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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Statistical description of small quantum systems beyond the weak-coupling limit.

Wen-ge Wang1

  • 1Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China. wgwang@ustc.edu.cn

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

We derived a statistical description for small quantum systems interacting with their environments. This method provides a renormalized self-Hamiltonian accounting for system-environment interactions, offering a canonical form for analysis.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter theory

Background:

  • Understanding quantum systems requires accurate statistical descriptions.
  • System-environment interactions significantly influence quantum dynamics.
  • Existing models may not fully capture weak, localized couplings.

Purpose of the Study:

  • Derive an explicit expression for the statistical description of small quantum systems.
  • Develop a renormalized self-Hamiltonian to account for system-environment interactions.
  • Analyze the nature of modifications to the self-Hamiltonian under different conditions.

Main Methods:

  • Derivation of an explicit statistical expression.
  • Renormalization of the system's self-Hamiltonian.
  • Analysis of system-environment interaction effects.

Main Results:

  • An explicit, canonical expression for statistical description is derived.
  • The expression features a renormalized self-Hamiltonian incorporating environmental influence.
  • For narrow-spectrum systems and large environments, modifications often exhibit mean-field behavior.

Conclusions:

  • The derived expression offers a refined statistical description for weakly coupled quantum systems.
  • Renormalized self-Hamiltonian captures essential system-environment interaction effects.
  • The study highlights potential deviations from mean-field approximations in certain scenarios.