Optimal trap shape for a Bose gas with attractive interactions

Dilute Bose gas with attractive interactions is considered at zero temperature, when practically all atoms are in Bose-Einstein condensate. The problem is addressed aiming at answering the question: What is the optimal trap shape allowing for the condensation of the maximal number of atoms with negative scattering lengths? Simple and accurate analytical formulas are derived allowing for an easy analysis of the optimal trap shapes. These analytical formulas are the main result of the paper.Comment: Latex file, 21 page

Neutron star properties with relativistic equations of state

We study the properties of neutron stars adopting relativistic equations of state of neutron star matter, calculated in the framework of the relativistic Brueckner-Hartree-Fock approximation for electrically charge neutral neutron star matter in beta-equilibrium. For higher densities more baryons (hyperons etc.) are included by means of the relativistic Hartree- or Hartree-Fock approximation. The special features of the different approximations and compositions are discussed in detail. Besides standard neutron star properties special emphasis is put on the limiting periods of neutron stars, for which the Kepler criterion and gravitation-reaction instabilities are considered. Furthermore the cooling behaviour of neutron stars is investigated, too. For comparison we give also the outcome for some nonrelativistic equations of state.Comment: 43 pages, 22 ps-figures, to be published in the International Journal of Modern Physics

Bose-Fermi variational theory of the BEC-Tonks crossover

A number-conserving hybrid Bose-Fermi variational theory is developed and applied to investigation of the BEC-Tonks gas crossover in toroidal and long cylindrical traps of high aspect ratio, where strong many-body correlations and condensate depletion occur.Comment: 4 pages RevTeX including 2 figures, uses epsfig. Submitted to Phys. Rev. Let

Remarks on Shannon's Statistical Inference and the Second Law in Quantum Statistical Mechanics

We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of the density matrix $\hat{\rho}(t)$, and the statistical amount of uncertainty of Shannon, $S= -k \sum_{n}p_{n}\ln p_{n}$, with $p_{n}=$ in the representation where the total energy and particle numbers are diagonal. These quantities satisfy the inequality $S\geq H$. We propose to interprete Shannon's statistical inference as specifying the {\em initial conditions} of the system in terms of $p_{n}$. A definition of macroscopic observables which are characterized by intrinsic time scales is given, and a quantum mechanical condition on the system, which ensures equilibrium, is discussed on the basis of time averaging. An interesting analogy of the change of entroy with the running coupling in renormalization group is noted. A salient feature of our approach is that the distinction between statistical aspects and dynamical aspects of quantum statistical mechanics is very transparent.Comment: 16 pages. Minor refinement in the statements in the previous version. This version has been published in Journal of Phys. Soc. Jpn. 71 (2002) 6

Wavelets: mathematics and applications

The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the multiresolution analysis and fast wavelet transform as a standard procedure for dealing with discrete wavelets. It is shown which specific features of signals (functions) can be revealed by this analysis, but can not be found by other methods (e.g., by the Fourier expansion). Finally, some examples of practical application are given (in particular, to analysis of multiparticle production}. Rigorous proofs of mathematical statements are omitted, and the reader is referred to the corresponding literature.Comment: 16 pages, 5 figures, Latex, Phys. Atom. Nuc

Nonlinear spin relaxation in strongly nonequilibrium magnets

A general theory is developed for describing the nonlinear relaxation of spin systems from a strongly nonequilibrium initial state, when, in addition, the sample is coupled to a resonator. Such processes are characterized by nonlinear stochastic differential equations. This makes these strongly nonequilibrium processes principally different from the spin relaxation close to an equilibrium state, which is represented by linear differential equations. The consideration is based on a realistic microscopic Hamiltonian including the Zeeman terms, dipole interactions, exchange interactions, and a single-site anisotropy. The influence of cross correlations between several spin species is investigated. The critically important function of coupling between the spin system and a resonant electric circuit is emphasized. The role of all main relaxation rates is analyzed. The phenomenon of self-organization of transition coherence in spin motion, from the quantum chaotic stage of incoherent fluctuations, is thoroughly described. Local spin fluctuations are found to be the triggering cause for starting the spin relaxation from an incoherent nonequilibrium state. The basic regimes of collective coherent spin relaxation are studied.Comment: Latex file, 31 page

Quantum motion of a neutron in a wave-guide in the gravitational field

We study theoretically the quantum motion of a neutron in a horizontal wave-guide in the gravitational field of the Earth. The wave-guide in question is equipped with a mirror below and a rough absorber above. We show that such a system acts as a quantum filter, i.e. it effectively absorbs quantum states with sufficiently high transversal energy but transmits low-energy states. The states transmitted are mainly determined by the potential well formed by the gravitational field of the Earth and the mirror. The formalism developed for quantum motion in an absorbing wave-guide is applied to the description of the recent experiment on the observation of the quantum states of neutrons in the Earth's gravitational field

