Nonadiabatic Berry's phase for a spin particle in a rotating magnetic field

Journal Article · Thu Nov 01 04:00:00 EST 1990 · Physical Review, A; (USA)

DOI:https://doi.org/10.1103/PhysRevA.42.5107· OSTI ID:6040246

Wang, S ^[1]

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1. Center of Theoretical Physics, Chinese Center of Advanced Science Technology (World Laboratory), Beijing (China) Department of Modern Physics, Lanzhou University, Lanzhou (People'sRepublic of China) Nuclear Science Division, Lawrence Berkeley Laboratory, University of California, Berkeley, CA (USA)

The time-dependent Schroedinger equation for a spin particle in a rotating magnetic field is solved analytically by the cranking method, and the exact solutions are employed to study the nonadiabatic Berry's phase. An alternative expression for Berry's phase is given, which shows that Berry's phase is related to the expectation value of spin along the rotating axis and gives Berry's phase a physical explanation besides its gauge geometric interpretation. This expression also presents a simple algorithm for calculating the nonadiabatic Berry's phase for Hamiltonians that are nonlinear functions of the SU(2) generators. It is shown that nonadiabaticity alters the time evolution ray and in turn changes its Berry's phase. For the SU(2) dynamical group, the nonadiabatic effect on Berry's phase manifests itself as spin alignment (a phenomenon in nuclear physics), and spin-alignment quantization (observed recently in high-spin nuclear physics) is related to Berry's-phase quantization.

• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6040246
• Journal Information: Physical Review, A; (USA), Journal Name: Physical Review, A; (USA) Vol. 42:9; ISSN 1050-2947; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
LIE GROUPS
MAGNETIC FIELDS
MECHANICS
ORIENTATION
PARTIAL DIFFERENTIAL EQUATIONS
PHASE STUDIES
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SPIN ORIENTATION
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
WAVE EQUATIONS