  We study the electronic and dynamic properties of a one-dimensional
Thue-Morse chain within the framework of the transfer model. By means of direct
diagonalization of the Hamiltonian matrix we first show that the trace map of
the transfer matrices is exactly the same as that in the diagonal model. Then,
by calculating several quantities such as the wave function, the Lyapunov
exponent, and the Landauer resistivity, we show that all the electronic states
are extended despite the singular continuity of the energy spectrum. Our
results indicate that the electronic properties of the Thue-Morse chain is
independent of the kind of the model, which is contrary to the result of
Chakrabarti et al. [Phys. Rev. Lett. 74, 1403 (1995)]. To deepen our
understanding, we study the dynamics of an electronic wave packet and show that
the wave packet spreads superdiffusively for long times with dynamic indices
intermediate between periodic and quasiperiodic chains. Several features of
dynamics distinctive from the case of the Fibonacci chain are discussed. We
also study the effects of electron-phonon interaction on the dynamics of the
wave packet by taking into account a kind of nonlinear interaction. Degree of
dynamic localization is shown to be crucially dependent on the strength of the
hopping energy and the nonlinear interaction parameter.
