Time-Energy coherent states and adiabatic scattering

TL;DR

This paper introduces time-energy coherent states as a basis for analyzing adiabatic scattering, relating scattering matrix elements to frozen data, and highlighting the importance of energy shift over Wigner time delay.

Contribution

It establishes a novel framework using time-energy coherent states, relates scattering data to frozen data, and introduces the concept of energy shift in adiabatic scattering analysis.

Findings

Diagonal scattering matrix elements relate to frozen on-shell data.

Error in frozen data cannot be estimated by Wigner time delay alone.

Energy shift determines the outgoing state for a given incoming state.

Abstract

Coherent states in the time-energy plane provide a natural basis to study adiabatic scattering. We relate the (diagonal) matrix elements of the scattering matrix in this basis with the frozen on-shell scattering data. We describe an exactly solvable model, and show that the error in the frozen data cannot be estimated by the Wigner time delay alone. We introduce the notion of energy shift, a conjugate of Wigner time delay, and show that for incoming state $\rho(H_0)$ the energy shift determines the outgoing state.