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Relation between classical and quantum particle systems.

Klaus Morawetz1

  • 1Max-Planck-Institute for the Physics of Complex Systems, Noethnitzer Strasse 38, 01187 Dresden, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary

This study establishes a direct link between classical and quantum many-body systems. This allows approximating dense classical systems using quantum perturbation theory, simplifying complex calculations for systems like plasmas.

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Area of Science:

  • Statistical Mechanics
  • Quantum Mechanics
  • Plasma Physics

Background:

  • Classical and quantum many-body systems present distinct analytical challenges.
  • Understanding the behavior of dense classical systems is crucial in various physics domains.

Purpose of the Study:

  • To establish an exact correspondence between N-body classical and (N-1)-body quantum systems.
  • To develop a method for approximating dense classical systems using quantum perturbation theory.
  • To demonstrate the applicability of this method using a one-component plasma example.

Main Methods:

  • Establishing an exact correspondence via the partition function.
  • Utilizing quantum perturbation theory with modified Planck's constant.
  • Applying quantum-Born results for dense Fermi systems.

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Main Results:

  • An exact correspondence between classical interacting systems and quantum systems is found.
  • The Kelbg potential, describing quasi-classical quantum systems, is reproduced.
  • Dense classical many-body systems can be approximated by quantum perturbation theory.
  • The dynamical behavior of a one-component plasma is accurately reproduced.

Conclusions:

  • The established correspondence offers a novel approach to studying dense classical many-body systems.
  • This method simplifies complex classical system analysis by leveraging quantum mechanics.
  • The findings provide a practical guide, exemplified by the relationship between quantum-Bruckner and classical plasma parameters.