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Journal of Hangzhou Teachers College

Study of electron feature in the time-evolution magnetic field

Bin Chen

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

As is well known, the phase changes with electron transport in the time-evolution magnetic field. In this paper, with evolution operator in tow-level systems, we obtain several exact solutions. Then we analyze their phase. By the time-dependent Schrdinger equation, we obtain dynamical phase, and then we have Aharonov-Anandan phase. At last, we compare them with Berry phase.

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As is well known, the phase changes with electron transport in the time-evolution magnetic field. In this paper, with evolution operator in tow-level systems, we obtain several exact solutions. Then we analyze their phase. By the time-dependent Schrdinger equation, we obtain dynamical phase, and then we have Aharonov-Anandan phase. At last, we compare them with Berry phase.
It is found that in a quantum system with cyclic Hamiltonian the time-dependent Schrodinger equation admits the Bloch type solutions which have the form of Bloch function with respect to the time. These solutions constitute an orthonormal basis of the solution space and lead to a new type of quantum phases. The new phases, called Bloch phases by the authors, are the special Aharonov-Anandan phases, and reduce to the Berry phases under the adiabatic approximation if the degeneracy of instantaneous eigenenergy is time-independent. The above conclusions are proved and calculation for the evolution of spin magnetic moments in a magnetic field precessing with constant angular velocity is exemplified.
We present a method for calculating the Aharonov-Anandan phase for time-independent Hamiltonians that avoids the calculation of evolution operators. We compare the generic method used to calculate the Aharonov-Anandan phase with the method proposed here through four examples; a spin-1/2 particle in a constant magnetic field, an arbitrary infinite-sized Hamiltonian with two known eigenvalues, a Fabry-Perot cavity with one movable mirror and a three mirrors cavity with a slightly transmissive movable middle mirror.