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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.

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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.