# 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.

## Keywords

Effective Field Theories Renormalization Group Nonperturbative Effects## Notes

### **Open Access**

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