707 research outputs found
Totally real Thue inequalities over imaginary quadratic fields
Let be an irreducible binary form of degree with integer
coefficients and with real roots. Let be an imaginary quadratic field, with
ring of integers . Let . We describe an efficient method how to
reduce the resolution of the relative Thue inequalities to the resolution of absolute Thue inequalities of type We illustrate our method with an explicit
example
Exciton Optical Absorption in Self-Similar Aperiodic Lattices
Exciton optical absorption in self-similar aperiodic one-dimensional systems
is considered, focusing our attention on Thue-Morse and Fibonacci lattices as
canonical examples. The absorption line shape is evaluated by solving the
microscopic equations of motion of the Frenkel-exciton problem on the lattice,
in which on-site energies take on two values, according to the Thue-Morse or
Fibonacci sequences. Results are compared to those obtained in random lattices
with the same stechiometry and size. We find that aperiodic order causes the
occurrence of well-defined characteristic features in the absorption spectra
which clearly differ from the case of random systems, indicating a most
peculiar exciton dynamics. We successfully explain the obtained spectra in
terms of the two-center problem. This allows us to establish the origin of all
the absorption lines by considering the self-similar aperiodic lattices as
composed of two-center blocks, within the same spirit of the renormalization
group ideas.Comment: 16 pages in REVTeX 3.0. 2 figures on request to F. D-A
([email protected]
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