Heriot-Watt Mathematics Report Series
HWM00-19, 10 Aug 2000
Analytical approach to the Davydov-Scott theory with on-site potential
Y Zolotaryuk and J C Eilbeck
Abstract
We propose an analytical approach to study the one-dimensional
acoustic polaron model that includes an on-site external potential
applied to each chain molecule. The key to the approach is an exact
discrete solution for the chain deformation field given in terms of
a (quasi)particle wavefunction. For this purpose we introduce a
whole variety of polynomial series which resemble the Chebyshev
polynomials. We call these series the hyperbolic Chebyshev
polynomials. Using next a properly chosen discrete trial function
for the wavefunction envelope, we obtain simple expressions for the
variational energy of the system. Contrary to an isolated molecular
chain, the polaron state (Davydov soliton) is shown to exist only
for appropriate system parameters while the delocalized (exciton)
state can always exist. As a result, the following three regimes
can be specified for the chain with an on-site potential: (i) the
polaron is a ground state and the exciton is a metastable state,
(ii) the polaron is a metastable state and the exciton is a
(delocalized) ground state, and (iii) the polaron state does not
exist and only the exciton exists, being a ground state. Two
characteristic dimensionless parameters are found in terms of which
a criterion of existence of (stable and metastable) polaron states
and their non-existence is formulated. Finally, pinning barrier for
the Davydov soliton is found to vanish in a particular case of
system parameters, resulting in a transparent regime of uniform
propagation of the soliton with very small size.
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Publication
Y Zolotaryuk, J C Eilbeck
, Analytical approach to the Davydov-Scott theory with on-site potential, Phys. Rev. B, 63, 054302-1 -, (2001).
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