Mean-field approximation for the molecular polaron withq2coupling

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Abstract
We investigate a two-state electronic system coupled quadratically to an oscillator. After a standard (mean-field) simplification of the Hamiltonian we obtain the energy levels of the system, from which the specific heat is then obtained. For the interesting case of one electron and for small bare-level separations the electron-phonon interaction causes the Schottky peak to move into the region of higher temperatures, while for large separations the effect of the interaction is small. The quadratic coupling increases the electronic level separation in contrast with the familiar band narrowing with linear coupling.