Quantum vacuum effects in non-relativistic quantum field theory

TL;DR

This paper investigates how nonlinear dispersion relations and boundary conditions affect quantum vacuum energy in a nonrelativistic 1D rotating system, revealing a regularization-independent behavior with potential experimental implications.

Contribution

It provides a non-perturbative analysis of quantum vacuum effects in a nonlinear Schrödinger quantum field theory with rotation and boundary conditions, highlighting a regularization-independent phenomenon.

Findings

Quantum vacuum energy exhibits a maximum at a critical ring size.

The competition between interaction and rotation can be balanced at a specific scale.

Cut-off regularization affects short-distance behavior but not long-distance vacuum energy.

Abstract

Nonlinearities in the dispersion relations associated with different interactions designs, boundary conditions and the existence of a physical cut-off scale can alter the quantum vacuum energy of a nonrelativistic system nontrivially. As a material realization of this, we consider a 1D-periodic rotating, interacting non-relativistic 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 Schoedinger quantum field theory with a quartic interaction potential and perform the calculations non-perturbatively in the interaction strength by exploiting the nonlinear structure of the associated nonlinear Schroedinger equation. Calculations are done in both zeta-regularization, as well as by introducing a cut-off 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 maxima and the force changes sign. The inclusion of a cut-off 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.