Effects of quantum potential on lower dimensional models of analogue gravity

Abstract

We address the issues related to the presence of the quantum potential term in a BEC on the observable Analogue Gravity systems. We show that the quantum potential term apparently gives rise to massive scalar excitations of length scales of the order O(1/ξ) in the lower dimensional space. Since, in 'analogue models' , there is a window for experimental observations generally in (2 + 1) or even lower dimensional space, one has to take proper account of the presence of these massive excitations to interpret the results.

Quantum potential induced UV-IR coupling in analogue Hawking radiation: From Bose-Einstein condensates to canonical acoustic black holes

“…a role of the order parameter of the system and thus |ψ(t, r)| 2 = n(t, r) is the density of the condensate, g = 4π 2 a/m parameterises the strength of the s-wave scattering (between different bosons in the gas) considered at the lowest order Born approximation with a being the s-wave scattering length and κ is some numerical prefactor of the nonlocal correction term corresponding to the specific coordinate system under consideration (for instance, κ = 1/2 for a 3-d Cartesian system [41]).…”

“…We have given a detailed description of the derivation of the above mentioned Gross-Pitaevskii equation with a non-local correction term in our previous paper [41]. In Eq.…”

“…( 24) would not have required a multiplication by any factor from left and hence, consequently, the large scale signature would have been completely absent in the expression of m. In our previous paper, see eqn. (23) of [41], we were able to construct a compact form to present the mass term because our formalism was in (3 + 1)-d Cartesian coordinates.…”

“…In our previous paper [41], we analyzed the situation in a flat background. But, for the large scale dynamics to see the curvature of spacetime, we must revert back systematically to the small length scales and this is exactly where our present analysis stands out to be very different from our previous analysis on flat spacetime.…”

“…In our previous paper [41], we have looked into the effect of the Lorentz-breaking quantum potential term in a different way. This is a term of immense importance in the context of analogue gravity because this gives rise to the dispersion relation which is used to present an 3 Refer to eqn.…”