Bose condensate

Ndi g5Ceo.i5Cu04, Lao.i8Sro.i5Cu04, Possible observation of Bose condensation by Mossbauer emission spectroscopy on Cu... 

Zn) and Ga( Zn) isotopes, the transition to the superconducting state leads to a change of the electron density on the metal sites, above the transition the center shift is determined by SOD, below by the influence of Bose condensation, a correlation between the change in electron density and the temperature of the transition to the superconducting state is found... 

In [10] a new type of a-cluster wave function describing an a-particle Bose condensed state was introduced,... 

For nonvanishing A in Eq. (1) the color symmetry is broken. Two of the three quark color degrees of freedom are coupled to bosonic Cooper pairs in the color antitriplet state which can form a Bose condensate.One can combine the chemical potentials Hu, Hd of u and d quarks by introducing Hq = (hu + Hd)/2 and hi = (hu — Hd)/% as the Lagrange multipliers related to, respectively, the quark number density nq and the isospin asymmetry n/. In thermal equilib-... 

Fig. 8.6. Schematic of a proposed configuration for the production of conditions for Bose-Einstein condensation of positronium using a pulsed, brightness-enhanced positron beam (see text for details). Reprinted from Physical Review B 49, Platzman and Mills, Possibilities for Bose condensation of positronium, 454-458, copyright 1994 by the American Physical Society.

Ultracold neutral plasmas may be produced by laser cooling and trapping of different types of neutral atoms [105] such as calcium, strontium, rubidium, cesium etc., by photoionizing Bose condensates [106] and also by spontaneous ionization of dense Rydberg atoms [107,108]. A review on ultracold neutral plasmas due to Killan et al. [61] gives an excellent disposition on the subject. 

The FrBhlich vibrational model does not address itself directly to ihe problem of the interaction between an external EM-field and the dissipative subsystem, but rather to ihe internal redistribution of photons and phonons upon excitation of the Bose-condensation state. In particular, the frequencies, oo, of the (coherent) vibrations are availalbe only within the framework of a... 

This obtainsonly if y in the sum on the rhs of Eq. (23) closely approachessuch that the number of photons in state 1, of lowest frequency a>, becomes much larger than any other number n, as energy pumping, S = ES, increases. This condensation of the photons into the lowest-frequency state is formally equivalent to the Bose condensation (138), and y, Eq. (18), plays a role analogous to the chemical potential in the Einstein condensation of a Bose-Einstein gas. 

If we now suggest a correspondence between the formal model of FrBhlich and the dissipative subsytem(s) and the equilibrium system discussed in Section 3.1, one may consider the processes which are operative, including interactions with an external EM field, as depicted schematically in Fig. (7). No compelling experimental evidence exists that the equilibrium system made up of the ordinary aqueous dielectrics, Sections 2.3 to 2.7, shows the Bose-condensation which arises in the Frtfhlich theory. In fact, even systems of sufficient complexity to exhibit low-lying vibrational modes and structural subtlety to play a direct role in biochemical reactions at the interface between biochemical and biological processes [a-chymotrypsin (90-91), lysozyme (92 ) and DNA (93)], fail to show features not predicted by the methods of Section 2. Since collisional perturbations, even when non-reactive, will provide a source of the energy inputs, S, this implies the absence of non-linear terms (x=0,A=0), Eq. (14), for such systems. 

Occurence of the Bose-condensation, Eq. (24), into the vibrational mode v-, implies vibrational excitation of the system into states v- = 1,2,.. While the intensity of absorption-emission lines gives information only about the difference in the number of molecules per cm in the upper and lower states connected by the photon, the intensities of Raman lines, in elastic light scattering at frequencies (uq - mn)> permit determination of the ratio of the number of molecules per cm in the excited state n and the lower state m. This ratio is given by (142) ... 

The preceeding discussion has dealt with the qualitative effects of the Bose-condensation on the attenuation function, ctDig(m)- In general, we require the frequencies and matrix elements p and PmnI for all the possible transitions, m ->-n, among the vibrational states postulated by FrBhlich, in order to characterize the resulting absorption spectra, Eq. (27),... 

The steady state results are shown in Figure 12. For c2 the single mode gets strongly excited, i.e. the energy is preferentially channeled into this mode (Bose condensation-like excitation). 

A description of the rather complicated transport formalism is beyond the scope of this article and will be omitted. For our purposes the important result is the excitation and stabilization of a single mode. Contrary to the results of the other models with a Bose condensation-like excitation, the coherently excited mode is the mode with the highest and not with the lowest frequency. 

Spinon states created by (+(k) have bare energies G(k), having a V-shape zero minimum at k = ko. Bose condensation results in an antiferromagnetic (AF) order of wave vector Q = 2ko = (f, f ) Within the lattice Brillouin zone (BZ) there are four inequivalent possibilities for k0 ( , and (, — ), thus introducing a broken symmetry. One has [4] ... 

The Bose condensation has been observed on Earth in laser-cooled (Chu,10 Cohen-Tannouji,11 and Phillips12) collections of alkali atoms in ultra-high vacuum at very low temperatures in 1995 (Cornell13 and... 

A superconductor exhibits perfect conductivity (See Section 7.2) and the Meissner effect (See Section 7.3) below some critical temperature, Tc. The transition from a normal conductor to a superconductor is a second-order, phase-transition which is also well-described by mean-field theory. Note that the mean-field condensation is not a Bose condensation nor does it require and energy gap. The mean-field theory is combined with London-Ginzburg-Landau theory through the concentration of superconducting carriers as follows ... 

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