Quantum nonlinear lattices and coherent state vectors

Demosthenes Ellinas, M. Johansson, Peter Leth Christiansen

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    Abstract

    Quantized nonlinear lattice models are considered for two different classes, boson and fermionic ones. The quantum discrete nonlinear Schrodinger model (DNLS) is our main objective, but its so called modified discrete nonlinear (MDNLS) version is also included, together with the fermionic polaron (FP) model. Based on the respective dynamical symmetries of the models, a method is put forward which by use of the associated boson and spin coherent state vectors (CSV) and a factorization ansatz for the solution of the Schrodinger equation, leads to quasiclassical Hamiltonian equations of motion for the CSV parameters. The so obtained evolution equations are intimately related to the respective evolution equations for the classical lattices, provided we account for the ordering rules (normal, symmetric) adopted for their quantization. Analysing the geometrical content of the factorization ansatz made for the state vectors invokes the study of the Riemannian and symplectic geometry of the CSV manifolds as generalized phase spaces. Next, we investigate analytically and numerically the behavior of mean values and uncertainties of some physically interesting observables as well as the modifications in the quantum regime of processes such as the discrete self trapping (DST), in terms of the Q-function and the distribution of excitation quanta of the lattice sites. Quantum DST in the symmetric ordering of lattice operators is found to be relatively enhanced with respect to the classical DST. Finally, the meaning of the factorization ansatz for the lattice wave function is explained in terms of disregarded quantum correlations, and as a quantitative figure of merit for that ansatz a correlation index is introduced. This index is given in terms of the norm of the difference between the true and factorized state vectors, and accounts for the quantum correlations of the lattice sites that develop during the time evolution of the systems. (C) 1999 Elsevier Science B.V. All rights reserved.
    Original languageEnglish
    JournalPhysica D: Nonlinear Phenomena
    Volume134
    Issue number1
    Pages (from-to)126-143
    ISSN0167-2789
    DOIs
    Publication statusPublished - 1999

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