Abstract
Two simple nonadiabatic model Hamiltonian, a generalized Rabi Hamiltonian and a caricature of the Fröhlich Hamiltonian are presented. The eigenvalue problem defined by the first is solved in Bargmann Hilbert space of analytical functions to demonstrate the methods. Results for the second are reported. Eigenvalues are given in terms of continued fractions, the eigenvectors as power series or Neumann series. The coefficients of the series are determined by simple three term recurrence relations. Using these results, the optical conductivity is calculated with Kubo's formulae. We correlate our results with experimental observations and the conventional small polaron theory.
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Kaspar, F. Optical conductivity by simple non-adiabatic model Hamiltonian. Z. Physik B - Condensed Matter 61, 243–250 (1985). https://doi.org/10.1007/BF01317790
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DOI: https://doi.org/10.1007/BF01317790