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Updated: Jul 6, 2026
09:25
NMR 15N Relaxation Experiments for the Investigation of Picosecond to Nanoseconds Structural Dynamics of Proteins
Published on: November 1, 2024
Occurrence of exponential relaxation in closed quantum systems
Christian Bartsch1, Robin Steinigeweg, Jochen Gemmer
1Fachbereich Physik, Universität Osnabrück, Barbarastrasse 7, D-49069 Osnabrück, Germany. cbartsch@uos.de
Summary
Exponential relaxation in closed systems occurs only when time scales separate and higher-order effects are negligible. The perturbation matrix structure, including Van Hove criteria, is crucial for this behavior.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter theory
Background:
- Understanding relaxation dynamics in closed quantum systems is fundamental.
- Previous models often assumed simplified conditions for exponential relaxation.
Purpose of the Study:
- To investigate the precise conditions for exponential relaxation in closed, finite quantum systems.
- To identify the role of perturbation structure in relaxation dynamics.
Main Methods:
- Utilized a time-convolutionless projection operator expansion.
- Analyzed specific initial states with vanishing inhomogeneity.
- Verified findings through numerical integration of the time-dependent Schrödinger equation.
Main Results:
- Exponential relaxation requires both a leading-order separation of time scales and negligible higher-order contributions.
- The perturbation matrix structure, not just strength, critically influences relaxation time.
- Identified specific criteria for perturbations, including adherence to the "Van Hove structure."
Conclusions:
- Exponential relaxation is a constrained phenomenon in closed systems, dependent on specific perturbation properties.
- The study provides a rigorous framework for predicting and understanding relaxation dynamics.
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