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Canonically Consistent Quantum Master Equation.

Tobias Becker1, Alexander Schnell1, Juzar Thingna2,3

  • 1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany.

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Summary
This summary is machine-generated.

This study introduces a new quantum master equation for open quantum systems. It accurately predicts steady states and improves dynamics beyond weak coupling, refining existing methods.

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Area of Science:

  • Quantum physics
  • Open quantum systems
  • Theoretical chemistry

Background:

  • Accurate modeling of open quantum systems is crucial for understanding complex phenomena.
  • Existing quantum master equations, like Born-Markov and Redfield, have limitations beyond weak system-bath coupling.
  • Positivity violation is a persistent issue in some quantum master equation formulations.

Purpose of the Study:

  • To develop a new class of quantum master equations that accurately capture the asymptotic steady state of open quantum systems.
  • To improve the dynamical accuracy of reduced systems beyond the weak coupling limit.
  • To address and correct issues like positivity violation in quantum dynamics.

Main Methods:

  • Incorporating knowledge of the reduced steady state directly into the quantum master equation dynamics.
  • Using the exact mean-force Gibbs state to correct the Redfield quantum master equation for equilibrium cases.
  • Benchmarking the new method against the exact solution of the damped harmonic oscillator.

Main Results:

  • The proposed quantum master equations correctly reproduce asymptotic steady states beyond the weak coupling limit.
  • The method refines archetypal Born-Markov and Redfield equations, enhancing dynamical accuracy.
  • Positivity violation is corrected, although complete positivity is not guaranteed.

Conclusions:

  • This canonically consistent quantum master equation offers a new perspective for open quantum system theory.
  • The method yields a reduced density matrix more accurate than commonly used Redfield and Lindblad equations.
  • The approach maintains similar conceptual and numerical complexity to existing methods.