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Quantum adiabatic expansion for dynamics in strong magnetic fields

Technical Report:

Abstract

In description of motion in a uniform strong magnetic field in the presence of external potentials the velocities of the cyclotron rotation and the guiding center coordinates are respectively fast and slow variables. We developed a quantum adiabatic expansion for this situation. In the adiabatic limit we find the effective action of the slow variables in which the energy `surfaces` are local Landau levels depending on the coordinates of the guiding centers. The levels are not equidistant and may exhibit avoided crossings at which the transitions between the levels are concentrated. The action includes additional terms arising from Berry phase. These terms modify the simplectic form of the dynamics of the guiding centers and effect the WKB quantization. As a result it has a form of flux quantization through closed classical orbit of an effective magnetic field which in addition to the original field includes inhomogenous terms arising from the Berry phase and depending on the external potential. We present explicit calculations for the potentials which are weakly inhomogenous on the scale of the magnetic length. The standard strong field projection on a single Landau level is the first term of our expansion. (author).
Publication Date:
May 01, 1992
Product Type:
Technical Report
Report Number:
WIS-PH-92-39
Reference Number:
SCA: 430200; 662110; PA: AIX-24:001737; SN: 93000913185
Resource Relation:
Other Information: PBD: May 1992
Subject:
43 PARTICLE ACCELERATORS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CYCLOTRONS; BEAM DYNAMICS; ADIABATIC APPROXIMATION; CALCULATION METHODS; MAGNETIC FIELDS; MATHEMATICS; QUANTUM MECHANICS; 430200; 662110; BEAM DYNAMICS, FIELD CALCULATIONS, AND ION OPTICS; THEORY OF FIELDS AND STRINGS
OSTI ID:
10108782
Research Organizations:
Weizmann Inst. of Science, Rehovoth (Israel). Dept. of Physics
Country of Origin:
Israel
Language:
English
Other Identifying Numbers:
Other: ON: DE93609388; TRN: IL9204902001737
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
[8] p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Entelis, Anatoli, and Shimon, Levit. Quantum adiabatic expansion for dynamics in strong magnetic fields. Israel: N. p., 1992. Web.
Entelis, Anatoli, & Shimon, Levit. Quantum adiabatic expansion for dynamics in strong magnetic fields. Israel.
Entelis, Anatoli, and Shimon, Levit. 1992. "Quantum adiabatic expansion for dynamics in strong magnetic fields." Israel.
@misc{etde_10108782,
title = {Quantum adiabatic expansion for dynamics in strong magnetic fields}
author = {Entelis, Anatoli, and Shimon, Levit}
abstractNote = {In description of motion in a uniform strong magnetic field in the presence of external potentials the velocities of the cyclotron rotation and the guiding center coordinates are respectively fast and slow variables. We developed a quantum adiabatic expansion for this situation. In the adiabatic limit we find the effective action of the slow variables in which the energy `surfaces` are local Landau levels depending on the coordinates of the guiding centers. The levels are not equidistant and may exhibit avoided crossings at which the transitions between the levels are concentrated. The action includes additional terms arising from Berry phase. These terms modify the simplectic form of the dynamics of the guiding centers and effect the WKB quantization. As a result it has a form of flux quantization through closed classical orbit of an effective magnetic field which in addition to the original field includes inhomogenous terms arising from the Berry phase and depending on the external potential. We present explicit calculations for the potentials which are weakly inhomogenous on the scale of the magnetic length. The standard strong field projection on a single Landau level is the first term of our expansion. (author).}
place = {Israel}
year = {1992}
month = {May}
}