Quantum Monte Carlo Simulations of the Davydov Model
Through an application of the quantum Monte Carlo technique, we investigate the thermal equilibrium properties of the one-dimensional model proposed by Davydov for the description of energy transport processes in the α-helix. The calculations in this paper are free from uncontrollable approximations. The deformation of the lattice about a single (mobile) excitation is computed at a number of temperatures for a variety of coupling strengths. Broad and smooth coherent localized quasi-particle units are observed at low temperatures for some parameters of the system. For the “standard” α-helix data, the quasi-particle is embedded in strong fluctuations and is very localized. At temperatures greater than a few Kelvins, the quasi-particle attains its most localized form. We also considered scenarios in which several excitations are present in the system simultaneously; some preliminary results for the density-density correlation are calculated. The structure of polaron clusters is found, and their implication for biological systems is discussed.
KeywordsMatrix Element Partition Function World Line Quantum Fluctuation Small Polaron
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