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Springer eBooks

Thermodynamic Analogies Between Bose-Einstein Condensation and Black-Body Radiation

Vı́ctor Romero-Rochı́n, Vanderlei Salvador Bagnato

Published Jan 1, 2003• 0 citations
Publisher
DOI
10.1007/978-1-4615-0207-4_16

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We present theoretical aspects concerning the thermodynamics of an ideal bosonic gas trapped by a harmonic potential. Working in the Grand Canonical ensemble we are able to properly identify the extensive thermodynamic variable equivalent to the volume and the intensive thermodynamic variable equivalent to the pressure. These are called the "harmonic volume" and the "harmonic pressure" and their physical meaning is discussed. With these variables, the problem of Bose-Einstein condensation is studied in terms of the behavior of the corresponding equation of state and in terms of measurable susceptibilities such as the heat capacities, the isothermal compressibility and the coefficient of thermal expansion. From the analysis, an interesting analogy with Black-Body radiation emerges, showing that at and below the critical temperature, the non-condensate fraction of atoms behaves thermodynamically like a gas of massless particles.
We extend the Gross-Pitaevskii equation to incorporate the effect of quantum fluctuations onto the flow of a weakly interacting Bose-Einstein condensate. Applying this framework to an analog black hole in a quasi-one-dimensional, transonic flow, we investigate how acoustic Hawking radiation back-reacts on the background condensate. Our results point to the emergence of stationary density and velocity undulations in the supersonic region (analogous to the black hole interior) and enable to evaluate the change in upstream and downstream Mach numbers caused by Hawking radiation. These findings provide new insight into the interplay between quantum fluctuations and analog gravity in Bose-Einstein condensates.
Inspired by a recent experiment by Steinhauer and co-workers, we present a simple model which describes the formation of an acoustic black hole in a Bose-Einstein condensate, allowing an analytical computation of the evolution in time of the corresponding density-density correlator. We show the emergence of analog Hawking radiation out of a "quantum atmosphere" region significantly displaced from the horizon. This is quantitatively studied both at T=0 and even in the presence of an initial temperature T, as is always the case experimentally.