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Long-range correlations in quantum-chaotic spectra.

Akhilesh Pandey1, Sanjay Puri, Sandeep Kumar

  • 1School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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We investigated long-range spectral correlations in random matrices, finding they are universal for single-band spectra but break down for multi-band spectra. This research is crucial for understanding conductance fluctuations in mesoscopic systems.

Area of Science:

  • Physics
  • Quantum Mechanics
  • Condensed Matter Physics

Background:

  • Spectral correlations in random matrices are crucial for understanding quantum systems.
  • Long-range spectral correlations offer insights complementary to short-range properties.
  • These properties are relevant for conductance fluctuations in mesoscopic systems.

Purpose of the Study:

  • To investigate the universality and breakdown of long-range spectral correlations in random matrices.
  • To characterize these correlations for both one-band and multi-band spectra.
  • To explore the presence of long-range correlations in quantum-chaotic systems.

Main Methods:

  • Analysis of spectral correlations in random matrix theory.
  • Characterization of universality and breakdown of correlations.

Related Experiment Videos

  • Formulation of a multiply-kicked quantum rotor model.

    • Main Results:

    • Universality of long-range spectral correlations observed for one-band spectra.
    • Breakdown of universality identified for multi-band spectra.
    • The multiply-kicked quantum rotor model demonstrates both long-range and short-range correlations.

    Conclusions:

    • Long-range spectral correlations are not universally present in all quantum-chaotic systems.
    • The developed quantum rotor model serves as a valuable system for studying both types of spectral correlations.
    • Understanding these correlations is key for advancements in mesoscopic physics and quantum transport.