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Transition-state theory reexamined.

Hans A Weidenmüller1

  • 1Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany.

Physical Review. E
|April 18, 2024
PubMed
Summary

This study models quantum systems using random-matrix theory. The average transmission probability depends on system formation, decay, and transport through resonant transition states.

Area of Science:

  • Quantum physics
  • Statistical mechanics

Background:

  • Quantum systems can be modeled as random-matrix ensembles.
  • Coupling between systems involves transition states and channels.

Purpose of the Study:

  • To analyze the average transmission probability in coupled quantum systems.
  • To understand the role of transition states and resonances.

Main Methods:

  • Utilizing random-matrix ensemble theory.
  • Describing system coupling via transition states.
  • Applying Breit-Wigner resonance formalism.

Main Results:

  • Average transmission probability is a product of three factors: entrance channel formation, exit channel decay, and transport.
  • Transition states contribute Breit-Wigner resonances.

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  • Resonances generally overlap.
  • Conclusions:

    • The derived formula provides a framework for understanding quantum transport in coupled systems.
    • Overlapping resonances are a key feature of the transmission probability.