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Tight-binding Hamiltonians with off-diagonal disorder are studied extensively in connection with localization phenomena. For instance, applying a random magnetic field to a square lattice amounts to assigning phases to the off-diagonal entries of H. A gauge transformation simplifies the resulting H to an equivalent Hamiltonian with apparently less disorder. This paper concerns the special case when non-zero entries of a Hamiltonian H are ± 1 between nearest-neighbor sites. Some thought shows that a one-dimensional chain Hamiltonian with this type of randomness can be transformed to that of an ordered chain by flipping the signs of selected basis functions, i.e. by a unitary transformation. Hence such a chain is not disordered at all. On the other hand, whether or not a similar H for a square lattice implies actual disorder is a topological question. The question can be put this way: Can one find a set of simple closed curves such that reversing the signs of basis functions inside the curves will change all non-zero H entries to +1? More generally one can ask about the extent of residual disorder and its effect on electronic properties of the model. We take up these questions on a periodic square lattice.

The Davydov's soliton propagation in the linear polymer chain is analyzed numerically by solving the discrete equations of motion for exciton and phonon amplitudes. The main difference with respect to the results of continual approximation is that two exciton–phonon coupling constants influence separately the soliton behavior. Their influence is studied both in the ideal chain and the chain with single impurity.

The dynamical response of one dimensional chains containing 55 till 309 atoms is investigated using a restricted molecular dynamics simulation scheme. The total momentum correlation function of an electron cloud shows resonances that are related to different collective excitation modes of the nano plasma. Spatially resolved cross correlation functions are calculated to deduce the spatial structure and strength of these resonance modes. The dependence of the corresponding resonance frequencies on temperature, density and chain size is investigated. The width of the resonances is analyzed in terms of a mode dependent collision frequency.

The dynamical response of one dimensional chains containing 55 till 309 atoms is investigated using a restricted molecular dynamics simulation scheme. The total momentum correlation function of an electron cloud shows resonances that are related to different collective excitation modes of the nano plasma. Spatially resolved cross correlation functions are calculated to deduce the spatial structure and strength of these resonance modes. The dependence of the corresponding resonance frequencies on temperature, density and chain size is investigated. The width of the resonances is analyzed in terms of a mode dependent collision frequency.