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Updated: Dec 14, 2025

15N CPMG Relaxation Dispersion for the Investigation of Protein Conformational Dynamics on the µs-ms Timescale
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Renormalization group as a Koopman operator.

William T Redman1

  • 1Interdepartmental Graduate Program in Dynamical Neuroscience, University of California, Santa Barbara, California 93106, USA.

Physical Review. E
|July 22, 2020
PubMed
Summary
This summary is machine-generated.

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Koopman operator theory connects directly to the renormalization group, enabling computation of critical exponents for classical spin systems without assuming translational invariance. This offers a new data-driven approach to renormalization group analysis.

Area of Science:

  • Statistical Mechanics
  • Dynamical Systems Theory
  • Renormalization Group Theory

Background:

  • The renormalization group (RG) is a powerful framework for understanding critical phenomena and universality.
  • Koopman operator theory provides a data-driven approach to analyzing nonlinear dynamical systems.

Purpose of the Study:

  • To establish a direct connection between Koopman operator theory and the renormalization group.
  • To demonstrate the computation of critical exponents using this unified framework.
  • To expand the applicability of RG methods to systems lacking translational invariance.

Main Methods:

  • Utilizing Koopman operator theory to analyze classical spin systems.
  • Computing critical exponents (e.g., η and δ) and their ratios from single observables.

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  • Applying the framework without assuming translational invariance.

    • Main Results:

    • A direct relationship between Koopman operator theory and the renormalization group was established.
    • Critical exponents and their ratios for classical spin systems were computed.
    • The method successfully identified universality classes.

    Conclusions:

    • The integration of Koopman operator theory and RG offers a novel, data-driven approach to critical phenomena.
    • This approach broadens the scope of RG applicability, particularly for systems without translational invariance.
    • It provides new avenues for identifying RG fixed points and their associated directions.