Quantum and semiclassical dynamics of a two-level system coupled to a bosonic degree of freedom

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Abstract
The Hamiltonian of a two-level system coupled to a boson mode is transformed to Bargmann's Hilbert space of analytical functions. The quantum dynamics is calculated with a suitable choice of a complete set of orthonormal functions in Bargmann space. A semiclassical approximation which is formulated as a dynamical Hamiltonian system is compared with the quantum dynamics. For the parameters under consideration, semiclassical dynamics is not at all appropriate to approximate the quantum dynamics. These parameters are suited to view the system as a two-site model of small-polaron dynamics.