Re-examining Einstein's $B$ coefficient and rate equations with the Rabi model

Abstract

Starting from the Rabi Hamiltonian, which is useful in arriving at non-perturbative results within the rotating wave approximation, we have found Einstein's $B$ coefficient to be time-dependent: $B(t)\propto |J_0({\omega }_{\gamma }t)|$ for a two-level 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 $B$ coefficient---even for very small ${\omega }_{\gamma }$---drives the system away from thermodynamic equilibrium at any finite temperature contrary to Einstein's assumption. The time-dependent generalized $B$ coefficient facilitates a path to go beyond Pauli's formalism of non-equilibrium statistical mechanics involving the quantum statistical Boltzmann (master) equation. In this context, we have obtained entropy production of the two-level system by revising Einstein's rate equations, while considering the $A$ coefficient to be the original time-independent one and the $B$ coefficient to be time-dependent.

arXiv comment12 pages and 5 figures. Major revision of the 2nd version. Accepted for publication in Journal of Statistical Mechanics: Theory and Experiment

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Cited by in corpus (1)

• Generalization of the Einstein coefficients and rate equations under the quantum Rabi oscillation