Abstract
In this set of lectures we revisit from a contemporary perspective a classic problem of polaron theory using a hierarchy of increasingly sophisticated variational methods. Polaron structure is represented by variational surfaces giving the optimal values of the complete set of exciton and phonon amplitudes for every value of the joint exciton-phonon crystal momentum κ. Our variational methods include the approach originally taken by Merrifield, that originally followed by Toyozawa, and a generalization that includes mixed global and local exciton-phonon correlations. Exact results in limiting parameter regimes that serve as benchmarks for variational calculations are presented. We find that the variational solutions include characteristic small polaron, large polaron, and nearly-free phonon structures and we examine in detail the manner in which these compete and/or coexist. Through such examination, the parameter space of the problem is mapped, with particular attention given to problematic areas such as the highly quantum mechanical weak-coupling regime and the highly nonlinear intermediate-coupling regime, and to the self-trapping transition that may be said to mark the onset of the strong-coupling regime. Complete exciton and phonon amplitudes and associated energy bands are presented in illustrative cases, and the principal trends in the ground state energy, polaron band width, and effective mass are identified. The internal structure of our variational Bloch states is examined for qualities that might reflect typical characteristics of solitons. We find that quantitative characteristics typical of solitons do not survive this close scrutiny.
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Lindenberg, K., Zhao, Y., Brown, D.W. (1997). A Variational Approach to Exciton-Phonon Coupling. In: Garrido, P.L., Marro, J. (eds) Fourth Granada Lectures in Computational Physics. Lecture Notes in Physics, vol 493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-14148-9_1
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