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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{S,i}$$\end{document}fS,i. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_{f_{S,i}}^{\lambda }$$\end{document}PfS,iλ be the probability of a pair of spins coupled to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda =0, 2, 4$$\end{document}λ=0,2,4, and 6 in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{S,i}$$\end{document}fS,i state. Obviously, when the strength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\lambda }$$\end{document}gλ of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}λ-channel is more negative, the basis-state with the largest \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_{f_{S,i}}^{\lambda }$$\end{document}PfS,iλ 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{S,i}$$\end{document}fS,i, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_{f_{S,i}}^{\lambda }$$\end{document}PfS,iλ is completely determined by symmetry. Thus, symmetry plays a very important role in determining the spin-structure of the g.s..

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 S_A, S_B and S_C 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 S_A, S_B and S_C, 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.

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.