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)


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
$$ \hat H = \Gamma \hbar ^2 \sum\limits_{j = 1}^m {\left( {\hat A_j ^ + \hat A_j + 1/2} \right)^2 + \hbar \varepsilon \sum\limits_{j,k = 1}^m {M_{jk} } \left( {\hat A_j ^ + \hat A_K + \hat A_K \hat A_j ^ + } \right)} /2 $$
which commutes with the norm operator
$$ \hat N = \hbar \left( {m/2 + \sum\limits_{j = 1}^m {\hat N_j } } \right) \equiv \hbar \left( {m/2 + \sum\limits_{j = 1}^m {\hat A_j ^ + \hat A_j } } \right) $$
whose eigenspaces are finite-dimensional.


Wigner Function Hamiltonian Operator Invariant Torus Laguerre Polynomial Semiclassical Limit 
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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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