Cataloged from PDF version of article.Thesis (M.S.): Bilkent University, Department of Physics, İhsan Doğramacı Bilkent University, 2018.Includes bibliographical references (leaves 50-55).The quantum thermal radiation from a black hole (BH) known as “Hawking
Radiation” or “Black Hole Evaporation” results from studying quantum fields
in the curved space-time of the horizon of a BH. Experimentally, the radiation
is difficult if not impossible to be detected from a real black hole with a mass
much higher than that of our sun, since the Radiation temperature is substantially
below that of microwave background radiation.
However, in 1981 Unruh showed an analogy between the propagation of
sound waves in any convergent fluid flow and that of the quantum field in a
gravitational field. He showed that if the background fluid is accelerated to
higher than the speed of sound then it can develop a horizon (point of no return)
for the sound waves. This is the so-called the sonic BH. This horizon will
emit thermal radiation in terms of sound wave quanta (phonons) in an analogy
to the thermal radiation of black holes (Analogue Hawking Radiation) (AHR).
Bose-Einstein Condensates (BECs) can be used as a background fluid developing
a sonic horizon for the phonon modes propagating through its background
due to the very low temperature of the BEC.
Recently in 2014, Steinhauer has reported the observation of self-Amplifying
Hawking radiation from the realization of an accelerated BEC. The experiment
reported an exponentially growing signal of modes trapped between a BH and
white hole (WH) horizon, where the white hole is the point where sound cannot
enter. Experimental signatures of AHR are a growing oscillating perturbation
of the condensate mean density and a characteristic pattern in density-density
correlation functions. However, the former mentioned oscillations may result
from the dynamical instabilities of the classical mean field density. In this work, we were able to reproduce the experimental results of density
modulations in the mean field, and thus without AHR, using only the mean
field Gross-Pitaevskii equation (GPE) for the BEC. Furthermore, we include
the quantum fluctuation to study the density-density correlation function that
is in qualitative agreement with the experiment using the truncated Wigner approximation
(TWA). Finally, we then calculate the One Body Density Matrix
(OBDM) to distinguish condensed from non-condensed atoms using the Penrose
Onsager criterion. We are able to contribute to a discussion in the literature regarding
the quantum field or mean field origin of the mean density oscillations
in the experiment.by Ahmed Refat Mohamed Mohamed Ouf.M.S
