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Calculating work in weakly driven quantum master equations: Backward and forward equations.

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This study demonstrates the equivalence of two methods for calculating work distribution characteristic functions in quantum master equations. These methods, quantum jump trajectories and energy measurements, align with classical stochastic theory approaches.

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Area of Science:

  • Quantum Physics
  • Statistical Mechanics
  • Quantum Information Theory

Background:

  • Weakly driven quantum master equations describe open quantum systems.
  • Calculating work distribution characteristic functions is crucial for understanding energy exchange in quantum systems.
  • Existing methods include quantum jump trajectories and energy measurements.

Purpose of the Study:

  • To demonstrate the equivalence of two distinct methods for calculating characteristic functions of work distribution.
  • To clarify the microscopic basis of the quantum jump trajectory method.
  • To reveal a novel equality concerning heat in quantum systems.

Main Methods:

  • Utilizing the quantum jump trajectory approach for characteristic functions.
  • Employing two energy measurements on the system and reservoir.
  • Drawing parallels with Kolmogorov backward and forward equations in classical stochastic theory.

Main Results:

  • The quantum jump trajectory method and the two-energy-measurement method are shown to be equivalent for calculating work distribution characteristic functions.
  • The microscopic underpinnings of the quantum jump trajectory method are elucidated.
  • A previously unrecognized equality related to heat transfer in these systems is identified.

Conclusions:

  • The equivalence of the forward and backward methods simplifies calculations in quantum thermodynamics.
  • The findings provide a deeper understanding of energy fluctuations in open quantum systems.
  • The revealed heat equality offers new avenues for theoretical and experimental investigations.