dorsal/arxiv
View SchemaQuantum nonlinear lattices and coherent state vectors
| Authors | Demosthenes Ellinas, Magnus Johansson, Peter L Christiansen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0001050 |
| URL | https://arxiv.org/abs/quant-ph/0001050 |
| Journal | Physica D, vol. 134, 126 - 143 (1999) |
Abstract
Quantized nonlinear lattice models are considered for two different classes, boson and fermionic ones. The quantum discrete nonlinear Schroedinger 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 Schroedinger equation, leads to quasiclassical Hamiltonian equations of motion for the CSV parameters. 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.
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"abstract": "Quantized nonlinear lattice models are considered for two different classes,\nboson and fermionic ones. The quantum discrete nonlinear Schroedinger model\n(DNLS) is our main objective, but its so called modified discrete nonlinear\n(MDNLS) version is also included, together with the fermionic polaron (FP)\nmodel. Based on the respective dynamical symmetries of the models, a method is\nput forward which by use of the associated boson and spin coherent state\nvectors (CSV) and a factorization ansatz for the solution of the Schroedinger\nequation, leads to quasiclassical Hamiltonian equations of motion for the CSV\nparameters. Analysing the geometrical content of the factorization ansatz made\nfor the state vectors invokes the study of the Riemannian and symplectic\ngeometry of the CSV manifolds as generalized phase spaces. Next, we investigate\nanalytically and numerically the behavior of mean values and uncertainties of\nsome physically interesting observables as well as the modifications in the\nquantum regime of processes such as the discrete self trapping (DST), in terms\nof the Q-function and the distribution of excitation quanta of the lattice\nsites. Quantum DST in the symmetric ordering of lattice operators is found to\nbe relatively enhanced with respect to the classical DST. Finally, the meaning\nof the factorization ansatz for the lattice wave function is explained in terms\nof disregarded quantum correlations, and as a quantitative figure of merit for\nthat ansatz a correlation index is introduced.",
"arxiv_id": "quant-ph/0001050",
"authors": [
"Demosthenes Ellinas",
"Magnus Johansson",
"Peter L Christiansen"
],
"categories": [
"quant-ph",
"nlin.SI"
],
"journal_ref": "Physica D, vol. 134, 126 - 143 (1999)",
"title": "Quantum nonlinear lattices and coherent state vectors",
"url": "https://arxiv.org/abs/quant-ph/0001050"
},
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