Journal of PLA University of Science and Technology

Correspondence between Berry's Phase and Lewis's Phase

Tong Yong, Pla Uni

Published Jan 1, 2001• 0 citations

Abstract

The existence of a special invariant for some time-dependent Hamiltonians is displayed and the Lewiss phase related to such an invariant becoming Berrys phase in the adiabatic limit is observed and the correspondence between Berrys phase and Lewiss phase is revealed in this paper.

Related papers

Correspondence between Berry's phase and Lewis's phase for quadratic Hamiltonians

Daniel A. Morales

The authors show the existence of a relation between Berry's phase and Lewis's phase for the case of quadratic Hamiltonians.

Journal of Physics A Mathematical and GeneralSep 21, 198868 citations

Berry phases and Hamiltonian time dependence

D J Moore

Shows that (non-adiabatic) Berry phases in time-independent systems arise for fundamentally different reasons than those for time-dependent systems. For time-independent Hamiltonians the Berry phases are seen to only depend on the chosen cyclic initial state, the Hamiltonian merely providing the appropriate period. The author also discusses two time-dependent examples where the time dependence arises from different sources, namely a two-level atom in an intense laser and a harmonic oscillator with a periodic forcing term.

Journal of Physics A Mathematical and GeneralDec 7, 199021 citations

Dynamical Invariants and Berry's Phase for Generalized Driven Harmonic Oscillators

Barbara Sanborn, Sergeĭ K. Suslov, Luc Vinet

We present quadratic dynamical invariant and evaluate Berry's phase for the time-dependent Schroedinger equation with the most general variable quadratic Hamiltonian.

arXiv:1108.5144Aug 25, 20116 citations

The Exact Solution, Berry's Phase and Coherent State for the Driven Generalized Time-Dependent Harmonic Oscillator

Jing‐Bo Xu, Tiezheng Qian, Xiao-Chun Gao

The Lewis' invariant and exact solution for the driven generalized time-dependent harmonic oscillator is found by making use of the Lewis-Riesenfeld quantum theory. Then, the adiabatic asymptotic limit of the exact solution is discussed and the Berry's phase for this system is obtained. We then proceed to use the exact solution to construct the coherent state and calculate the corresponding exact classical phase angle. This phase angle can give the Hannay's angle in the adjabatic limit. The relation between the exact Lewis' phase and the corresponding classical phase angle is discussed.

Communications in Theoretical PhysicsOct 1, 19910 citations

Berry's phase and wavefunctions for time-dependent Hamilton systems

P. G. L. Leach

An alternative derivation of Berry's phase (1985) to that given by Morales (1988) is given for non-autonomous Hamiltonian systems which admit an energy-like first integral. The generality of the problems treated is greater.

Journal of Physics A Mathematical and GeneralJun 21, 199028 citations

Explicit form of Berry phase for time dependent harmonic oscillators in noncommutative space

Manjari Dutta, Shreemoyee Ganguly, Sunandan Gangopadhyay

Abstract In this paper we look for the existence of Berry phase in time dependent harmonic oscillators in noncommutative space. Two systems are considered in our study in the noncommutative framework. The first one is a system in which a scale invariant term is present in the Hamiltonian from the beginning, and the second one is a system in which a scale invariant term emerges due to a change of variables from the noncommutative to the commutative ones. We first compute the eigenstates of both the systems using the Lewis invariant approach. We then employ the Lewis invariant technique to obtain the geometric phase under adiabatic approximation. We also calculate the Berry phase explicitly by choosing appropriate forms of the time dependent parameters appearing in the Hamiltonian. Our analysis surprisingly reveals that a scale invariant time reversal symmetry breaking term may not always lead to a non trivial Berry phase.

Physica ScriptaAug 30, 20224 citations