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Classical invariants and the quantum-classical link

Wisniacki1, Vergini

  • 1Departamento de Fisica, Comision Nacional de Energia Atomica, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina and Departamento de Fisica "J.J. Giambiagi," FCEN, UBA, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires, Argen.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

Classical periodic orbits can be reconstructed from quantum data in chaotic systems. This study demonstrates how quantum mechanics gives rise to classical hyperbolic structures, revealing the quantum-classical link.

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Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Chaos theory

Background:

  • Classical invariants of Hamiltonian systems are theoretically linked to quantum spectra.
  • Semiclassical methods connect periodic orbits with eigenfunctions and eigenenergies in classical chaotic systems.

Purpose of the Study:

  • To construct smooth functions localized around periodic orbits using solely quantum information.
  • To elucidate the emergence of classical hyperbolic structures from quantum mechanics in chaotic systems.
  • To discuss the quantum-classical correspondence in detail.

Main Methods:

  • Utilizing trace formulas derived from quantum information.
  • Developing highly localized functions in the vicinity of periodic orbits.
  • Analyzing the relationship between quantum data and classical structures.

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Main Results:

  • Successfully constructed smooth functions pinpointing periodic orbits from quantum data.
  • Demonstrated the emergence of classical hyperbolic structures from quantum mechanics.
  • Provided insights into the quantum-classical link in chaotic systems.

Conclusions:

  • Quantum information can be used to reconstruct classical periodic orbits.
  • The study highlights the quantum mechanical origins of classical structures in chaos.
  • A deeper understanding of the quantum-classical correspondence is achieved.