Derivative-Coupling Models and the Nuclear-Matter Equation of State

The equation of state of saturated nuclear matter is derived using two different derivative-coupling Lagrangians. We show that both descriptions are equivalent and can be obtained from the sigma-omega model through an appropriate rescaling of the coupling constants. We introduce generalized forms of this rescaling to study the correlations amongst observables in infinite nuclear matter, in particular, the compressibility and the effective nucleon mass.Comment: 16 pages, 6 figures, 36 kbytes. To appear in Zeit. f. Phys. A (Hadrons and Nuclei

Adipocytes harbor a glucosylceramide biosynthesis pathway involved in iNKT cell activation

Background: Natural killer T (NKT) cells in adipose tissue (AT) contribute to whole body energy homeostasis. Results: Inhibition of the glucosylceramide synthesis in adipocytes impairs iNKT cell activity. Conclusion: Glucosylceramide biosynthesis pathway is important for endogenous lipid antigen activation of iNKT cells in adipocytes.Significance: Unraveling adipocyte-iNKT cell communication may help to fight obesity-induced AT dysfunction.Overproduction and/or accumulation of ceramide and ceramide metabolites, including glucosylceramides, can lead to insulin resistance. However, glucosylceramides also fulfill important physiological functions. They are presented by antigen presenting cells (APC) as endogenous lipid antigens via CD1d to activate a unique lymphocyte subspecies, the CD1d-restricted invariant (i) natural killer T (NKT) cells. Recently, adipocytes have emerged as lipid APC that can activate adipose tissue-resident iNKT cells and thereby contribute to whole body energy homeostasis. Here we investigate the role of the glucosylceramide biosynthesis pathway in the activation of iNKT cells by adipocytes.UDP-glucose ceramide glucosyltransferase (Ugcg), the first rate limiting step in the glucosylceramide biosynthesis pathway, was inhibited via chemical compounds and shRNA knockdown in vivo and in vitro. beta-1,4-Galactosyltransferase (B4Galt) 5 and 6, enzymes that convert glucosylceramides into potentially inactive lactosylceramides, were subjected to shRNA knock down. Subsequently, (pre)adipocyte cell lines were tested in co-culture experiments with iNKT cells (IFN gamma and 114 secretion).Inhibition of Ugcg activity shows that it regulates presentation of a considerable fraction of lipid self-antigens in adipocytes. Furthermore, reduced expression levels of either B4Galt5 or -6, indicate that B4Galt5 is dominant in the production of cellular lactosylceramides, but that inhibition of either enzyme results in increased iNKT cell activation. Additionally, in vivo inhibition of Ugcg by the aminosugar AMP-DNM results in decreased iNKT cell effector function in adipose tissue.Inhibition of endogenous glucosylceramide production results in decreased iNKT cells activity and cytokine production, underscoring the role of this biosynthetic pathway in lipid self-antigen presentation by adipocytes

Adipocytes harbor a glucosylceramide biosynthesis pathway involved in iNKT cell activation

Background: Natural killer T (NKT) cells in adipose tissue (AT) contribute to whole body energy homeostasis. Results: Inhibition of the glucosylceramide synthesis in adipocytes impairs iNKT cell activity. Conclusion: Glucosylceramide biosynthesis pathway is important for endogenous lipid antigen activation of iNKT cells in adipocytes.Significance: Unraveling adipocyte-iNKT cell communication may help to fight obesity-induced AT dysfunction.Overproduction and/or accumulation of ceramide and ceramide metabolites, including glucosylceramides, can lead to insulin resistance. However, glucosylceramides also fulfill important physiological functions. They are presented by antigen presenting cells (APC) as endogenous lipid antigens via CD1d to activate a unique lymphocyte subspecies, the CD1d-restricted invariant (i) natural killer T (NKT) cells. Recently, adipocytes have emerged as lipid APC that can activate adipose tissue-resident iNKT cells and thereby contribute to whole body energy homeostasis. Here we investigate the role of the glucosylceramide biosynthesis pathway in the activation of iNKT cells by adipocytes.UDP-glucose ceramide glucosyltransferase (Ugcg), the first rate limiting step in the glucosylceramide biosynthesis pathway, was inhibited via chemical compounds and shRNA knockdown in vivo and in vitro. beta-1,4-Galactosyltransferase (B4Galt) 5 and 6, enzymes that convert glucosylceramides into potentially inactive lactosylceramides, were subjected to shRNA knock down. Subsequently, (pre)adipocyte cell lines were tested in co-culture experiments with iNKT cells (IFN gamma and 114 secretion).Inhibition of Ugcg activity shows that it regulates presentation of a considerable fraction of lipid self-antigens in adipocytes. Furthermore, reduced expression levels of either B4Galt5 or -6, indicate that B4Galt5 is dominant in the production of cellular lactosylceramides, but that inhibition of either enzyme results in increased iNKT cell activation. Additionally, in vivo inhibition of Ugcg by the aminosugar AMP-DNM results in decreased iNKT cell effector function in adipose tissue.Inhibition of endogenous glucosylceramide production results in decreased iNKT cells activity and cytokine production, underscoring the role of this biosynthetic pathway in lipid self-antigen presentation by adipocytes