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Spectroscopic studies in open quantum systems

Rotter1, Persson, Pichugin

  • 1Max-Planck-Institut fur Physik komplexer Systeme, D-01187 Dresden, Germany.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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Non-Hermitian Hamiltonians describe open quantum systems, with complex eigenvalues revealing state energies and widths. Interference phenomena like resonance trapping and level repulsion demonstrate how these eigenvalues avoid crossing in the complex plane.

Area of Science:

  • Quantum mechanics
  • Mesoscopic physics
  • Wave phenomena

Background:

  • Open quantum systems are described by non-Hermitian Hamiltonians.
  • Complex eigenvalues of these Hamiltonians represent state energies and widths.
  • Interference phenomena like level repulsion and resonance trapping occur between neighboring resonance states.

Purpose of the Study:

  • To illustrate the interplay between the real and imaginary parts of the Hamiltonian (Re(H) and Im(H)).
  • To calculate S-matrix poles and wave functions for a microwave resonator.
  • To investigate the impact of resonator area and waveguide coupling on resonance properties.

Main Methods:

  • The method of exterior complex scaling was employed for calculations.
  • Analysis of interference phenomena, including level repulsion and resonance trapping.

Related Experiment Videos

  • Investigation of wave function structure changes due to Re(H) and Im(H).

    • Main Results:

    • Complex eigenvalues avoid crossing in the complex plane, exhibiting level repulsion and resonance trapping.
    • Resonator properties (area, waveguide opening) influence S-matrix poles and wave functions.
    • Wave function structures show permanent changes due to Re(H) and Im(H).

    Conclusions:

    • The resonance picture in a microwave resonator mirrors many-body systems, despite lacking two-body forces.
    • Interplay between resonance trapping and level repulsion is crucial but not captured by standard statistical theories.
    • Non-Hermitian Hamiltonians offer a powerful framework for understanding complex quantum phenomena in open systems.