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Characteristic functions based on a quantum jump trajectory.

Fei Liu1, Jingyi Xi2

  • 1School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China.

Physical Review. E
|January 14, 2017
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Summary
This summary is machine-generated.

This study introduces a straightforward method to derive characteristic functions (CFs) for quantum master equations (QMEs) using quantum jump trajectories. This approach simplifies stochastic thermodynamics and aligns with existing methods.

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Area of Science:

  • Quantum Thermodynamics
  • Statistical Mechanics
  • Quantum Information Theory

Background:

  • Characteristic functions (CFs) are crucial for analyzing probability densities of stochastic thermodynamic quantities in quantum master equations (QMEs).
  • Current methods for deriving CFs involve complex first-principles approaches, projecting system and environment evolution equations.

Purpose of the Study:

  • To investigate the feasibility of deriving CFs for QMEs directly from quantum jump trajectories.
  • To establish a self-contained framework for stochastic thermodynamics within QMEs.
  • To explore the practical implications for verifying quantum fluctuation relations.

Main Methods:

  • Utilized the concept of quantum jump trajectories to define thermodynamic quantities like heat, work, and entropy production.
  • Derived evolution equations for CFs directly from the trajectory-based approach.
  • Compared the trajectory-derived CF evolution equations with those from the conventional first-principles method.

Main Results:

  • Demonstrated that CFs for QMEs can be straightforwardly derived from quantum jump trajectories.
  • Confirmed that the trajectory-based derivation yields equations fully consistent with the first-principles approach.
  • Showcased the practical significance of these findings for experimental verification of quantum fluctuation relations.

Conclusions:

  • The trajectory-based method offers a simpler and more direct route to stochastic thermodynamics in QMEs.
  • The consistency with first-principles methods validates the trajectory approach.
  • The results pave the way for more realistic experimental tests of quantum fluctuation relations using techniques like photocounting.