Related Experiment Videos
Resurgence in quasiclassical scattering
1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Street 38, D-01187 Dresden, Germany.
Physical Review Letters
|March 14, 2003
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.
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.