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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Transient features of quantum open maps.

Leonardo Ermann1, Gabriel G Carlo, Juan M Pedrosa

  • 1Departamento de Física Teórica, GIyA, Comisión Nacional de Energía Atómica, Buenos Aires, Argentina. ermann@tandar.cnea.gov.ar

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Quantum mechanics reveals sensitivity in chaotic map resonances. Small openings lead to delocalization, impacting eigenfunction distributions and short-time behaviors.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Area of Science:

  • Quantum chaos
  • Mathematical physics
  • Dynamical systems

Background:

  • Classical chaotic maps share asymptotic properties but differ in short-time dynamics.
  • Quantization of these maps is explored to understand quantum behavior.

Purpose of the Study:

  • Investigate the impact of openings' shape and size on quantized chaotic maps.
  • Analyze the phase space localization of resonances relative to the repeller.

Main Methods:

  • Studying families of open chaotic maps with varying opening characteristics.
  • Quantizing these maps to examine resonance and eigenfunction distributions.
  • Analyzing phase space localization of resonances.

Main Results:

  • Resonance and eigenfunction distributions are sensitive to the initial shape and size of openings.
  • Strong delocalization effects are observed when the area of openings is smaller than Planck's constant (ℏ).

Conclusions:

  • The quantum behavior of chaotic systems is highly sensitive to the geometry of their openings.
  • Quantum effects, like delocalization, emerge significantly when system features approach the scale of Planck's constant.