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Classical and quantum periodically driven scattering in one dimension.

M Henseler1, T Dittrich, K Richter

  • 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
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This study reveals that harmonically driven one-dimensional potential wells can generate chaotic scattering on both classical and quantum levels. Quantum dynamics exhibit multiphoton exchanges and coherent tunneling, revealing signatures of classical chaos.

Area of Science:

  • Physics
  • Quantum Mechanics
  • Nonlinear Dynamics

Background:

  • Chaotic scattering in classical systems is well-understood.
  • The quantum mechanical behavior of driven potentials, especially concerning chaos, remains an active area of research.

Purpose of the Study:

  • To investigate irregular scattering in harmonically driven one-dimensional potential wells.
  • To explore the classical and quantum dynamics of these systems and identify signatures of chaos.

Main Methods:

  • Classical and quantum level analysis of driven potential wells.
  • Application of Floquet scattering theory for exact quantum dynamics.
  • Phase-space representation for identifying classical chaos signatures.

Main Results:

Related Experiment Videos

  • Demonstrated that ac-driven square and smooth wells generate chaotic scattering.
  • Introduced pseudointegrable scattering for oscillating bottom wells.
  • Observed multiphoton exchanges and coherent tunneling in the deep quantum regime.
  • Identified signatures of classical chaotic scattering in quantum dynamics.

Conclusions:

  • Harmonically driven potentials are sufficient to induce chaotic scattering.
  • Quantum scattering exhibits complex resonance structures and phenomena like coherent tunneling.
  • Quantum dynamics can reflect classical chaotic behavior in driven systems.