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Quantum pseudointegrable Hamiltonian impact system.

Omer Yaniv1, Vered Rom-Kedar1

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Summary
This summary is machine-generated.

This study quantizes a pseudointegrable Hamiltonian system, finding energy level statistics resemble pseudointegrable billiards. Wave functions do not equidistribute in configuration space at high energies, indicating unique system dynamics.

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Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Mathematical physics

Background:

  • Pseudointegrable Hamiltonian systems present unique quantization challenges.
  • Understanding wave function behavior is crucial for characterizing quantum systems.

Purpose of the Study:

  • To quantize a toy model of a pseudointegrable Hamiltonian impact system.
  • To investigate the properties of its wave functions and energy levels.
  • To compare its characteristics with pseudointegrable billiards.

Main Methods:

  • Application of Einstein-Brillouin-Keller quantization conditions.
  • Verification of Weyl's law.
  • Analysis of wave function density and energy level statistics.
  • Analytical and numerical demonstrations of equidistribution properties.

Main Results:

  • Energy level statistics align with those of pseudointegrable billiards.
  • Wave function density remains non-zero at high energies, concentrating on projected classical level sets.
  • Absence of equidistribution in configuration space at the large energy limit.

Conclusions:

  • The quantized pseudointegrable model exhibits distinct wave function behavior compared to typical systems.
  • This lack of equidistribution suggests a breakdown of ergodicity in the configuration space for this model.
  • The findings offer insights into the quantum-classical correspondence in non-integrable systems.