Electromagnetic fluctuation and collective modes in relativistic bosonic superfluid in mixed dimensions

TL;DR

This paper investigates electromagnetic fluctuations and collective excitations in relativistic bosonic superfluids across different dimensions, revealing the existence of roton modes in 3+1D and their absence in 2+1D, with detailed dispersion analysis.

Contribution

It introduces a detailed analysis of collective modes in relativistic bosonic superfluids in mixed dimensions, including conditions for roton modes and dispersion relations.

Findings

Roton mode exists in (3+1) dimensions under specific conditions.

No roton-like excitation in (2+1) dimensions.

Derived dispersion relations for surface plasmons and asymptotic behaviors.

Abstract

In Gaussian approximation, we investigate the marginal electromagnetic fluctuation in models of charged relativistic bosonic superfluids in three and two spatial dimensions at zero temperature. The electromagnetism is modeled by the ordinary Maxwell term and the non-local pseudo-electrodynamics action in these dimensions respectively. We explore the collective excitations in these systems by integrating the superfluid velocity fields. In (3+1) dimensions, we derive the roton mode reminiscent of what was discovered in the context of the free relativistic Bose-Einstein condensate as a generalization of the Higgs mode and determine the necessary and sufficient condition for the roton to exist. In (2+1) dimensions, besides solving the dispersion relation for the surface plasmon, we prove there cannot be roton-like excitation in this model as opposed to its (3+1) dimensional counterpart, and additionally derive the asymptotic lines of the dispersion in the limits of long wavelength and short distance.