Geometric Phase Curvature Statistics

The probability distribution of the magnitude C of the curvature 2-form, that underlies the quantum geometric phase and the reaction force of geometric magnetism, is calculated for an ensemble of three-parameter Hamiltonians represented by the gaussian unitary ensemble of N  ×  N matrices. The distr...

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Bibliographic Details
Published inJournal of statistical physics Vol. 180; no. 1-6; pp. 297 - 303
Main Authors Berry, M. V., Shukla, Pragya
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2020
Springer
Springer Nature B.V
Subjects
Curvature
Magnetism
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Statistics
Theoretical
Degeneracies
2-form
Random-matrix
Quantum statistics
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Summary:The probability distribution of the magnitude C of the curvature 2-form, that underlies the quantum geometric phase and the reaction force of geometric magnetism, is calculated for an ensemble of three-parameter Hamiltonians represented by the gaussian unitary ensemble of N  ×  N matrices. The distributions are determined analytically: exactly for N  = 2 and approximately for N  ≥ 3, and compared with simulations. The distributions decay asymptotically as 1/ C 5/2 ; this is a consequence of the codimension of energy-level degeneracies in the ensemble.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-019-02400-6