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Gradient Echo Quantum Memory in Warm Atomic Vapor

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Published on: November 11, 2013

A semiclassical initial-value representation for quantum propagator and boltzmann operator.

Yun-An Yan¹, Jian Liu², Jiushu Shao³

¹School of Physics and Optoelectronic Engineering, Ludong University, Shandong 264025, China.

Journal of Computational Chemistry

|December 28, 2018

Summary

This summary is machine-generated.

This study develops a uniform semiclassical approximation for quantum propagators and Boltzmann operators. The method determines classical dynamics and accurately calculates thermal correlation functions for linear systems.

Keywords:

Boltzmann operator correction operator imaginary-time semiclassical approximation semiclassical dynamics

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Area of Science:

Quantum mechanics
Statistical mechanics
Computational physics

Background:

The quantum propagator and Boltzmann operator are essential for describing quantum systems.
Existing semiclassical approximations often lack uniformity or require pre-defined classical dynamics.

Purpose of the Study:

To derive a uniform semiclassical approximation for the quantum propagator.
To extend this method for approximating the Boltzmann operator.
To develop a novel approach for calculating thermal correlation functions.

Main Methods:

Application of the correction operator method to the position-momentum integral representation.
Derivation of a semiclassical approximation for the quantum propagator.
Extension to approximate the Boltzmann operator using a complex Hamiltonian.

Main Results:

The developed method determines classical dynamics intrinsically.
The approximate Boltzmann operator is exact for linear systems.
A complex-time quantum propagator shows promise for general systems.

Conclusions:

The proposed semiclassical method offers a robust way to approximate quantum propagators and Boltzmann operators.
This approach provides accurate thermal correlation functions, especially for linear systems.
The complex-time propagator is a viable tool for general quantum system analysis.