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  • Letter
  • Open Access

Quantum vacuum effects in nonrelativistic quantum field theory

Matthew Edmonds1,2,*, Antonino Flachi3,2,†, and Marco Pasini4,2,‡

  • 1ARC Centre of Excellence in Future Low-Energy Electronics Technologies, School of Mathematics and Physics, University of Queensland, St Lucia, QLD 4072, Australia
  • 2Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan
  • 3Department of Physics, Keio University, 4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521, Japan
  • 4Department of Mathematics, Computer Science, and Physics, University of Udine, Via delle Scienze 206 I-33100 Udine, Italy and INFN, via Valerio 2 - 34127 Trieste, Italia

  • *m.edmonds@uq.edu.au
  • †flachi@phys-h.keio.ac.jp
  • ‡marco.pasini@uniud.it
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Phys. Rev. D 108, L121702 – Published 11 December, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L121702

Abstract

Nonlinearities in the dispersion relations associated with different interactions designs, boundary conditions, and the existence of a physical cutoff scale can alter the quantum vacuum energy of a nonrelativistic system nontrivially. As a material realization of this, we consider a one-dimensional-periodic rotating, interacting nonrelativistic setup. The quantum vacuum energy of such a system is expected to comprise two contributions: a fluctuation-induced quantum contribution and a repulsive centrifugal-like term. We analyze the problem in detail within a complex Schödinger quantum field theory with a quartic interaction potential and perform the calculations nonperturbatively in the interaction strength by exploiting the nonlinear structure of the associated nonlinear Schrödinger equation. Calculations are done both in zeta-regularization as well as by introducing a cutoff scale. We find a generic, regularization-independent behavior, where the competition between the interaction and rotation can be balanced at some critical ring size, where the quantum vacuum energy has a maximum and the force changes sign. The inclusion of a cutoff smoothes out the vacuum energy at small distance but leaves unaltered the long-distance behavior. We discuss how this behavior can be tested with ultracold atoms.

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Phys. Rev. D 108, L121702– Published 11 December, 2023
  • Received 25 August 2023
  • Accepted 11 October 2023
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