Fall to the centre in atom traps and point-particle EFT for absorptive systems

• Published in: The journal of high energy physics Vol. 2018; no. 8; pp. 1 - 39
• Main Authors: Plestid, R., Burgess, C. P., O’Dell, D. H. J.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2018; Springer Nature B.V; SpringerOpen
• Subjects: Absorptivity; Atom traps; Boundary conditions; Charged particles; Classical and Quantum Gravitation; Effective Field Theories; Elementary Particles; Emitters; Field theory; High energy physics; Invariance; Nonperturbative Effects; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Renormalization Group; Scale invariance; String Theory; Wire; Effective Field Theories; Renormalization Group; Nonperturbative Effects
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2018)059

A bstract 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.