\mathcal{P}}_{p}(\ensuremath{\omega})$. Finally, the role of system-bath coupling strength and the memory effect is analyzed in the context of average kinetic and potential energies of the dissipative charged magneto-oscillator.

T \rightarrow 0

exhibit a power law decay with the coefficients of the power laws being completely different for the two masses, affecting the overall dynamics of the coupled system. The effect of the bath-induced force on mass m1 mediated by the interaction of m2 with the common heat bath is studied and the results are highlighted in the presence of an external magnetic field. It is shown that the effect of cyclotron frequency increases the correlation functions at an instant of time, lowering the rate of temporal decay of the correlation functions. The results in the absence of a magnetic field are also presented, which are extremely important for investigating the movements of the atoms in protein molecules at low temperatures.