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By C. J. Pethick, H. Smith

In 1925 Einstein anticipated that at low temperatures debris in a gasoline may perhaps all live within the comparable quantum kingdom. This gaseous kingdom, a Bose-Einstein condensate, was once produced within the laboratory for the 1st time in 1995 and investigating such condensates is among the so much energetic parts in modern physics. The authors of this graduate-level textbook clarify this interesting new topic when it comes to uncomplicated actual ideas, with out assuming distinctive previous wisdom. Chapters conceal the statistical physics of trapped gases, atomic houses, cooling and trapping atoms, interatomic interactions, constitution of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. challenge units also are incorporated.

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3P–3S for Na. If the potential in which the electron moved were purely Coulombic, these states would be degenerate. However the s-electron wave function penetrates the core of the atom to a greater extent than does that of the p electron, which is held away from the nucleus by virtue of its angular momentum. 3 Response to an electric field 53 more effective for a p electron than for an s electron, and as a result the s state has a lower energy than the p state. 42), and the difference increases with increasing Z.

The specific heat is then given by C αN k 1 + (α − 1) ζ(α) 2α+1 Tc T α . 70) This approximate form is useful even at temperatures only slightly above Tc . 3 Specific heat close to Tc Having calculated the specific heat at high temperatures and at temperatures less than Tc we now determine its behaviour near Tc . We shall see that it exhibits a discontinuity at Tc if α exceeds 2. By contrast, for a uniform Bose gas (for which α equals 3/2) the specific heat at constant volume is continuous at Tc , but its derivative with respect to temperature is discontinuous.

The source of the singular behaviour is the term proportional to δµ, since the chemical potential µ is identically zero for temperatures less than Tc and becomes non-zero (in fact, negative) above the transition. To determine the nature of the singularity it is sufficient to consider temperatures just above Tc , and evaluate the change (from zero) of the chemical potential, δµ, to lowest order in T − Tc . The non-zero value δµ of the chemical potential results in a contribution to the internal energy given by (∂E/∂µ)δµ.

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