By L. Pitaevskii, S. Stringari
This booklet is an introductory textual content to the physics of Bose-Einstein condensation. This phenomenon, first estimated through Einstein in 1925 has been discovered experimentally in 1995 in a impressive sequence of experiments whose significance has been famous by means of the award of the 2001 Nobel Prize in Physics. The condensate is admittedly a brand new nation of topic, the place quantum-mechanical wave services of atoms behave as coherent subject waves within the comparable means as coherent gentle waves relating to a laser. The authors supply a theoretical presentation of the most strategies underlying the physics of dilute atomic gases in stipulations of tremendous low temperatures the place quantum results play a very important position. the most attempt is dedicated to dialogue of the suitable theoretical features exhibited by means of those systms, corresponding to the concept that of order parameter, lengthy diversity order, superfluidity and coherence. The mathematical formalism is gifted in a kind handy for useful use. The booklet develops the speculation of Bose gases ranging from the pioneering Bogoliubov technique and offers certain emphasis to the recent actual gains exhibited by way of non-uniform gases that are produced within the fresh experiments with magnetic and optical traps. those beneficial properties contain the selection of the equilibrium profiles, the collective oscillations, the mechanism of the growth of the gasoline after liberating the capture, the interference styles got by way of overlapping condensates, the rotational houses revealing the results of superfluidity the Josephson-like phenomena assocaited with the coherence of the section, the past suggest box phenomena exhibited via quantum gases in stipulations of diminished dimensionality. The e-book additionally discusses the alaogies and adjustments with the physics of ""classical"" superfluids like liquid helium and introduces a few of the significant good points of trapped Fermi gases at low temperature, stating the results of superfluidity.
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Extra info for Bose-Einstein Condensation
Flo\y). Idealizatioll of Ihe procpss ('onsists in assuming tho :\Iach number to equal zero within this rpgion of speeds because small disturbancps (SOlllld oscillations) propagatp ill c\]l incompressihle l1llic! at an inlinitely high spope! ane!. conspqupntly, the ratio of the f1ight speec! to that of sOllne! tOllds to zero. Modern craft hayp high airspeeds at which flow O\'PI' them is attended by a considerahle changp in the rrpSSllre and. cOllseql1elltly. by a substantial change in thp densit~, all(1 temperature.
1. Basic Information from Aerodynamics 57 The values of c yo are usually very small even for asymmetric configurations (at low 6e and a) and equal zero exactly for craft with axial symmetry. 6 » Static Lateral Stability To analyse the lateral stability of a craft, one must consider jointly the nature of the change in the rolling and sideslip angles upon thesimultaneous action of the perturbing rolling j1:y and yawing Mit moments. If after the stopping of sllch action these angles diminish, tending to their initial values, we have static lateral stability.
The position of a craft relative to this coordinate system is determined by three angles: the yawing (course) angle ~J, the pitching angle &, and the rolling (banking) angle "(. The angle ~ is formed by the projection of the longitudinal body axis Ox onto the horizontal plane x~Oy~ (Ox *) and the axis Ox~; this angle is positive if the axis Ox~ coincides with the projection of Ox* by clockwise rotation about the axis Oy~. The angle & is that between the axis Ox and the horizontal plane x~Oz; and will be positive if this plane is below the longitudinal -------- - - - - - -..