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Coarse-graining in quantum mechanics: Distinguishable and indistinguishable particles.

Patrick G Sahrmann1, Gregory A Voth1

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This study introduces novel coarse-grained (CG) modeling for quantum systems, enabling simulations of indistinguishable particles. These advances accelerate the simulation of thermal quantum systems across various temperatures.

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Area of Science:

  • Computational physics
  • Quantum mechanics
  • Statistical mechanics

Background:

  • Coarse-grained (CG) modeling enhances molecular simulation scales.
  • Current CG methods primarily address classical systems, leaving quantum systems largely unexplored.

Purpose of the Study:

  • To develop fundamental advances in particle-based, bottom-up CG theory for quantum statistical mechanics.
  • To extend CG modeling to include indistinguishable quantum particles (bosons and fermions).
  • To introduce a variational optimization procedure for CG model parameterization.

Main Methods:

  • Expansion of the bottom-up CG formalism to incorporate indistinguishable quantum particles.
  • Introduction of a variational optimization procedure based on the relative entropy minimization (REM) principle.
  • Bridging classical and quantum REM methods via a semiclassical expansion.

Main Results:

  • Demonstration of CG models for both distinguishable and indistinguishable quantum systems.
  • Numerical examples include a harmonically trapped bosonic system and liquid water.
  • The developed methods are applicable to a range of quantum systems.

Conclusions:

  • The presented theoretical results enable accelerated simulations of thermal quantum systems.
  • This approach facilitates the study of distinguishable particles at higher temperatures and indistinguishable particles at lower temperatures.
  • Advances in CG theory open new avenues for quantum system simulations.