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If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not immune...
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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
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Quantum chaotic resonances from short periodic orbits.

M Novaes1, J M Pedrosa, D Wisniacki

  • 1School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient method for calculating quantum resonances in chaotic systems by localizing states on classical orbits. The approach accurately approximates long-lived states, aligning with the fractal Weyl law.

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Area of Science:

  • Quantum mechanics
  • Chaos theory
  • Mathematical physics

Background:

  • Calculating quantum resonances in chaotic systems is computationally challenging.
  • Previous methods often struggle with the complexity of background states.

Purpose of the Study:

  • To develop a more efficient approach for computing quantum resonances and their wave functions.
  • To approximate long-lived states in chaotic scattering systems.

Main Methods:

  • Constructing states localized on classical periodic orbits.
  • Adapting these states to the system's dynamics.
  • Utilizing short periodic orbits (up to the Ehrenfest time).

Main Results:

  • The method requires only a few localized states to construct a resonance.
  • Accurate approximations of long-lived states are obtained.
  • The number of computed long-lived states matches the fractal Weyl law conjecture.

Conclusions:

  • The new approach significantly improves efficiency compared to existing methods.
  • The accuracy is validated using the open quantum baker map.
  • This method provides a powerful tool for studying quantum chaos.