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

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.