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Quantized orbits and resonant transport

Satija1, Sundaram

  • 1Department of Physics, George Mason University, Fairfax, Virginia 22030, USA.

Physical Review Letters
|September 16, 2000
PubMed
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Researchers found new quantized energy bands in a semiclassical model of the kicked Harper model. These bands reveal resonant transport phenomena, linking classical and quantum dynamics through a natural scaling law.

Area of Science:

  • Physics
  • Quantum Mechanics
  • Nonlinear Dynamics

Background:

  • The kicked Harper model exhibits complex dynamics, including classical accelerator modes.
  • Understanding the semiclassical limit and quantum-classical correspondence is crucial for characterizing such systems.

Purpose of the Study:

  • To derive an integrable semiclassical Hamiltonian from a tight-binding representation of the kicked Harper model.
  • To investigate the emergence of new quantized orbital bands and their relation to classical dynamics.
  • To establish a natural scaling law connecting classical and quantum couplings.

Main Methods:

  • Utilizing a tight-binding representation to formulate a semiclassical Hamiltonian.
  • Analyzing "quantized" bands of orbits within the semiclassical framework.

Related Experiment Videos

  • Identifying correlations between orbit frequencies and classical accelerator modes.

    • Main Results:

    • An integrable semiclassical Hamiltonian was obtained, featuring "quantized" bands of orbits.
    • New bands emerged when renormalized Harper parameters surpassed specific integer multiples of pi/2.
    • Commensurate orbit frequencies were linked to classical accelerator modes, indicating resonant transport.
    • Signatures of superdiffusive and resonant transport were observed in both classical and quantum regimes.

    Conclusions:

    • The study reveals a natural scaling law that bridges classical and quantum couplings, essential for correspondence.
    • The findings highlight the role of resonant transport and quantized bands in the semiclassical kicked Harper model.
    • This work provides insights into quantum-classical correspondence in periodically driven systems.