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Related Experiment Video

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Accuracy of perturbative master equations.

C H Fleming¹, N I Cummings

¹Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 27, 2011

Summary

This summary is machine-generated.

Accurate solutions for open quantum systems require higher-order master equations than typically used. This study reveals inaccuracies in steady states and positivity violations from standard order-2n master equations.

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Area of Science:

Quantum mechanics
Open quantum systems
Theoretical physics

Background:

Master equations are used to describe the dynamics of open quantum systems.
Perturbative expansions are common for system-environment interactions.
Existing master equations may lead to inaccuracies.

Purpose of the Study:

To investigate the required order of master equations for accurate full-time solutions in open quantum systems.
To identify and demonstrate inaccuracies arising from lower-order master equations.
To assess the impact on commonly used master equation formalisms.

Main Methods:

Analysis of master equations with perturbative expansions.
Derivation of required master equation order for specific accuracy levels.
Examination of steady-state and positivity properties.
Comparison with exact solutions in a specific model.

Main Results:

Full-time solutions of order-2n accuracy necessitate an order-(2n+2) master equation.
Order-2n master equations exhibit order-2n inaccuracies in steady states.
Positivity violations of order-2n occur with order-2n master equations.
These inaccuracies are demonstrated in a solvable model.

Conclusions:

Standard master equations (e.g., Born-Markov, Redfield) may not provide sufficient accuracy for coupling-sensitive properties.
Higher-order master equations are crucial for reliable predictions in open quantum systems.
The findings impact the validity of results derived from common theoretical frameworks.