Adaptive resummation of Markovian quantum dynamics

Area of Science:

• Quantum Mechanics
• Theoretical Physics
• Computational Physics

Background:

• Markovian open quantum systems are fundamental in quantum mechanics.
• Existing methods for approximating their evolution often struggle with convergence, especially without small parameters.
• Accurate analytical approximations are crucial for understanding and predicting quantum phenomena.

Purpose of the Study:

• To introduce a novel method for obtaining analytic approximations to the evolution of Markovian open quantum systems.
• To ensure optimal convergence of these approximations, even when no small parameter is present.
• To demonstrate the method's efficacy on benchmark quantum problems.

Main Methods:

• The core method involves resumming a generalized Dyson series.
• This resummation technique is designed for optimal convergence.
• The approach is validated using two specific examples: spatial detection of a free particle and the Landau-Zener problem with dephasing.

Main Results:

• The developed approximations are shown to be asymptotically exact.
• The method achieves high accuracy, with errors on the per mill level.
• This accuracy is maintained across the entire parameter range tested.

Conclusions:

• The generalized Dyson series resummation provides a powerful tool for approximating open quantum system dynamics.
• The method offers a robust and accurate alternative to existing approximation techniques.
• This work has implications for the theoretical and computational study of quantum systems.