Quantum dynamics near a classical separatrix

Journal Article · Thu Apr 01 04:00:00 EST 1993 · Physical Review A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.47.2496· OSTI ID:6711229

Cary, J R; Rusu, P ^[1]

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1. Department of Physics, University of Colorado, Boulder, Colorado 80309-0390 (United States)

Quantum-mechanical evolution in a slowly varying double-well potential is analyzed in the semiclassical limit to determine the transition probability due to loss of adiabatic invariance of states having energy close to that of a separatrix in the equivalent classical system. Transformation to the rotating-axis basis reduces the problem to the integration of a set of coupled differential equations. In the adiabatic limit the integration is carried out by the method of successive approximations. For adiabatic parameter [epsilon] of the order of the inverse, 1/[ital N], of the number of quantum states with energy below the separatrix, the spread of the quantum adiabatic invariant is exponentially small in the inverse of the adiabaticity parameter. Surprisingly, the transition to this quantum adiabatic behavior occurs far below the minimum transition frequency of the system.

• DOE Contract Number: FG02-85ER53207; FG02-86ER40302
• OSTI ID: 6711229
• Journal Information: Physical Review A; (United States), Journal Name: Physical Review A; (United States) Vol. 47:4; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ADIABATIC INVARIANCE
ENERGY-LEVEL TRANSITIONS
MATHEMATICAL SPACE
MECHANICS
PHASE SPACE
POTENTIALS
QUANTUM MECHANICS
SPACE
TIME DEPENDENCE
TRAJECTORIES