Fall to the Centre in Atom Traps and Point-Particle EFT for Absorptive Systems

TL;DR

This paper applies point-particle effective field theory to analyze atom interactions with a charged wire, revealing new absorptive boundary conditions and RG flow behaviors that differ from traditional self-adjoint cases, with potential experimental implications.

Contribution

It introduces a PPEFT approach to the fall to the center problem with absorption, identifying complex fixed points and novel boundary conditions in wire-atom systems.

Findings

Existence of complex fixed points for g > g_c

Absorptive boundary conditions lead to non-self-adjoint extensions

Potential experimental observation of scale invariance breaking

Abstract

Polarizable atoms interacting with a charged wire do so through an inverse-square potential, $V = - g/r^2$. This system is known to realize scale invariance in a nontrivial way and to be subject to ambiguities associated with the choice of boundary condition at the origin, often termed the problem of `fall to the center'. Point-particle effective field theory (PPEFT) provides a systematic framework for determining the boundary condition in terms of the properties of the source residing at the origin. We apply this formalism to the charged-wire/polarizable-atom problem, finding a result that is not a self-adjoint extension because of absorption of atoms by the wire. We explore the RG flow of the complex coupling constant for the dominant low-energy effective interactions, finding flows whose character is qualitatively different when $g$ is above or below a critical value, $g_c$. Unlike the self-adjoint case, (complex) fixed points exist when $g> g_c$, which we show correspond to perfect absorber (or perfect emitter) boundary conditions. We describe experimental consequences for wire-atom interactions and the possibility of observing the anomalous breaking of scale invariance.