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Dynamics of quantum systems.

I Rotter1

  • 1Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
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This study links quantum system eigenvalues to S-matrix poles for resonance states. It reveals branch points cause avoided crossings and influence quantum dynamics in open and closed systems.

Area of Science:

  • Quantum mechanics
  • Theoretical physics
  • Mathematical physics

Background:

  • The behavior of quantum systems, including resonance states, is often described using Hamilton operators and S-matrix theory.
  • Understanding the relationship between discrete states and resonance states is crucial for various quantum phenomena.

Purpose of the Study:

  • To derive a general relation between the eigenvalues of an effective Hamilton operator and the poles of the S matrix.
  • To investigate the origin of avoided crossings in quantum systems.
  • To analyze the influence of branch points on quantum dynamics.

Main Methods:

  • Derivation of a theoretical relation between Hamilton operator eigenvalues and S-matrix poles.
  • Analysis of quantum systems, including many-particle systems and quantum billiards.

Related Experiment Videos

  • Investigation of avoided crossings and branch points in the complex plane.
  • Analytical and numerical study of a two-level system.

    • Main Results:

    • A unified relation is established for isolated and overlapping resonance states.
    • Avoided crossings are traced to branch points in the complex plane.
    • Branch points can manifest as double poles of the S matrix, impacting system dynamics.
    • The dynamics of a two-level system are thoroughly analyzed.

    Conclusions:

    • The derived relation provides a comprehensive understanding of quantum system resonances.
    • Branch points play a critical role in the dynamics of both open and closed quantum systems.
    • The study offers insights into the fundamental behavior of quantum states and their interactions.