Construction of (1+1)D Analogue gravity model of BEC with specifi c velocity field

Abstract

The aim of the thesis is to construct a (1+1)D analogue model of gravity for a BEC. Analogue gravity is observed in such models based on a background pro file and that is where it is needed to know what all it takes to experimentally get a particular velocity pro file. In this work we have tried to develop a model with hyperbolic tangent velocity pro file and indicate the particular con fining potential which will result in such pro file. Here we derive what PDE the fluctuation of velocity potential follows at independent order of length scale in a stationary, non-homogeneous Bose-Einstein condensation. A global solution of this model will help continuous velocity tracking backward from infi nity to the analogue event horizon in such system . Solutions of these PDEs i.e fluctuation fi elds, are signifi cant to calculate Hawking radiation in analogue model.