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International Journal of Theoretical Physics

Relativistic Bosons in Time-Harmonic Electric Fields

Ovidiu Buhucianu, Marina–Aura Dariescu, Ciprian Dariescu

Published Sep 9, 2011• 10 citations
Publisher
DOI
10.1007/s10773-011-0931-7

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The present work is studying the behavior of relativistic fermions in parallel electric and magnetic fields, oriented along Oz. As expected, in the particular case of static field intensities, the temporal part of the wave function is expressed in terms of the parabolic cylinder functions. When the static electric field is replaced by a time-harmonic one, the ultra-relativistic particles are described by a Mathieu-type equation, of purely imaginary parameter. Below the first branching point, which imposes a maximum value for the electric intensity, one may use a series expansion of the Mathieu's functions to derive the corresponding wave functions and the conserved current density components. Finally, we obtain a nontrivial quantization law of the longitudinal momentum, pz.
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.