Classification theorem for principal fibre bundles, Berry`s phase, and exact cycle evolution

Technical Report · Mon Mar 01 00:00:00 EST 1993

DOI:https://doi.org/10.2172/10137684· OSTI ID:10137684

Bohm, A; Boya, L J; Mostafazadeh, A ^[1]; Rudolph, G ^[2]

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1. Texas Univ., Austin, TX (United States). Center for Particle Physics
2. Leipzig Univ. (Germany). Fachbereich Physik

The relation between the two mathematical interpretations of the geometric (Berry) phase is discussed, using either the fibre bundle over parameter space or over projective Hilbert space. It turns out that these two geometric constructions are linked by the classification theorem for vector bundles. The classification theorem provides the means to classify the parameter space bundles for adiabatic evolution and for non-adiabatic cyclic evolution of the statevectors.

• Research Organization: Texas Univ., Austin, TX (United States). Center for Particle Physics
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: FG03-93ER40757
• OSTI ID: 10137684
• Report Number(s): DOE/ER/40757-005; ON: DE93011114; IN: CPP-93-05
• Resource Relation: Other Information: PBD: Mar 1993
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL SPACE
CLASSIFICATION
QUANTUM MECHANICS
SCHROEDINGER EQUATION
HILBERT SPACE
EIGENVALUES
EIGENVECTORS
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CLASSICAL AND QUANTUM MECHANICS