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

  • R. Plestid
  • C. P. Burgess
  • D. H. J. O’Dell
Open Access
Regular Article - Theoretical Physics


Polarizable atoms interacting with a charged wire do so through an inverse-square potential, V = −g/r2. 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, gc. Unlike the self-adjoint case, (complex) fixed points exist when g > gc, 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.


Effective Field Theories Renormalization Group Nonperturbative Effects 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • R. Plestid
    • 1
    • 2
  • C. P. Burgess
    • 1
    • 2
  • D. H. J. O’Dell
    • 1
  1. 1.Department of Physics & AstronomyMcMaster UniversityHamiltonCanada
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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