Trans planckian issues and analogue gravity from bec to acoustic black holes

Abstract

To account for the non local interactions in a Bose Einstein Condensate BEC an additionof a minimal correction term to the standard Gross Pitaevskii model effectively can make thehealing length or characteristic length decrease more rapidly with the increase of s wavescattering length a From emergent gravity perspectives this shrinking of via tuning athrough Feshbach resonance in principle does make the short wavelength i e high energy regime more accessible experimentally by pushing the Lorentz breaking dispersion even moretowards the UV side 1 The effects of the Lorentz breaking quantum potential term in theBEC dynamics on independent multiple scales can be captured through a UV IR coupling ofthe phonon excitation modes with the emergence of the massive minimally coupled free Klein Gordon field The analysis was argued on a 3 1 D flat spacetime where the presence of themass term gives a hint to cure the infrared divergences through a nonzero threshold for thelarge wavelength phonon excitations say Kz 0 modes as perceived by an observer sittingon x 56256 56320 y plane on lower dimensional models of emergent spacetimes 2 The analysis wasextended for a canonical acoustic black hole on a 3 1 D curved spacetime through presentingan emergent gravity model up to O 2 accuracy In our formalism the growth rate of thelarge wavelength 8216 secondary 8217 modes is found to hold the clue to extract the lost informationregarding the short wavelength 8216 primary 8217 1 modes And hence this can actually reveal therelative abundance of the originally Hawking radiated quanta in a 3 1 D canonically curvedbackground 3 Thiswaywe could address the trans Planckian issues in Physics via introducingthe analogue Planck length the healing length of the underlying cond mat system say BECin our case is the analogue of the Planck length p 10 56256 56320 35m in Gravity and shrinking this to an arb newline