Classification theorem for principal fibre bundles, Berry's phase, and exact cycle evolution
- Texas Univ., Austin, TX (United States). Center for Particle Physics
- 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; USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG03-93ER40757
- OSTI ID:
- 6615566
- Report Number(s):
- DOE/ER/40757-005; ON: DE93011114
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL SPACE
CLASSIFICATION
QUANTUM MECHANICS
EIGENVALUES
EIGENVECTORS
HILBERT SPACE
SCHROEDINGER EQUATION
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
WAVE EQUATIONS
661100* - Classical & Quantum Mechanics- (1992-)
GENERAL PHYSICS
MATHEMATICAL SPACE
CLASSIFICATION
QUANTUM MECHANICS
EIGENVALUES
EIGENVECTORS
HILBERT SPACE
SCHROEDINGER EQUATION
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
WAVE EQUATIONS
661100* - Classical & Quantum Mechanics- (1992-)