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Related Experiment Videos

Limit cycles in quantum theories.

Stanisław D Głazek1, Kenneth G Wilson

  • 1Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, 00-681 Warsaw, Poland.

Physical Review Letters
|December 18, 2002
PubMed
Summary

Quantum Hamiltonians may exhibit common limit cycle and chaotic behaviors, unlike classical models. This study presents the simplest quantum model Hamiltonian showing such renormalization group dynamics, analytically solvable.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Renormalization group theory

Background:

  • Classical models typically show fixed points in critical behavior.
  • Quantum systems may exhibit more complex renormalization group flows.

Purpose of the Study:

  • To identify and analyze the simplest quantum model Hamiltonian displaying limit cycle and chaotic renormalization group behavior.
  • To contrast quantum renormalization group dynamics with classical observations.

Main Methods:

  • Analysis of a discrete Hermitian matrix model.
  • Application of a nonperturbative renormalization group equation.
  • Analytical solution of the renormalization group flow.

Main Results:

  • The simplest quantum Hamiltonian exhibiting both limit cycle and chaotic renormalization group behavior is identified.
  • The model involves two coupling constants governed by a specific renormalization group equation.
  • The renormalization group flow is analytically soluble.

Conclusions:

  • Renormalization group limit cycles and chaos appear to be common in quantum Hamiltonians.
  • This finding contrasts with the prevalence of fixed points in classical critical phenomena.
  • The presented model offers a tractable system for studying complex quantum renormalization group dynamics.

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