Geometry and entanglement in the scattering matrix

Francesco Bariani, Davide Sarchi, Iacopo Carusotto

We develop a scattering-matrix formalism to numerically study the resonant scattering of light on generic assemblies of atoms. Protocols to eliminate the artifacts of the method and extract physical information from the numerical data are discussed. The efficiency of the approach is validated by comparing its predictions with analytical results in simple geometries.Paper withdrawn.

K. Mishima, Michitoshi Hayashi, S. H. Lin

Bahaa Al Sayegh, Wissam Chemissany

We investigate the critical behavior and real-time scattering dynamics of the interacting $φ^4$ quantum field theory in (1+1)-dimensions using uniform matrix product states (uMPS) and the time-dependent variational principle (TDVP). A finite-entanglement scaling analysis at $λ= 0.8$ bounds the critical mass-squared to $μ_c^2 \in ]-0.2595,-0.2594[$ and provides a quantitative map of the symmetric, near-critical, and spontaneously broken regimes. Using these ground states as asymptotic vacua, we simulate two-particle collisions in a sandwich geometry and extract the elastic scattering probability $P_{11\to 11}(E)$ and Wigner time delay $Δt(E)$ using a sandwich geometry protocol. We find strongly inelastic scattering in the symmetric phase ($P_{11\to 11} \simeq 0.712$, $Δt \simeq -158$ for $μ^2 = +0.2$) and almost perfectly elastic collisions in the spontaneously broken phase ($P_{11\to 11} \simeq 1$, $Δt \simeq -108$ for $μ^2=-0.1$ and $P_{11\to 11} \simeq 1$, $Δt \simeq -177.781$ for $μ^2=-0.5$). Crucially, the scattering protocol exhibits a distinctive divergence near the critical coupling; we show that this behavior serves as a dynamical signature of the quantum critical point, arising directly from the closing of the mass gap. These results demonstrate that TDVP-based uMPS can effectively probe nonperturbative scattering and critical dynamics in lattice field theories with controlled entanglement truncation.

Stephen S. Bullock, Gavin K. Brennen

Bahaa Al Sayegh, Wissam A Chemissany

We investigate the critical behavior and real-time scattering dynamics of the interacting 𝜙4 quantum field theory in (1+1) dimensions using uniform matrix product states (uMPS) and the time-dependent variational principle (TDVP). A finite-entanglement scaling analysis at 𝜆=0.8 bounds the critical mass-squared to 𝜇2𝑐∈]−0.2595,−0.2594[ and provides a quantitative map of the symmetric, near-critical, and spontaneously broken regimes. Using these ground states as asymptotic vacua, we simulate two-particle collisions in a sandwich geometry and extract the elastic scattering probability 𝑃11→11⁡(𝐸) and Wigner time delay Δ⁢𝑡⁡(𝐸) using a sandwich geometry protocol. We find strongly inelastic scattering in the symmetric phase (𝑃11→11≃0.712, Δ⁢𝑡≃−158 for 𝜇2=+0.2) and almost perfectly elastic collisions in the spontaneously broken phase (𝑃11→11≃1, Δ⁢𝑡≃−108 for 𝜇2=−0.1 and 𝑃11→11≃1, Δ⁢𝑡≃−177.781 for 𝜇2=−0.5). Crucially, the scattering protocol exhibits a distinctive divergence near the critical coupling; we show that this behavior serves as a dynamical signature of the quantum critical point, arising directly from the closing of the mass gap. These results demonstrate that TDVP-based uMPS can effectively probe nonperturbative scattering and critical dynamics in lattice field theories with controlled entanglement truncation.

Z. AskariPour Ravari, Z. Riazi

We present a theoretical study of the evolution of polarization entanglement and quantum coherence in 511 keV photon pairs produced by para-positronium decay during successive Compton scattering events. We start with a maximally entangled Bell state and employ the generalized Stokes-Mueller formalism to derive the two-photon density matrix following single-, double-, and triple-Compton scattering, explicitly considering both polar and azimuthal scattering geometries. Using this framework, we quantify the degradation of quantum correlations through concurrence (as a measure of entanglement) and the $l_1$-norm (as a measure of coherence). Our results demonstrate that entanglement is highly sensitive to the scattering geometry and disappears near right-angle scattering, while quantum coherence remains finite even in regimes where entanglement vanishes completely. These findings provide a unified description of polarization-dependent decoherence in annihilation photon pairs and clarify the distinct roles of entanglement and coherence in realistic two-photon interactions. These results are relevant for quantum-enhanced positron emission tomography and highlight the persistence of quantum resources in scattering-dominated media.