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Related Experiment Video

Updated: Jan 16, 2026

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels
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Dynamic and geometric shifts in wave scattering.

Konstantin Yu Bliokh1,2,3, Zeyu Kuang4, Stefan Rotter4

  • 1Donostia International Physics Center (DIPC), Donostia-San Sebastián 20018, Spain.

Reports on Progress in Physics. Physical Society (Great Britain)
|September 25, 2025
PubMed
Summary
This summary is machine-generated.

This study extends the geometric-dynamic phase decomposition to wave scattering. It reveals that expectation value shifts in observables during scattering can be separated into geometric and dynamic parts.

Keywords:
Berry phasegeometric phasesoptical beam shiftsoptical forceswave scatteringwavefront shaping

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Area of Science:

  • Physics
  • Wave Scattering
  • Quantum Mechanics

Background:

  • The geometric-dynamic phase decomposition is fundamental in wave evolution.
  • This concept is crucial in quantum mechanics, optics, and condensed matter physics.

Purpose of the Study:

  • To extend the geometric-dynamic decomposition from wave-evolution phase to wave scattering.
  • To analyze shifts in expectation values of observables in wave scattering problems.

Main Methods:

  • Utilized a unitary scattering matrix and the generalized Wigner-Smith operator (GWSO).
  • Investigated gradients of the scattering matrix with respect to conjugate variables.
  • Decomposed GWSO and expectation-value shifts into gauge-invariant dynamic and geometric parts.

Main Results:

  • Demonstrated that expectation value shifts in wave scattering admit gauge-invariant decompositions.
  • Identified dynamic and geometric contributions related to gradients of scattering matrix eigenvalues and eigenvectors.
  • Illustrated the theory with examples like frequency shifts, momentum shifts, optical forces, beam shifts, and Wigner time delays.

Conclusions:

  • The generalized Wigner-Smith operator provides a unifying framework for wave scattering.
  • This framework illuminates the interplay between geometry and dynamics in diverse physical systems.
  • The theory is applicable to a broad range of wave scattering phenomena.