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Fermionic oscillator in a fermionic bath.

Arnab Ghosh1, Sudarson Sekhar Sinha, Deb Shankar Ray

  • 1Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

This study considers quantum dissipation in fermionic systems. A new method using fermionic coherent states and Grassmann variables derives a Fokker-Planck equation, extending existing quantum field theory approaches.

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Area of Science:

  • Quantum mechanics
  • Quantum optics
  • Statistical mechanics

Background:

  • Fermionic oscillators exhibit unique anticommutation properties.
  • Understanding quantum dissipation is crucial for open quantum systems.
  • Previous work by Cahill and Glauber established a density operator approach for fermionic fields.

Purpose of the Study:

  • To investigate quantum dissipation in a fermionic oscillator interacting with a fermionic environment.
  • To develop a theoretical framework for describing nonequilibrium quantum phenomena in fermionic systems.
  • To extend the density operator approach to the nonequilibrium domain.

Main Methods:

  • Utilizing an expansion of the reduced density operator in terms of fermionic coherent states.
  • Employing anticommuting numbers, also known as Grassmann variables.
  • Deriving a Fokker-Planck equation for the quasiprobability distribution function.

Main Results:

  • A Fokker-Planck equation for the quasiprobability distribution function of a fermionic oscillator in a fermionic environment was successfully derived.
  • The anticommuting nature of fermionic eigenvalues was central to the derivation.
  • The developed method provides a means to analyze quantum dissipation in fermionic systems.

Conclusions:

  • The density operator approach can be extended to the nonequilibrium domain for fermionic fields.
  • This work offers a new perspective on quantum dissipation in many-body fermionic systems.
  • The derived Fokker-Planck equation is a valuable tool for studying open quantum fermionic systems.