Reexamining Einstein's $B$ coefficient and rate equations with the Rabi model
Abstract
Starting from the Rabi Hamiltonian, which is useful in arriving at nonperturbative results within the rotating wave approximation, we have found Einstein's $B$ coefficient to be timedependent: $B(t)\proptoJ_0(\omega_\gamma t)$ for a twolevel system (atom or molecule) in thermal radiation field. Here $\omega_\gamma$ is the corresponding Rabi flopping (angular) frequency and $J_0$ is the zeroth order Bessel function of the first kind. The resulting oscillations in the $B$ coefficienteven for very small $\omega_\gamma$drives the system away from thermodynamic equilibrium at any finite temperature contrary to Einstein's assumption. The timedependent generalized $B$ coefficient facilitates a path to go beyond Pauli's formalism of nonequilibrium statistical mechanics involving the quantum statistical Boltzmann (master) equation. In this context, we have obtained entropy production of the twolevel system by revising Einstein's rate equations, while considering the $A$ coefficient to be the original timeindependent one and the $B$ coefficient to be timedependent.
 Publication:

arXiv eprints
 Pub Date:
 July 2017
 arXiv:
 arXiv:1707.00283
 Bibcode:
 2017arXiv170700283I
 Keywords:

 Quantum Physics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 12 pages and 5 figures. Major revision of the 2nd version. Accepted for publication in Journal of Statistical Mechanics: Theory and Experiment