The inelastic scattering rates of quasiparticles in a two-dimensional d-wave superconductor, which arise from interactions with either acoustic phonons or other quasiparticles, are calculated within second order perturbation theory. We discover a strong enhancement of scattering with collinear momenta, brought about by the special kinematics of the two-dimensional fermions with Dirac-like spectrum near the nodes of the d-wave order parameter. In the case of a local instantaneous interparticle potential we find that either an RPA-type resummation of the perturbation series or an inclusion of non-linear corrections to the Dirac spectrum is called for in order to obtain a finite scattering rate in the limit ω/T→0. In either way, we find drastic changes in the scattering rate, as compared to the naively expected cubic temperature dependence.The inelastic scattering rates of quasiparticles in a two-dimensional d-wave superconductor, which arise from interactions with either acoustic phonons or other quasiparticles, are calculated within second order perturbation theory. We discover a strong enhancement of scattering with collinear momenta, brought about by the special kinematics of the two-dimensional fermions with Dirac-like spectrum near the nodes of the d-wave order parameter. In the case of a local instantaneous interparticle potential we find that either an RPA-type resummation of the perturbation series or an inclusion of non-linear corrections to the Dirac spectrum is called for in order to obtain a finite scattering rate in the limit ω/T→0. In either way, we find drastic changes in the scattering rate, as compared to the naively expected cubic temperature dependence.

Aug 28, 20210 citations

Perturbation theory of a many-fermion system

Robert William Jones, Franz Mohling

Nuclear Physics AAug 1, 197021 citations

A Unitary Fixed Point Away from Threshold: Momentum-Surface EFT for Strong Mixing

Lorenzo De Ros, Javier Reig Navarro

Radiative capture in a non-relativistic system can become non-perturbative even when the underlying transition interaction is weak. We demonstrate this mechanism in a simple quantum-mechanical two-channel model with a systematic power counting, where strong mixing between scattering and bound states develops in a narrow region around a finite momentum $k_0$ , leading to a perturbative violation of unitarity. In this regime, the enhanced contributions factorize, reducing the dynamics to a free scattering state interacting through a strong local coupling. Under RG evolution in the factorization scale, this local interaction approaches a unitary fixed point, analogous to that of systems with an anomalously large scattering length. This motivates an EFT organized around the finite-momentum surface $|\mathbf{k}|=k_0$ , describing fermions at unitarity with a linear dispersion relation. The resummation resulting from the EFT restores unitarity and provides a systematic expansion for both elastic scattering and radiative capture.Radiative capture in a non-relativistic system can become non-perturbative even when the underlying transition interaction is weak. We demonstrate this mechanism in a simple quantum-mechanical two-channel model with a systematic power counting, where strong mixing between scattering and bound states develops in a narrow region around a finite momentum $k_0$, leading to a perturbative violation of unitarity. In this regime, the enhanced contributions factorize, reducing the dynamics to a free scattering state interacting through a strong local coupling. Under RG evolution in the factorization scale, this local interaction approaches a unitary fixed point, analogous to that of systems with an anomalously large scattering length. This motivates an EFT organized around the finite-momentum surface $|\mathbf{k}|=k_0$, describing fermions at unitarity with a linear dispersion relation. The resummation resulting from the EFT restores unitarity and provides a systematic expansion for both elastic scattering and radiative capture.

arXiv:2609.25219Sep 21, 20260 citations

Perturbation theory of a many-fermion system

Robert William Jones, Franz Mohling, Richard L. Becker

Nuclear Physics AFeb 1, 197416 citations

k_0

, leading to a perturbative violation of unitarity. In this regime, the enhanced contributions factorize, reducing the dynamics to a free scattering state interacting through a strong local coupling. Under RG evolution in the factorization scale, this local interaction approaches a unitary fixed point, analogous to that of systems with an anomalously large scattering length. This motivates an EFT organized around the finite-momentum surface

|\mathbf{k}|=k_0

, describing fermions at unitarity with a linear dispersion relation. The resummation resulting from the EFT restores unitarity and provides a systematic expansion for both elastic scattering and radiative capture.