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Derivation of the Tight-Binding Approximation for Time-Dependent Nonlinear Schrödinger Equations

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Abstract

In this paper, we consider the nonlinear one-dimensional time-dependent Schrödinger equation with a periodic potential and a bounded perturbation. In the limit of large periodic potential, the time behavior of the wavefunction can be approximated, with a precise estimate of the remainder term, by means of the solution to the discrete nonlinear Schrödinger equation of the tight-binding model.

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Authors and Affiliations

  1. Department of Physics, Informatics and Mathematics, University of Modena e Reggio Emilia, Modena, Italy

    Andrea Sacchetti

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  1. Andrea Sacchetti
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Correspondence to Andrea Sacchetti.

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Communicated by Vieri Mastropietro.

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This paper is partially supported by GNFM-INdAM.

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Sacchetti, A. Derivation of the Tight-Binding Approximation for Time-Dependent Nonlinear Schrödinger Equations. Ann. Henri Poincaré 21, 627–648 (2020). https://doi.org/10.1007/s00023-019-00872-6

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