Abstract
A great many techniques have been developed so far for solving polaron problems. Frequently used analytical approaches, in the context of the Frohlich model, Holstein model, and Davydov model, are variational methods [1], perturbative treatments [2], and Ansatz methods [3]. Great success has been achieved in obtaining accurate results for such physical quantities as polaron energy and effective mass, e. g. by Feynman’s variational method for the Frohlich polaron problem. There are however still some subtle issues that need to be made clear. To list a few from the author’s interests: a) How abrupt is the self-trapping transition?1 b) Can the translational symmetry be broken due to the self-trapping? c) How does one describe the polaron dynamics at general temperatures? Numerical simulations, such as the Quantum Monte Carlo method [4], can provide us in principle, with exact answers within error bars for certain physical observables. However, there are still many difficulties in obtaining definitive answers these problems.
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