Floquet versus non-Floquet solutions for a periodic Hamiltonian

摘要

The situation of a particle interacting with two electric fields, one static and the other periodic in time, may be of interest in the study of the conductance of nanostructures. The static field corresponds to a bias voltage applied between the two electrodes, while the oscillatory field is due to laser illumination. The problem can be described by a variety of Hamiltonians, some time periodic, others not. Following some recent investigations about the solution of the one-dimensional wave equation for the time-dependent linear potential, it is shown that there are solutions of the time-dependent Schrodinger equation with a periodic Hamiltonian that do not follow the usual Floquet pattern of being the product of an energy-dependent exponential by a time-periodic factor. We show how to relate the two types of solutions, those conforming with the Floquet ansatz and the non-Floquet ones. (C) 2006 Wiley Periodicals, Inc.