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Parametric evolution for a deformed cavity.

D Cohen1, A Barnett, E J Heller

  • 1Department of Physics, Harvard University, Cambridge, MA 02138, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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We studied how quantum system properties change with boundary deformation. The parametric kernel reveals nonunitary evolution, nonperturbative features, and nonuniversal saturation, challenging random-wave models.

Area of Science:

  • Quantum chaos
  • Statistical mechanics
  • Mesoscopic physics

Background:

  • Classically chaotic systems exhibit complex dynamics.
  • Quantum eigenstates of such systems are sensitive to boundary conditions.
  • Parametric dependence of quantum properties is crucial for understanding system evolution.

Purpose of the Study:

  • To investigate the parametric evolution of quantum eigenstates in a classically chaotic system.
  • To analyze the behavior of the parametric kernel (local density of states) under boundary deformation.
  • To elucidate the nonunitary nature and emergent features of this evolution.

Main Methods:

  • Theoretical analysis of a Hamiltonian describing a particle in a deforming cavity.
  • Calculation of the parametric kernel P(n/m) as a function of boundary deformation (deltax).

Related Experiment Videos

  • Numerical demonstration using two distinct deformation processes.

    • Main Results:

    • Observed nonunitary evolution in the parametric kernel.
    • Identified emergence of nonperturbative features.
    • Demonstrated final nonuniversal saturation and limitations of random-wave theory.

    Conclusions:

    • Parametric evolution of quantum eigenstates in chaotic systems is complex and nonunitary.
    • Emergent features challenge simplified models like random-wave theory.
    • Understanding these phenomena is key for quantum chaos and mesoscopic physics.