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Related Experiment Videos

Variational procedure for time-dependent processes.

R Englman1, A Yahalom

  • 1Department of Physics and Applied Mathematics, Soreq NRC, Yavne 81800, Israel. englman@vms.huji.ac.il

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2004
PubMed
Summary

A new variational Lagrangian method simplifies density matrix time evolution. This flexible approach applies to various systems, including hydrodynamics and transport theory, and is validated on a two-level system.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Theoretical physics

Background:

  • Describing the time evolution of quantum systems is crucial.
  • Existing methods can be complex for arbitrary density matrices.
  • Connecting quantum dynamics with macroscopic phenomena like hydrodynamics is challenging.

Purpose of the Study:

  • To propose a simple variational Lagrangian for density matrix time evolution.
  • To demonstrate the formalism's applicability to diverse physical systems.
  • To validate the method using a two-level system.

Main Methods:

  • A variational Lagrangian is formulated using density factorization.
  • The Lagrangian includes only kinetic energy terms.
  • The method is tested on a two-level system interacting with an oscillator and in a dissipative mode.

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Main Results:

  • The proposed variational Lagrangian successfully describes the time development of arbitrary density matrices.
  • The formalism unifies concepts from quantum mechanics, hydrodynamics (Navier-Stokes equations), and transport theory.
  • It naturally recaptures the Rayleigh-Onsager least dissipation function condition.

Conclusions:

  • The variational Lagrangian offers a flexible and unifying framework for studying time evolution in various physical systems.
  • This approach provides a simplified yet powerful tool for theoretical and applied research.
  • The method's success on the two-level system demonstrates its practical utility.