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Chinese Physics C

HIGH-ORDER ADIABATIC APPROXIMATIONS FOR EVOLUTION OF DEGENERATE QUANTUM MECHANICAL SYSTEM AND NON-ABELIAN INDUCED GAUGE STRUCTURE

Chen Sun

Published Jan 1, 1990• 0 citations
OpenAlex

Abstract

In this paper high-order adiabatic approximate method is proposed to study the evolution of degenerate quantum systums with slowly-changing parameters and varying symmetry. We not only prove the quantum adiabatic theorem for degenerate cases and discuss the corresponding non-abelian induced gauge structure, but also point out the non-adiabatic corrections resulting from higher-order approximations. With nuclear quadrupole resonance as an explicit example, we use this method to analyse observable effects of non-abelian Berry's phases in adiabatic and non-adiabatic experimental process.

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Chinese Physics C•Jan 1, 1988•0 citations
In this paper high-order adiabatic approximate method is proposed to study the evolution of degenerate quantum systums with slowly-changing parameters and varying symmetry. We not only prove the quantum adiabatic theorem for degenerate cases and discuss the corresponding non-abelian induced gauge structure, but also point out the non-adiabatic corrections resulting from higher-order approximations. With nuclear quadrupole resonance as an explicit example, we use this method to analyse observable effects of non-abelian Berry's phases in adiabatic and non-adiabatic experimental process.
A high-order adiabatic-approximation method is proposed to study the time evolution of degenerate quantum-mechanical systems with slowly changing Hamiltonians. We not only discuss the quantum adiabatic theorem, induced gauge structure, and non-Abelian Berry's phase factors in the first-order approximation, but we also give nonadiabatic corrections for problems in the second-order approximation. With the nuclear quadrupole resonance as an explicit example, we analyze the above-mentioned questions in detail and point out the observable effects of non-Abelian Berry's phase factors for nonadiabatic transitions between two instantaneous states in an improvement of Tycko's experiment.
The induced topological action relevant to the non-Abelian Berry's phase factor (NABPF) is derived by combining the high-order adiabatic approximation (HOAA) method with Kuratsuji and Iida's adiabatic path integral formulation. The non-adiabatic corrections for the transition amplitude are thereby obtained and the corresponding graphic representations are defined for convenience in the calculation. The gauge invariant properties and the dynamical implications of the non-Abelian induced topological action are also analyzed in detail. Finally, some explicit calculations for a model of physics are carried out as examples.
In this paper the evolution of a quantum system driven by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation (HOAA) method with Berry's phase, which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized force harmonic oscillator is discussed as an illustrative example.
By using group representation theory, th quasi-adiabatic approximation solution of the schrodinger equation of a quantum system with slowly-changing Hamiltonian are presented in this paper. We not only obtained the Berry phase factor and strictly proved the quantum adiabatic theorem as the zeroth-order approximation, but also studied the universal Berry phase factor and its geometrical interpretation when the adiabatic condition is violated. It is pointed out that this universal Berry phase factor has observable effects.