Dynamic and geometric shifts in wave scattering
Year: 2025
Type: article
Abstract: Since Berry’s pioneering 1984 work, the separation of geometric and dynamic contributions in the phase of an evolving wave has become fundamental in physics, underpinning diverse phenomena in quantum mechanics, optics, and condensed matter. Here we extend this geometric-dynamic decomposition from the wave-evolution phase to a distinct class of wave scattering problems, where observables (such as frequency, momentum, or position) experience shifts in their expectation values between the input and output wave states. We describe this class of problems using a unitary scattering matrix and the associated generalized Wigner–Smith operator (GWSO), which involves gradients of the scattering matrix with respect to conjugate variables (time, position, or momentum, respectively). We show that both the GWSO and the resulting expectation-values shifts admit gauge-invariant decompositions into dynamic and geometric parts, related respectively to gradients of the eigenvalues and eigenvectors of the scattering matrix. We illustrate this general theory through a series of examples, including frequency shifts in polarized-light transmission through a time-varying waveplate (linked to the Pancharatnam–Berry phase), momentum shifts at spatially varying metasurfaces, optical forces, beam shifts upon reflection at a dielectric interface, and Wigner time delays in 1D scattering. This unifying framework illuminates the interplay between geometry and dynamics in wave scattering and can be applied to a broad range of physical systems.
Source: Reports on Progress in Physics
Authors: Konstantin Y Bliokh, Zeyu Kuang, Stefan Rotter
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,680
Awards: G1593789316, G5832273713, G715470558
OpenAlex ID: W4414495895