TY - JOUR

T1 - A geometrical approach to non-adiabatic transitions in quantum theory

T2 - Applications to NMR, over-barrier reflection and parametric excitation of quantum oscillator

AU - Marinov, M. S.

AU - Strahov, E.

PY - 2001/3/2

Y1 - 2001/3/2

N2 - This paper deals with non-adiabatic processes (i.e. processes excluded by the adiabatic theorem) from the geometrical (group-theoretical) point of view. An approximate formula for the probabilities of the non-adiabatic transitions is derived in the adiabatic regime for the case when the parameter-dependent Hamiltonian represents a smooth curve in the Lie algebra and the quantal dynamics is determined by the corresponding Lie group evolution operator. We treat the spin precession in a time-dependent magnetic field and the over-barrier reflection problem in a uniform way using the first-order dynamical equations on SU(2) and SU(1.1) group manifolds, respectively. A comparison with analytic solutions for simple solvable models is provided.

AB - This paper deals with non-adiabatic processes (i.e. processes excluded by the adiabatic theorem) from the geometrical (group-theoretical) point of view. An approximate formula for the probabilities of the non-adiabatic transitions is derived in the adiabatic regime for the case when the parameter-dependent Hamiltonian represents a smooth curve in the Lie algebra and the quantal dynamics is determined by the corresponding Lie group evolution operator. We treat the spin precession in a time-dependent magnetic field and the over-barrier reflection problem in a uniform way using the first-order dynamical equations on SU(2) and SU(1.1) group manifolds, respectively. A comparison with analytic solutions for simple solvable models is provided.

UR - http://www.scopus.com/inward/record.url?scp=0035794098&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/34/8/317

DO - 10.1088/0305-4470/34/8/317

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AN - SCOPUS:0035794098

SN - 0305-4470

VL - 34

SP - 1741

EP - 1752

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 8

ER -