Four-dimensional photonic lattices and discrete tesseract solitons

We theoretically study discrete photonic lattices in more than three dimensions and point out that such systems can exist in continuous three-dimensional (3D) space. We study discrete diffraction in the linear regime, and predict the existence of four-dimensional (4D) tesseract solitons in nonlinear 4D periodic photonic lattices. Finally, we propose a design towards a potential realization of such periodic 4D lattices in experiments.Comment: Submitted to PRL on 14 May 201

Least squares fitting the three-parameter inverse Weibull density

The inverse Weibull model was developed by Erto [10]. In practice, the unknown parameters of the appropriate inverse Weibull density are not known and must be estimated from a random sample. Estimation of its parameters has been approached in the literature by various techniques, because a standard maximum likelihood estimate does not exist. To estimate the unknown parameters of the three-parameter inverse Weibull density we will use a combination of nonparametric and parametric methods. The idea consists of using two steps: in the first step we calculate an initial nonparametric density estimate which needs to be as good as possible, and in the second step we apply the nonlinear least squares method to estimate the unknown parameters. As a main result, a theorem on the existence of the least squares estimate is obtained, as well as its generalization in the $l_p$ norm ($1leq p<infty$). Some simulations are given to show that our approach is satisfactory if the initial density is of good enough quality

Ground state properties of a one-dimensional strongly-interacting Bose-Fermi mixture in a double-well potential

We calculate the reduced single-particle density matrix (RSPDM), momentum distributions, natural orbitals and their occupancies, for a strongly interacting one-dimensional Bose-Fermi mixture in a double-well potential with a large central barrier. For mesoscopic systems, we find that the ground state properties qualitatively differ for mixtures with even number of particles (both odd-odd and even-even mixtures) in comparison to mixtures with odd particle numbers (odd-even and even-odd mixtures). For even mixtures the momentum distribution is smooth, whereas the momentum distribution of odd mixtures possesses distinct modulations; the differences are observed also in the off-diagonal correlations of the RSPDM, and in the occupancies of natural orbitals. The calculation is based on a derived formula which enables efficient calculation of the RSPDM for mesoscopic mixtures in various potentials.Comment: 10 figure

Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions

The asymptotic form of the wave functions describing a freely expanding Lieb-Liniger gas is derived by using a Fermi-Bose transformation for time-dependent states, and the stationary phase approximation. We find that asymptotically the wave functions approach the Tonks-Girardeau (TG) structure as they vanish when any two of the particle coordinates coincide. We point out that the properties of these asymptotic states can significantly differ from the properties of a TG gas in a ground state of an external potential. The dependence of the asymptotic wave function on the initial state is discussed. The analysis encompasses a large class of initial conditions, including the ground states of a Lieb-Liniger gas in physically realistic external potentials. It is also demonstrated that the interaction energy asymptotically decays as a universal power law with time, $E_\mathrm{int}\propto t^{-3}$.Comment: Section VI added to v2; published versio

Tetrahydrophthalazine Derivative »Sodium Nucleinate« Exert its Anti-Inflammatory Effects through Inhibition of Oxidative Burst in Human Monocytes

We described the use of a new chemical substance Sodium nucleinate (SN) as an immunomodulatory substance exhibiting antiinflammatory properties. Sodium nucleinate (SN) registrated in Russian Federation as Tamerit®, is 2-amino- -1,2,3,4-tetrahydrophthalazine-1,4-dione sodium salt dihydrate, derivative of well known chemical substance luminol. To comprehend the mechanisms of SN immunomodulatory activity, we examined the SN modulation of the oxidative burst responses of whole blood human monocytes and polimorphonuclear cells (PMC) stimulated with phorbol 12-myristate 13-acetate (PMA) or E. coli suspension in vitro. SN did not inhibit the proportion of neutrophils and monocytes phagocytosing E. coli. Oxidative burst responses of monocytes stimulated with PMA were strongly inhibited at SN concentration ranging from 10–500 mg/ml, less efficient inhibitor was SN in E. coli stimulated monocytes (inhibition range was from 50–500 mg/ml SN). SN inhibited PMC oxidative burst only in range 100–500 mg/ml SN. In conclusion, we found SN as an efficient inhibitor of oxidative burst in monocytes. Since ROS generation in monocytes/macrophages has been found to be important for LPS-driven production of several proinflammatory cytokines, SN may exsert its antiinflammatory effects through monocyte/macrophage oxidative burst inhibition

Lieb-Liniger gas in a constant force potential

We use Gaudin's Fermi-Bose mapping operator to calculate exact solutions for the Lieb-Liniger model in a linear (constant force) potential (the constructed exact stationary solutions are referred to as the Lieb-Liniger-Airy wave functions). The ground state properties of the gas in the wedge-like trapping potential are calculated in the strongly interacting regime by using Girardeau's Fermi-Bose mapping and the pseudopotential approach in the $1/c$-approximation ($c$ denotes the strength of the interaction). We point out that quantum dynamics of Lieb-Liniger wave packets in the linear potential can be calculated by employing an $N$-dimensional Fourier transform as in the case of free expansion

The matrix of a linear operator in a pair of ordered bases

In the lecture it is shown how to represent a linear operator by a matrix. This representation allows us to define an operation with matrices