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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Diffraction and tunneling in systems with mixed phase space.

Akiyuki Ishikawa1, Atushi Tanaka, Kensuke S Ikeda

  • 1Department of Physics, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo 192-0397, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2012
PubMed
Summary
This summary is machine-generated.

Diffraction controls quantum transitions in sharply divided phase spaces, influencing regular-to-chaotic region shifts. Its subtle role depends on wave function properties and coordinate choices.

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Area of Science:

  • Quantum dynamics
  • Statistical mechanics
  • Mathematical physics

Background:

  • Dynamical tunneling is a quantum phenomenon observed in systems with divided phase space.
  • Diffraction effects arise from discontinuities or indifferentiable points within a system.
  • Understanding these effects is crucial for characterizing quantum transitions in complex systems.

Purpose of the Study:

  • To investigate the role of diffraction in quantum transitions within two-dimensional area-preserving maps.
  • To clarify the interplay between diffraction and dynamical tunneling in mixed phase space.
  • To determine if chaos influences the regular-to-chaotic transition in sharply divided phase spaces.

Main Methods:

  • Analysis of two-dimensional area-preserving maps with sharply divided phase space.
  • Investigation of diffraction effects in relation to dynamical tunneling.
  • Semiclassical treatment of edge contributions of the one-step propagator.

Main Results:

  • Diffraction controls the quantum transition between regular and chaotic regions when the phase space border is sharp.
  • The manifestation of diffraction is subtle and depends on the wave function's support and coordinate system.
  • In cases without diffraction sources in the wave function support, diffraction mixes with tunneling, creating a hybrid process.

Conclusions:

  • Chaos does not influence the regular-to-chaotic transition when the phase space is sharply divided.
  • Diffraction plays a key role in regular-to-chaotic transitions under specific conditions related to phase space structure.
  • The study clarifies the nuanced nature of diffraction in mixed phase space dynamics.