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Related Experiment Videos

Resurgence in quasiclassical scattering.

R E Prange1

  • 1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Street 38, D-01187 Dresden, Germany.

Physical Review Letters
|March 14, 2003
PubMed
Summary

This study introduces a resurgent expression for Wigner's R matrix, ensuring a unitary scattering matrix. This is crucial for quasiclassical spectral theory, especially when resonance width and spacing are comparable.

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Area of Science:

  • Quantum mechanics
  • Mathematical physics
  • Spectral theory

Background:

  • Resurgence in quasiclassical spectral theory relates long periodic orbits to short ones for a real spectral determinant.
  • A key question is whether long scattering orbits can similarly yield a unitary quasiclassical scattering matrix.

Purpose of the Study:

  • To find a resurgent and manifestly Hermitean expression for Wigner's R matrix.
  • To establish conditions for a unitary quasiclassical scattering matrix.

Main Methods:

  • Development of a resurgent expression for Wigner's R matrix.
  • Analysis of the Hermiticity of the R matrix expression.

Main Results:

  • A resurgent and manifestly Hermitean expression for Wigner's R matrix was derived.
  • This expression implies a unitary scattering matrix in quasiclassical spectral theory.

Conclusions:

  • The derived resurgent expression for Wigner's R matrix guarantees a unitary scattering matrix.
  • This finding is particularly significant when the average resonance width is comparable to the average resonance spacing.

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