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Intermediate-times dilemma for open quantum system: Filtered approximation to the refined weak-coupling limit.

Marek Winczewski1, Antonio Mandarino1,2, Gerardo Suarez1

  • 1International Centre for Theory of Quantum Technologies, <a href="https://ror.org/011dv8m48">University of Gdańsk</a>, Jana Bażyńskiego 1A, Gdańsk, 80-309, Poland.

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The filtered approximation (FA) provides accurate dynamics for open quantum systems across intermediate timescales, overcoming limitations of existing secular and quasisecular master equations. This new non-Markovian approach ensures completely positive dynamics.

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Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Condensed matter physics

Background:

  • The Davies-GKSL secular Markovian master equation is widely used for open quantum systems but fails at short timescales.
  • Quasisecular master equations work for short times but not for longer intervals.
  • Existing methods struggle with intermediate timescales (the "gray zone") or are computationally intensive.

Purpose of the Study:

  • To develop a novel approach for accurately describing the dynamics of open quantum systems in the intermediate-time regime.
  • To overcome the limitations of the Davies-GKSL and quasisecular master equations.
  • To provide a mathematically well-structured and computationally efficient method for quantum dynamics.

Main Methods:

  • Introduced the filtered approximation (FA) to the refined weak-coupling limit.
  • Developed a non-Markovian master equation based on the FA.
  • Applied the FA to spin-boson and qutrit-boson systems exhibiting multiple timescales.

Main Results:

  • The FA successfully captures quantum system dynamics in the intermediate-time regime, a region not well-described by previous methods.
  • The derived non-Markovian equation guarantees completely positive dynamics.
  • Demonstrated the FA's effectiveness in systems with distinct short and long timescales, such as spin-boson and qutrit-boson models.

Conclusions:

  • The filtered approximation offers a robust and accurate method for describing open quantum system dynamics across various timescales.
  • This approach bridges the gap left by secular and quasisecular approximations, particularly in the challenging intermediate-time regime.
  • The FA provides a computationally feasible and mathematically sound alternative for complex quantum dynamics.