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Published on: May 30, 2014
Nonequilibrium work distribution of a quantum harmonic oscillator
1Department of Physics, University of Augsburg, Augsburg, Germany.
Summary
We analytically calculated the work distribution for a quantum harmonic oscillator with changing frequency. Our findings detail work probability densities for different conditions and confirm the quantum Jarzynski equality.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Thermodynamics
Background:
- The quantum harmonic oscillator is a fundamental model in quantum mechanics.
- Understanding work distribution in quantum systems is crucial for thermodynamics and quantum information.
- Previous studies have explored work in quantum systems, but analytical solutions for time-dependent frequencies are complex.
Purpose of the Study:
- To analytically calculate the work distribution of a quantum harmonic oscillator with arbitrary time-dependent angular frequency.
- To derive detailed expressions for work probability density under various conditions.
- To verify the quantum Jarzynski equality for this system.
Main Methods:
- Analytical calculation of work distribution.
- Derivation of probability density functions for adiabatic and nonadiabatic processes.
- Analysis in the limits of low and high temperatures.
- Verification of the quantum Jarzynski equality.
Main Results:
- Detailed analytical expressions for the work distribution were obtained.
- Work probability densities were determined for both adiabatic and nonadiabatic processes.
- The study provides insights into work fluctuations in quantum systems across different temperature regimes.
- The quantum Jarzynski equality was confirmed.
Conclusions:
- The work provides a comprehensive analytical framework for understanding work distribution in quantum harmonic oscillators with time-varying frequencies.
- The results are applicable to both equilibrium and non-equilibrium quantum thermodynamics.
- This research validates fundamental principles like the quantum Jarzynski equality in a complex quantum system.
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