Universal statistics of wave functions in chaotic and disordered systems

@article{Hu1998UniversalSO,
  title={Universal statistics of wave functions in chaotic and disordered systems},
  author={Bambi Hu and Baowen Li and Wenguo Wang},
  journal={EPL},
  year={1998},
  volume={50},
  pages={300-306}
}
We study a new statistics of wave functions in several chaotic and disordered systems: the random matrix model, band random matrix model, the Lipkin model, chaotic quantum billiard and the 1D tight-binding model. Both numerical and analytical results show that the distribution function of a generalized Riccati variable, defined as the ratio of components of eigenfunctions on basis states coupled by perturbation, is universal, and has the form of a Lorentzian distribution. 
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References

SHOWING 1-10 OF 22 REFERENCES

Supersymmetry and trace formulae : chaos and disorder

Semiclassical Theory of Spectral Statistics and Riemann Zeros J.P. Keating. Quantum Chaos: Lessons from Disordered Metals A. Altland, et al. Supersymmetric Generalization of Dyson's Brownian Motion

Quantum signatures of chaos

The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2,

Stochastic behavior in classical and quantum hamiltonian systems : Volta Memorial Conference, Como, 1977

Integrable and stochastic behaviour in dynamical astronomy.- Adiabatic and stochastic motion of charged particles in the field of a single wave.- Numerical study of particle motion in two waves.-

Random Matrices, 2nd edition (Academic Press, San Diego

  • Guhr T., Müller-Groeling A. and Weidenmüller H. A., Phys. Rep.,
  • 1991

Random Matrices, Academic Press, San Diego

  • Second Edition,
  • 1991

Phys. Rep

  • Phys. Rep
  • 1991

Phys. Rev. E

  • Phys. Rev. E
  • 1998

Int. J. Mod. Phys. Chaos, Solitons & Fractals

  • Int. J. Mod. Phys. Chaos, Solitons & Fractals
  • 1219

Thouless D J, Phys. Rep

  • Thouless D J, Phys. Rep
  • 1492