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A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids

1
Institute of Physics, University of Brasilia, P.O. Box 04455, Brasília 70919-970, DF, Brazil
2
International Center for Physics, University of Brasilia, Brasilia 70910-900, DF, Brazil
3
Instituto Federal de Brasília, Campus Estrutural, Brasília 71255-200, DF, Brazil
*
Author to whom correspondence should be addressed.
Quantum Reports 2019, 1(2), 193-207; https://doi.org/10.3390/quantum1020017
Received: 12 September 2019 / Revised: 20 October 2019 / Accepted: 22 October 2019 / Published: 28 October 2019
We consider a quantum charged particle moving in the x y plane under the action of a time-dependent magnetic field described by means of the linear vector potential of the form A = B ( t ) y ( 1 + β ) , x ( 1 β ) / 2 . Such potentials with β 0 exist inside infinite solenoids with non-circular cross sections. The systems with different values of β are not equivalent for nonstationary magnetic fields or time-dependent parameters β ( t ) , due to different structures of induced electric fields. Using the approximation of the stepwise variations of parameters, we obtain explicit formulas describing the change of the mean energy and magnetic moment. The generation of squeezing with respect to the relative and guiding center coordinates is also studied. The change of magnetic moment can be twice bigger for the Landau gauge than for the circular gauge, and this change can happen without any change of the angular momentum. A strong amplification of the magnetic moment can happen even for rapidly decreasing magnetic fields. View Full-Text
Keywords: circular gauge; Landau gauge; arbitrary linear gauge; stepwise variation; center-of-orbit coordinates; relative coordinates; elliptic and hyperbolic solenoids; angular momentum; magnetic moment; squeezing circular gauge; Landau gauge; arbitrary linear gauge; stepwise variation; center-of-orbit coordinates; relative coordinates; elliptic and hyperbolic solenoids; angular momentum; magnetic moment; squeezing
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Dodonov, V.V.; Horovits, M.B. A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids. Quantum Reports 2019, 1, 193-207.

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