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Reduced density matrices and phase-space distributions in thermofield dynamics.

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This summary is machine-generated.

Thermofield dynamics (TFD) provides a framework for thermal effects. The inverse Bogoliubov transformation (iBT) variant simplifies calculations, enabling accurate thermal reduced particle distributions for quantum systems.

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Area of Science:

  • Quantum mechanics
  • Theoretical chemistry
  • Quantum optics

Background:

  • Thermofield dynamics (TFD) is a framework for thermal effects in quantum mechanics.
  • TFD uses a duplicated state space and Bogoliubov transformations.
  • A variant, inverse Bogoliubov transformation (iBT), transfers transformations to the propagator.

Purpose of the Study:

  • Derive formal expressions for the reduced 1-particle density matrix (1-RDM) in the iBT-TFD representation.
  • Define 1-RDM and Wigner distributions for thermal harmonic oscillators.
  • Develop approximate schemes for higher-dimensional distributions.

Main Methods:

  • Derivation of formal expressions for 1-RDM using real and tilde mode correlations.
  • Application to thermal harmonic and anharmonic oscillators.
  • Combination of iBT-TFD with tensor network methods for quantum propagation.

Main Results:

  • Formal expressions for 1-RDM derived from the reduced 2-particle density matrix.
  • 1-RDM and Wigner distributions defined for thermal harmonic oscillators.
  • Demonstration of methods for anharmonic oscillators.

Conclusions:

  • The iBT-TFD variant provides a tractable method for calculating thermal reduced particle distributions.
  • The derived formalisms are applicable to various quantum systems, including anharmonic oscillators.
  • This work facilitates the study of thermal effects in complex quantum systems.