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Related Experiment Video

Updated: Dec 30, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Computing characteristic functions of quantum work in phase space.

Yixiao Qian¹, Fei Liu¹

¹School of Physics, Beihang University, Beijing 100191, China.

Physical Review. E

|January 23, 2020

Summary

Researchers analytically derived characteristic functions (CFs) for various quantum harmonic oscillators. A new numerical method was also developed to approximate CFs for general quantum systems, offering broader applicability in quantum mechanics research.

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Area of Science:

Quantum mechanics
Statistical physics

Background:

Characteristic functions (CFs) are essential for describing quantum systems in phase space.
Previous methods for calculating CFs were system-specific and lacked unification.

Purpose of the Study:

To develop a simple and unified analytical method for deriving CFs of driven harmonic oscillators.
To propose a general numerical method for approximating CFs in quantum systems.

Main Methods:

Analytical derivation of CFs for forced, time-dependent mass/frequency, and coupled harmonic oscillators.
Development of a numerical approximation for CFs to ℏ² order for general quantum systems.

Main Results:

A unified analytical approach for calculating CFs of several harmonic oscillator types.
A novel numerical method demonstrated on time-dependent frequency oscillators and power-law potentials.

Conclusions:

The study provides a versatile framework for analyzing quantum harmonic oscillators.
The proposed numerical method enhances the accessibility of CF calculations for complex quantum systems.