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Physical Review A

Angular momentum of open quantum systems in external magnetic field

Sh. A. Kalandarov, Ilkhom B. Abdurakhmanov, Z. Kanokov, G. G. Adamian, N. V. Antonenko

Published Jun 17, 2019• 12 citations
Publisher

Abstract

The non-Markovian dynamics of a charged harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in external uniform magnetic field. The analytical expression is derived for the asymptotic angular momentum. The orbital diamagnetism of quantum system in a dissipative environment is studied.
DOI
10.1103/physreva.99.062109

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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.
The influence of an external magnetic field on the non-Markovian dynamics of an open two-dimensional quantum system is investigated. The fluctuations of collective coordinate and momentum and transport coefficients are studied for a charged harmonic oscillator linearly coupled to a neutral bosonic heat bath. It is shown that the dissipation of collective energy slows down with increasing strength of the external magnetic field. The role of magnetic field in the diffusion processes is illustrated by several examples.
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We obtain the quantum Langevin equation (QLE) of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a quantum heat bath through momentum variables. The bath is modeled as a collection of independent quantum harmonic oscillators. The QLE involves a random force which does not depend on the magnetic field, and a quantum-generalized classical Lorentz force. These features are also present in the QLE for the case of particle-bath coupling through coordinate variables. However, significant differences are also observed. For example, the mean force in the QLE is characterized by a memory function that depends explicitly on the magnetic field. The random force has a modified form with correlation and commutator different from those in the case of coordinate-coordinate coupling. Moreover, the coupling constants, in addition to appearing in the random force and in the mean force, also renormalize the inertial term and the harmonic potential term in the QLE.
In this work, we consider the dissipative dynamics of a quantum Brownian magneto-oscillator in contact with different types of environment at zero temperature as well as at high temperatures. We derive closed-form expressions of decay rate and heating rate for the magneto-oscillator in contact with Ohmic, sub-Ohmic, and super-Ohmic environments with non-Markovian characteristics. The present study is useful in determining the relationship between the thermalization dynamics of a magneto-oscillator and different forms of environmental spectrum and external magnetic field. Although our study is limited to the short-time (Non-Markovian) and long-time (Markovian) regimes, it manifests that one can actually tune the effective coupling of the system reservoir either by tuning oscillator frequency through reservoir engineering techniques or changing external magnetic field. Thus the present work establishes the essential role of non-Markovian dissipation and the crucial role of magnetic field in the environment induced decoherence and decay processes of the dissipative magneto-oscillator.
We obtain the generalized susceptibility for the motion of a charged oscillator in a harmonic potential well in the presence of a uniform external magnetic field, and linearly coupled to a heat bath, by using the generalized quantum Langevin equation we obtained in an earlier paper. The result is then used to calculate the autocorrelation function of the position operator of the oscillator by the fluctuation-dissipation theorem. The free energy of the oscillator is then obtained in terms of the determinant of the susceptibility matrix. Applications are made to two types of heat baths: the Ohmic case and the case of blackbody radiation. As a special case (no heat bath) of our general formalism, a well-known eigenspectrum result is obtained but in a simple and rather novel fashion.