# Quantum scars

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 Observed numerically in unpublished work [1], scars were later brought to the attention of the physics community in [2], where the theoretical explanation for their existence was presented.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

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