Physical Review A

Energy spectrum shift for a nonadiabatic process

O. J. Kwon, B. H. Cho

Published Oct 1, 1990• 2 citations

Abstract

We derive the semiclassical quantization rule for the external system in two interacting systems for a nonadiabatic process. It is shown that this semiclassical quantization rule accommodates the contribution of the averaged value of the geometrical phase per one evolution of the external system.

DOI: 10.1103/physreva.42.4374

Related papers

Non-Abelian geometric phase and generalized invariant method

Ohjong Kwon, Chang-Jun Ahn, Y. D. Kim

We quantitatively formulate the nonadiabatic non-Abelian geometric phase by generalizing the Lewis invariant method to a degenerate case, which is reduced to Wilczek and Zee's [Phys. Rev. Lett. 52, 2111 (1984)] non-Abelian geometric phase in the adiabatic limit. We also derive the effective propagator accommodating the nonadiabatic non-Abelian geometric phase and the semiclassical quantization rule in the adiabatic limit.

Physical Review ANov 1, 199210 citations

Effective action for a nonadiabatic quantum process

Aurel Bulgac

A sum rule for the so-called quantum phases is established, without assuming adiabatic evolution. By considering two interacting quantum systems, conventionally designated as a boson and a fermionic one, we evaluate the effective bosonic action after integrating out the fermionic variables. This effective action contains a nontrivial topological part, which has the same origin as the quantum adiabatic phase. However, the derivation does not rely on any adiabatic assumption.

Physical Review AJun 1, 198823 citations

Semi-Classical Quantization for Multi-Dimensional Coupled-Channel Equation

Kazuhiro Yabana, H. Horiuchi

Multi-dimensional coupled-channel equation is treated by the WKB approximation for the main purpose of deriving the semi-classical quantization rule for it. A somewhat general type of the multi-dimensional coupled-channel Hamiltonian is presented which enables us to derive the semiclassical quantization rule for the energy spectra. As in the one-dimensional case, the WKB wave function has an additional phase besides the usual phase ∫Σpsdxs, and the quantization rule should include the contribution from this additional phase. The structure of the WKB wave function in the adiabatic representation is also discussed.

Progress of Theoretical PhysicsMar 1, 198710 citations

Scattering Phase Correction for Semiclassical Quantization Rules in Multi-Dimensional Quantum Systems

Huang Wen-Min, Chung‐Yu Mou, Cheng-Hung Chang

While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny's transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semiclassical Landauer–Büttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.

Communications in Theoretical PhysicsFeb 1, 20101 citation

Effective Action for Adiabatic Process: Dynamical Meaning of Berry and Simon's Phase

Hiroshi Kuratsuji, Shinji Iida

By applying the path integral method to two interacting systems, it is shown that the specific phase Γ appearing in the quantum adiabatic process recently found by Berry and Simon is obtained as an additive action to the conventional dynamical action function. This scheme naturally gives a dynamical meaning to Berry and Simon’s topological phase, which leads to a novel form of semiclassical quantization rule including the phase Γ.

Progress of Theoretical PhysicsSep 1, 1985157 citations

Bohr–Sommerfeld, WKB, and modified semiclassical quantization rules

D. J. W. Geldart, David Kiang

The WKB approximation for energy eigenvalues can be advantageously introduced to students when the Bohr–Sommerfeld quantization rule is discussed. A simple heuristic derivation of these quantization rules is given. Exceptional cases occur when conditions necessary for the validity of semiclassical approximations are violated, but appropriate modifications can still provide useful semiclassical approximations even in such cases. Various situations are illustrated by examples.

American Journal of PhysicsFeb 1, 198611 citations