Spin-textures of medium-body boson systems with trapped spin-f cold atoms.

The spin-textures of bound medium-body systems with spin-[Formula: see text] atoms ([Formula: see text]) have been studied. The Hamiltonian is assumed to be dominated by the two-body interaction favoring parallel spins. The system with particle number [Formula: see text] and [Formula: see text] is first chosen, and the Hamiltonian is exactly diagonalized by using Fock-states as basis-states, thereby all the eigenenergies and eigenstates are obtained and a detailed analysis is made. Then the cases with [Formula: see text] and [Formula: see text] are further studied. Since the total spin S is conserved, the eigenstates having the same S form an S-group. Let the lowest (highest) energy state of an S-group be called a bottom-state (top-state). We found that all the bottom-states are bipartite product states with constituent states describing fully polarized subsystems containing [Formula: see text] and [Formula: see text] ([Formula: see text]) particles, respectively. For two bottom-states different in [Formula: see text], the one with a larger [Formula: see text] is higher. For two having the same [Formula: see text], the one with a smaller S is higher. Whereas all the top-states are found to be essentially a product state of the pairs, in each pair the two spins are coupled to [Formula: see text] if the strength of the [Formula: see text]-channel is more repulsive than the others. For the states belonging to an S-group, the higher one would contain more pieces. As the energy goes up, larger pieces (those containing more than two particles) will disappear.

Spin structures of the ground states of four body bound systems with spin 3 cold atoms.

We consider the case that four spin-3 atoms are confined in an optical trap. The temperature is so low that the spatial degrees of freedom have been frozen. Exact numerical and analytical solutions for the spin-states have been both obtained. Two kinds of phase-diagrams for the ground states (g.s.) have been plotted. In general, the eigen-states with the total-spin S (a good quantum number) can be expanded in terms of a few basis-states [Formula: see text]. Let [Formula: see text] be the probability of a pair of spins coupled to [Formula: see text], and 6 in the [Formula: see text] state. Obviously, when the strength [Formula: see text] of the [Formula: see text]-channel is more negative, the basis-state with the largest [Formula: see text] would be more preferred by the g.s.. When two strengths are more negative, the two basis-states with the two largest probabilities would be more important components. Thus, based on the probabilities, the spin-structures (described via the basis-states) can be understood. Furthermore, all the details in the phase-diagrams, say, the critical points of transition, can also be explained. Note that, for [Formula: see text], [Formula: see text] is completely determined by symmetry. Thus, symmetry plays a very important role in determining the spin-structure of the g.s..

A stable spin-structure found in a 3-body system with spin-3 cold atoms and its role in N-body condensates.

We have found a stable spin-structure of N [Formula: see text] 3 system in which three spin-3 atoms are trapped and coupled to total spin S [Formula: see text] 3. We have proved that a pair of this structure is nearly an exact solution for N [Formula: see text] 6 systems in a very broad district in the parameter-space. Comparing with the well-known singlet pairs, this pair is a more promising candidate to serve as a building block for large N systems with spin-3 atoms. This is because the spin-structure of the latter can be modified depending on the interactions to reduce the energy while the singlet pairs can not. In fact, we have proved that, for a specific set of strengths (a point in the parameter-space) the product state based on this pair is an exact solution of the N-body Hamiltonian. Thus, in the neighborhood of this point, the product state will appear as an approximate solution. However, how broad this neighborhood would be remains to be clarified.

Spin-structures of the Bose-Einstein condensates with three kinds of spin-1 atoms.

We have performed a quantum mechanic calculation (including solving the coupled Gross-Pitaevskii equations to obtain the spatial wave functions, and diagonalizing the spin-dependent Hamiltonian in the spin-space to obtain the total spin state) together with an analytical analysis based on a classical model. Then, according to the relative orientations of the spins SA, SB and SC of the three species, the spin-structures of the ground state can be classified into two types. In Type-I the three spins are either parallel or anti-parallel to each other, while in Type-II they point to different directions but remain to be coplanar. Moreover, according to the magnitudes of SA, SB and SC, the spin-structures can be further classified into four kinds, namely, p + p + p (all atoms of each species are in singlet-pairs), one species in f (fully polarized) and two species in q (a mixture of polarized atoms and singlet-pairs), two in f and one in q, and f + f + f. Other combinations are not allowed. The scopes of the parameters that supports a specific spin-structure have been specified. A number of spin-structure-transitions have been found. For Type-I, the critical values at which a transition takes place are given by simple analytical formulae, therefore these values can be predict.

Singularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates.

An approach is proposed to solve the coupled Gross-Pitaevskii equations (CGP) of the 3-species BEC in an analytical way under the Thomas-Fermi approximation (TFA). It was found that, when the strength of a kind of interaction increases and crosses over a critical value, a specific type of state-transition will occur and will cause a jump in the total energy. Due to the jump, the energy of the lowest symmetric state becomes considerably higher. This leaves a particular opportunity for the lowest asymmetric state to replace the symmetric states as the ground state. It was further found that the critical values are related to the singularity of either the matrix or a sub-matrix of the CGP. These critical values are not arising from the TFA but inherent in the CGP, and they can be analytically expressed. Furthermore, a model (in which two kinds of atoms separated from each other asymmetrically) has been proposed for the evaluation of the energy of the lowest asymmetric state. With this model the emergence of the asymmetric ground state is numerically confirmed under the TFA. The theoretical formalism of this paper is quite general and can be generalized for BEC with more than three species.

IgA-CK-BB complex with CK-MB electrophoretic mobility can lead to erroneous diagnosis of acute myocardial infarction.

This patient, on admission, presented with a tentative diagnosis of myocardial infarction: the electrocardiogram showed a nonspecific ST-segment and T-wave abnormalities, and total creatine kinase (CK; EC 2.7.3.2) activity was slightly increased (238 U/L). However, a high electrophoretic value for CK-MB (50% of total CK activity) and the electrophoretic pattern of lactate dehydrogenase (EC 1.1.1.27) isoenzymes ruled out myocardial infarction. The isoenzyme migrating as CK-MB was found later to contain no immunologically normal CK-M subunits, and it was bound to IgA. A mixture of the patient's serum and a human serum control containing all CK isoenzymes showed altered electrophoretic mobility only for CK-BB, indicating that the patient's serum contained antibodies to the B unit of CK. Elution from a Sephadex G-200 column showed that the peak at which most of the anodic CK was eluted corresponded to a molecular mass of approximately 200 kDa. Evidently this atypical isoenzyme was an IgA-CK-BB complex. Because this macro CK type 1 can mimic CK-MB, it may therefore be a source of confusion.

Serum levels of total IgE in non-allergic children. Influence of genetic and environmental factors.

The purpose of this study was to establish the range of total serum IgE in a healthy population lacking personal and family history of allergy, as well as the influence of genetic factors (family history of allergy), environmental factors (degree of air pollution), age, and sex on the serum IgE levels. Using a commercial enzyme immunoassay (Phadezym IgE Prist) the mean serum level of IgE was determined in 363 non-atopic children from 0 to 12 years of age. The geometric mean of serum IgE increased according to age, indicating a positive correlation between both. Higher mean values of serum IgE were found for children with a family history of allergy, than for children without (27.82 and 14.49 U/ml respectively). The percentage of variation due to age was about 94.5% in children with no family history of allergy. The mean value of serum IgE increased with the degree of air pollution in the living area (15.49 U/ml in non-polluted areas, 20.78 U/ml in very polluted areas). However, the influence of air pollution was smaller than the influence of family history on the mean values of serum IgE. The mean value of serum IgE was not modified by sex.

Abnormal electrophoretic mobility of creatine kinase isoenzyme in serum of an otherwise healthy person.

We describe the abnormal electrophoretic mobility of a creatine kinase isoenzyme in the serum of an apparently healthy individual. In agarose gel electrophoresis this isoenzyme migrates more toward the cathode than does the MM isoenzyme. It is more resistant to heat and more strongly inhibited by urea than the normal MM isoenzyme. We performed gel filtration, on a Sephadex G-200 column, of the patient's serum and observed two distinct isoenzymes with different relative molecular masses; a normal isoenzyme of 80,000 daltons and another abnormal one of 240,000 daltons. We performed serum immunoelectrophoresis but did not observe any immune complex formation involving the abnormal isoenzyme.