Nonadiabatic Geometric Phase for the Cyclic Evolution of a Time-Dependent Hamiltonian System
نویسندگان
چکیده
The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic squeezed states correspond to the periodic and quasiperiodic solutions of an effective Hamiltonian defined on an extended phase space, respectively. The geometric phase of the cyclic squeezed state is found to be a phase-space area swept out by a periodic orbit. Furthermore, a class of cyclic states are expressed as a superposition of an infinte number of squeezed states. Their geometric phases are found to be independent of h̄, and equal to −(n+1/2) times the classical nonadiabatic Hannay angle. PACS: 03.65.Bz, 03.65.Sq, 42.50.Dv Typeset using REVTEX
منابع مشابه
Evolution of Gaussian Wave Packet and Nonadiabatic Geomet- rical Phase for the time-dependent Singular Oscillator
The geometrical phase of a time-dependent singular oscillator is obtained in the framework of Gaussian wave packet. It is shown by a simple geometrical approach that the geometrical phase is connected to the classical nonadiabatic Hannay angle of the generalized Harmonic oscillator. Explicitly time-dependent problems present special difficulties in classical and quantum mechanics. However, they...
متن کاملNonadiabatic Factor Accompanying Magnetic Translation of a Charged Particle
The quantum adiabatic theorem incorporating the Berry phase phenomenon can be characterized as a factorization of the time evolution operator into the product of a path-dependent geometric factor, a usual dynamical factor and a nonadiabatic factor that approaches the identity in the adiabatic limit. We study a case where all these factors can be constructed explicitly and where the instantaneou...
متن کاملUnification of the family of Garrison-Wright's phases
Inspired by Garrison and Wight's seminal work on complex-valued geometric phases, we generalize the concept of Pancharatnam's "in-phase" in interferometry and further develop a theoretical framework for unification of the abelian geometric phases for a biorthogonal quantum system modeled by a parameterized or time-dependent nonhermitian hamiltonian with a finite and nondegenerate instantaneous ...
متن کاملThe Quantum Adiabatic Approximation and the Geometric Phase
A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ) = ∑ l U (l)(τ) with U (l)(τ) being at least of the order ν. In particular U (0)(τ) corresponds to the adiabatic approximation and yields Berry’s adiabatic phase. It is sh...
متن کاملNovel quantum description for nonadiabatic evolution of light wave propagation in time-dependent linear media
A simple elegant expression of nonadiabatic light wave evolution is necessary in order to have a deeper insight for complicated optical phenomena in light science as well as in everyday life. Light wave propagation in linear media which have time-dependent electromagnetic parameters is investigated by utilizing a quadratic invariant of the system. The time behavior of the nonadiabatic geometric...
متن کامل