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

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.

arXiv comment31 pages, 4 figures, minor changes in ordering of sections, new references added

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• Duality between the quantum inverted harmonic oscillator and inverse square potentials
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• Fall-to-the-centre as a $\mathcal{P}\mathcal{T}$ symmetry breaking transition
• Influence Through Mixing: Hotspots as Benchmarks for Basic Black-Hole Behaviour
• On the EFT of Dyon-Monopole Catalysis