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Universal eigenvector statistics in a quantum scattering ensemble.

B Mehlig1, M Santer

  • 1Theoretische Quantendynamik, Institut für Physik, Albert-Ludwigs Universität Freiburg, Freiburg, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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We analyzed eigenvector statistics in non-Hermitian matrices for open quantum systems. Our findings show these correlations match predictions for Ginibre

Area of Science:

  • Quantum physics
  • Matrix theory
  • Statistical mechanics

Background:

  • Open quantum systems are described by non-Hermitian matrices.
  • Eigenvector statistics are crucial for understanding system dynamics.
  • Previous studies focused on specific matrix ensembles.

Purpose of the Study:

  • To calculate eigenvector statistics in large non-Hermitian matrices.
  • To investigate correlations of eigenvectors for eigenvalues at the center of the density of states.
  • To compare these statistics with existing models for random matrices.

Main Methods:

  • Ensemble averaging of non-Hermitian matrices.
  • Analysis in the limit of large matrix size.
  • Comparison with Ginibre's random matrix ensemble.

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Main Results:

  • Derived eigenvector statistics for a specific ensemble of non-Hermitian matrices.
  • Showed that ensemble-averaged eigenvector correlations match theoretical predictions.
  • Identified the applicability of Ginibre's ensemble results to open quantum systems.

Conclusions:

  • Eigenvector correlations in open quantum systems follow universal behavior.
  • The study provides a link between open quantum systems and random matrix theory.
  • Results are relevant for understanding quantum chaos and system dynamics.