Bose fluid

For completeness, a brief summary of the PI equilibrium structures at the pair level for the homogeneous and isotropic Bose fluid, composed of zero-spin particles, is given here. The reader is referred to Ref. 36 for further details. For the sake of simplicity, the primitive propagator Eq. (19) is used in the following discussion. Thus, the grand partition function for the fluid under the action of a nonlocalizing field T can be written as... 

Clearly, parallel developments and results dealt with in other parts of this section hold for the case of this Bose fluid. This implies, for example, that accurate/ estimates could be computed via an OZ2 equation for centroids. This further extension still remains unexplored, as no related calculations have been reported so far. 

In a simplistic and conservative picture the core of a neutron star is modeled as a uniform fluid of neutron rich nuclear matter in equilibrium with respect to the weak interaction (/3-stable nuclear matter). However, due to the large value of the stellar central density and to the rapid increase of the nucleon chemical potentials with density, hyperons (A, E, E°, E+, E and E° particles) are expected to appear in the inner core of the star. Other exotic phases of hadronic matter such as a Bose-Einstein condensate of negative pion (7r ) or negative kaon (K ) could be present in the inner part of the star. 

The global Hamiltonian for a Bose quantum fluid written in the hydrodynamic form [19] is... 

Honey of Boses Moisten 2 troy ounces red rose, in moderately fine powder, with fluid ounce diluted alcohol pack it firmly in a conical glass percolator, and displace 6 fluid drachms with diluted alcohol. Beserve this, and percolate i pint more evaporate this bist by a water-bath to 10 fluid drachms, add the reserved liquid, and mix with 25 troy ounces clarified honey. ( CT. S. Ph.) Added to water, it makes an elegant astringent wash and gargle for foul and tender gums, sore mouth, sore t oat, relaxed uvula, ic. 

Boses.— Horse, 1 to 3 pints.—Cattle, 1 to 8 pints.— Sheep, 5 to 15 fluid ounces.—Fio, 5 to 15 fluid ounces.— Doo, 2 to 5 fluid ounces. 

Boses.— Hobse,6 to 8 fluid ounces.—8 to 10 fluid ounces.—Sheep, 2 to 4 fluid ounces.—Pio, 1 to 2 fluid ounces.—Doo, to 1 fluid ounce. 

J.-P. Hansen, D. Levesque, and D. Schiff, The fluid-solid phase transition of a hard sphere Bose system at zero temperature, Phys. Rev. A 3, 775-780 (1971). 

At very low pressures and temperatures close to 0 K, a fourth state of matter has been discovered. This is the Bose-Einstein condensate. Eric A. Cornell obtained the Nobel prize in 2001 for his work on the Bose-Einstein condensate and fourth state of matter. The critical point of the pure substance can be seen in Figure 2.1. Beyond this point, the liquid and gas are indistinguishable from each other and exist as a fluid. Are there similar critical points at the end of the fusion curve and sublimation curves The PVT and other phenomena at very low pressures and temperatures are subjects of exploratory research. The critical point may also be viewed as the highest pressure and temperature at which a pure chemical species is observed to exist in vapor/liquid equilibrium [2]. The vertical line in Figure 2.1 is an isotherm, and a horizontal line in Figure 2.1 is an isobar. The solid lines in Figure 2.1 indicate a... 

Figure 19 l ire viscous force of a single tactile piston vs. the piston moving velocity at different electric fields from 0 to 2.0 kV/mm. The TR fluids is Rheobay TP A1 3565 ERF from Bayer AG. Reproduced with permission from G. J. Monkman, S. Egersdorfer, II. Bose, and M. Baumann, J. Phys. D Appl. Phys. 37 (2004)794... 

It is tempting to identify the superfluid and normal fluid components of He II with the atoms of the condensate and excited states, respectively, of an ideal Bose-Einstein gas, but this, too, turns out to be a gross oversimplification. Nonetheless, it is clear that Bose-Einstein statistics do play an essential role in determining the properties of the liquid. If one calculates the Bose-Einstein condensation temperature of an ideal gas with the same density and atomic mass as liquid " He, one finds 7 3.1 K, and the difference between this value and 7 may plausibly be ascribed to the influence of the interatomic forces. The presence of a condensate of " He atoms in the zero momentum state has recently been confirmed by inelastic neutron scattering measurements. As shown in Fig. 14, the condensate fraction rises from zero at Tx towards an asymptotic limit of about 14% at low temperatures. This departure from the approximately 100% condensate characteristic of an ideal gas for r 7c is an expected consequence of the non-negligible interatomic forces. Of couse, as already noted in Fig. 13, the superfluid component does form 100% of the liquid at 7 = 0 and it cannot, therefore, be directly identified with the condensate fraction. 

The bosonic order parameter may be, as a first approximation, set to unity, (i/ (r)) = 1, within the Tisza s phenomenological two-fluid model of Bose-Einstein condensation [100] ... 

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