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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Published on: May 30, 2014

Quantum kinetic equation in the closed-time-path formalism

¹Department of Physics, Faculty of Science and Technology, Keio University, Yokohama 223, Japan.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|December 2, 2000

Summary

This study presents a generalized quantum kinetic equation derived using a closed-time-path formalism. It extends the Boltzmann equation by incorporating memory effects and initial correlations for quantum systems.

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Area of Science:

Quantum field theory
Statistical mechanics
Many-body physics

Background:

The Boltzmann equation is a cornerstone for describing particle transport in dilute systems.
Limitations exist in describing quantum systems with memory effects and initial correlations.
A need for a more comprehensive kinetic equation in quantum regimes.

Purpose of the Study:

To systematically derive a quantum kinetic equation.
To generalize the Boltzmann equation for quantum systems.
To incorporate memory effects and initial correlations.

Main Methods:

Utilizing the closed-time-path (CTP) formalism.
Introducing a probe to calculate the expectation value of the number operator.
Employing an inversion formula to derive the equation of motion.

Main Results:

A quantum kinetic equation derived from first principles.
The derived equation generalizes the Boltzmann equation, including memory effects.
Calculations extended to third order in interaction, considering initial correlations.

Conclusions:

The CTP formalism provides a robust framework for deriving quantum kinetic equations.
The generalized equation offers a more complete description of quantum transport.
This work lays the foundation for studying complex quantum phenomena.