Studies of the Microscopic Validity of the Discrete Nonlinear Schrödinger Equation
V M Kenkre, U. New Mexico
Semiclassical equations of motion such as the discrete nonlinear
Schroedinger equation (equivalently, the discrete selftrapping equation)
and extensions, have served as a point of departure for a huge amount of
analysis of transport in quantum systems, particularly in the context of
Davydov solitons [1]. Serious questions regarding their validity have been
raised recently, the clearest such study being that of Grigolini and
collaborators [2]. Our exact analysis of a simplified system supports some
of the conclusions drawn in [2] regarding the questionable status of
semiclassical starting points. However, it also results in a precise limit
in which the semiclassical starting point is exact [3]. In addition, we
find excellent agreement of the exact results with those of the memory
approach, an approximation suggested many years ago for the transport of
exciton dynamics [4].
[1] See, for example, Davydov's Soliton Revisited: Self-Trapping of
Vibrational Energy in Protein}, eds. P.L. Christiansen and A.C. Scott
(Plenum Press, New York,1990).
[2] D.Vitali, P.Allegrini, and P.Grigolini, Chem. Phys.180, 297 (1994).
[3] M.Salkola, A.R. Bishop, V.M. Kenkre, and S. Raghavan,
Phys. Rev. B 52, August (1995); V.M. Kenkre, S. Raghavan, A.R. Bishop and
M.Salkola, UNM-LANL preprint.
[4] V. M. Kenkre, Phys. Rev. B 12, 2150 (1975).
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