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Explicit analytical solution for scaling quantum graphs.

Yu Dabaghian1, R Blümel

  • 1Department of Physics, Wesleyan University, Middletown, CT 06459-0155, USA. ydabaghian@wesleyan.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
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Scaling quantum graphs, models of quantum chaos, are surprisingly analytically solvable for any topology. This analytical solvability is unexpected for chaotic systems.

Area of Science:

  • Quantum mechanics
  • Mathematical physics

Background:

  • Quantum graphs are mathematical models used to study quantum chaotic systems.
  • Typically, quantum chaotic systems are not explicitly analytically solvable.

Purpose of the Study:

  • To demonstrate the analytical solvability of scaling quantum graphs with arbitrary topology.
  • To address the unexpected nature of this solvability in the context of quantum chaos.

Main Methods:

  • The study focuses on analytical methods applied to quantum graphs.
  • The research involves scaling properties and topological considerations.

Main Results:

  • Explicit analytical solutions are shown to exist for scaling quantum graphs.
  • This solvability holds true for graphs of arbitrary topology.

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Conclusions:

  • The findings challenge the conventional understanding of quantum chaotic systems.
  • This work opens new avenues for studying quantum chaos through explicitly solvable models.