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Eigenvalue Statistics and Eigenstate Wigner Functions for the Discrete Self-Trapping Equation

  • Mario Salerno
Part of the NATO ASI Series book series (NSSB, volume 243)

Abstract

In some recent papers [1, 2] the discrete self-trapping (DST) equation [3] was shown to be an effective working model to analyse the semiclassical limit of the quantum version of classically non-integrable dynamics [4-]. Canonical quantisation of the DST eq. with m freedoms leads in fact to the Hamiltonian
$$ \hat H = \Gamma \hbar ^2 \sum\limits_{j = 1}^m {\left( {\hat A_j ^ + \hat A_j + 1/2} \right)^2 + \hbar \varepsilon \sum\limits_{j,k = 1}^m {M_{jk} } \left( {\hat A_j ^ + \hat A_K + \hat A_K \hat A_j ^ + } \right)} /2 $$
(1)
which commutes with the norm operator
$$ \hat N = \hbar \left( {m/2 + \sum\limits_{j = 1}^m {\hat N_j } } \right) \equiv \hbar \left( {m/2 + \sum\limits_{j = 1}^m {\hat A_j ^ + \hat A_j } } \right) $$
(2)
whose eigenspaces are finite-dimensional.

Keywords

Wigner Function Hamiltonian Operator Invariant Torus Laguerre Polynomial Semiclassical Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Mario Salerno
    • 1
  1. 1.Dipartimento di Fisica TeoricaUniversità di SalernoSalernoItaly

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