DISSIPATIVE MOTION OF AN ELECTRON-PHONON SYSTEM IN A UNIFORM ELECTRIC-FIELD - AN EXACT SOLUTION

Starting with Heisenberg's equations of motion, we have calculated the exact time-dependent drift velocity of a single electron that is harmonically coupled to a phonon bath according to the Caldeira-Leggett (CL) Hamiltonian and accelerated by a uniform electric field. Contrary to the conventional perturbational approach, the external field may be turned on abruptly at an arbitrary initial time; hence, the drift velocity reflects the genuine physical response to the electric field. The electron motion is shown to be irreversible if, for appropriate phonon-dispersion relations, the number of phonon modes approaches infinity. Although it has been devised for other purposes, the CL electron-phonon Hamiltonian, including the electric-field term, provides an exactly solvable transport model, highlighting interesting features of nonequilibrium thermodynamics, such as entropy production.