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Transport and dynamics on open quantum graphs.

F Barra1, P Gaspard

  • 1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, Code Postal 231, B-1050 Brussels, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
PubMed
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We introduce a Wigner function for graphs to study the classical limit of quantum mechanics. This reveals transport properties in extended open graphs, linking classical diffusion to quantum scattering resonances and time evolution.

Area of Science:

  • Quantum mechanics
  • Graph theory
  • Statistical physics

Background:

  • The classical limit of quantum mechanics is a fundamental concept.
  • Understanding quantum systems on graphs requires new theoretical tools.

Purpose of the Study:

  • To introduce a Wigner function for quantum mechanics on graphs.
  • To compare classical and quantum dynamics on graph structures.
  • To investigate transport properties in extended open graphs.

Main Methods:

  • Introduction of a graph-based Wigner function.
  • Comparison of classical dynamics (diffusion) with quantum dynamics (propagator).
  • Analysis of scattering resonances and time evolution.

Main Results:

Related Experiment Videos

  • The classical limit of quantum mechanics on graphs is successfully studied.
  • Classical diffusion processes are generated on extended open graphs.
  • Transport properties are linked to quantum scattering resonances and time evolution.

Conclusions:

  • The Wigner function provides a novel approach to quantum mechanics on graphs.
  • The study bridges classical diffusion and quantum dynamics in graph systems.
  • Scattering resonances and time evolution are key indicators of transport properties.