Quantum scars

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Prof. Lev Kaplan, Department of Physics and Engineering Physics, Tulane University, New Orleans, LA, was invited on 31 March 2011.

Short note and Related References added by Scholarpedia Editor D.Shepelyansky in May 2020

Wavefunction scarring is the anomalous enhancement of quantum eigenstate intensities along unstable periodic orbits of a classically chaotic system. Observed numerically in unpublished work [1], scars were later brought to the attention of the physics community in [2], where the theoretical explanation for their existence was presented. Numerical evidence and associated analytical work (followed later by experimental tests in a variety of systems) showed that scarring was a statistically significant correction to ergodic eigenstates of a classically ergodic system described by the Shnirelman theorem [3] in the semiclassical limit. Related publications and references can be found in [4],[5].

Related References

  1. S.W.McDonald, preprint based om PhD thesis, University of California, Lawrence Berkeley Lab, report No LBL-14837 (1983); University Microfilms No 8413506
  2. E.J.Heller, "Bound-state eigenfunctions of classically chaotic Hamiltonian systems: scars of periodic orbits", Phys. Rev. Lett. 53: 1515 (1984)
  3. A.I. Shnirelman, Ergodic properties of eigenfunctions, Uspekhi Mat. Nauk. 29(6(180)): 181 (1974)
  4. E.B.Bogomolny, "Smoothed wave functions of chaotic quantum systems", Physica D 31(2): 169 (1988)
  5. L.Kaplan, "Scars in quantum chaotic wavefunctions", Nonlinearity 12: R1 (1999)

See also internal links

Bohigas-Giannoni-Schmit conjecture, Microwave billiards and quantum chaos, Quantum chaos, Random matrix theory, Shnirelman theorem

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