New evaluation of neutron lifetime from UCN storage experiments and beam experiments

The analysis of experiments on measuring neutron lifetime has been made. The latest most accurate result of measuring neutron lifetime [Phys. Lett. B 605, 72 (2005)] 878.5 \pm 0.8 s differs from the world average value [Phys. Lett. B 667, 1 (2008)] 885.7 \pm 0.8 s by 6.5 standard deviations. In view of this both the analysis and the Monte Carlo simulation of experiments [Phys. Lett. B 483, 15 (2000)] and [Phys. Rev. Lett. 63, 593 (1989)] have been performed. Systematic errors about -6 s have been found in both experiments. The table of results of neutron lifetime measurements is given after corrections and additions have been made. A new world average value of neutron lifetime makes up 880.0 \pm 0.9 s. Here is also presented a separate analysis of experiments on measuring neutron lifetime with UCN and experiments on the beams. The average neutron lifetime for experiments with UCN is equal to 879.3(0.6) s, while for experiments on the beams it is equal to 889.1(2.9) s. The present difference of average values for both groups is (3.3 sigma) and needs consideration. The contribution of beam experiments into the world average value is not high, therefore it does not influence the above analysis. However, it is an independent problem to be solved. It seems desirable that the precision of beam experiments should be enhanced.Comment: 7 pages, 4 figures, 2 table

A New World Average Value for the Neutron Lifetime

The analysis of the data on measurements of the neutron lifetime is presented. A new most accurate result of the measurement of neutron lifetime [Phys. Lett. B 605 (2005) 72] 878.5 +/- 0.8 s differs from the world average value [Phys. Lett. B 667 (2008) 1] 885.7 +/- 0.8 s by 6.5 standard deviations. In this connection the analysis and Monte Carlo simulation of experiments [Phys. Lett. B 483 (2000) 15] and [Phys. Rev. Lett. 63 (1989) 593] is carried out. Systematic errors of about -6 s are found in each of the experiments. The summary table for the neutron lifetime measurements after corrections and additions is given. A new world average value for the neutron lifetime 879.9 +/- 0.9 s is presented.Comment: 27 pages, 13 figures; Fig.13 update

Q-systems, Heaps, Paths and Cluster Positivity

We consider the cluster algebra associated to the $Q$-system for $A_r$ as a tool for relating $Q$-system solutions to all possible sets of initial data. We show that the conserved quantities of the $Q$-system are partition functions for hard particles on particular target graphs with weights, which are determined by the choice of initial data. This allows us to interpret the simplest solutions of the Q-system as generating functions for Viennot's heaps on these target graphs, and equivalently as generating functions of weighted paths on suitable dual target graphs. The generating functions take the form of finite continued fractions. In this setting, the cluster mutations correspond to local rearrangements of the fractions which leave their final value unchanged. Finally, the general solutions of the $Q$-system are interpreted as partition functions for strongly non-intersecting families of lattice paths on target lattices. This expresses all cluster variables as manifestly positive Laurent polynomials of any initial data, thus proving the cluster positivity conjecture for the $A_r$ $Q$-system. We also give an alternative formulation in terms of domino tilings of deformed Aztec diamonds with defects.Comment: 106 pages, 38 figure

Ultra cold neutron trap as a tool to search for dark matter with long-range radius of forces

The problem of possible application of an ultracold neutron (UCN) trap as a detector of dark matter particles with long-range radius of forces has been considered. Transmission of small recoil energy in scattering is a characteristic of long-range forces. The main advantage of the ultracold neutron technique lies in possibility of detecting recoil energy as small as $10^{-7}$ eV. Here are presented constraints on the interaction potential parameters: $U(r)=a r^{-1} e^{-r/\lambda}$ for dark matter particles and neutrons, as well as on the density value of long-range dark matter on the Earth. The possible mechanism of accumulation of long-range dark matter on the Earth surface is considered and the factor of density increase on the Earth surface is evaluated. The results of the first experiment on search of astronomical day variation of ultracold neutron storage time are under discussion.Comment: 17 pages, 19 figures. arXiv admin note: substantial text overlap with arXiv:1109.339

Cluster algebras of type A2(1)A_2^{(1)}

In this paper we study cluster algebras \myAA of type $A_2^{(1)}$. We solve the recurrence relations among the cluster variables (which form a T--system of type $A_2^{(1)}$). We solve the recurrence relations among the coefficients of \myAA (which form a Y--system of type $A_2^{(1)}$). In \myAA there is a natural notion of positivity. We find linear bases \BB of \myAA such that positive linear combinations of elements of \BB coincide with the cone of positive elements. We call these bases \emph{atomic bases} of \myAA. These are the analogue of the "canonical bases" found by Sherman and Zelevinsky in type $A_{1}^{(1)}$. Every atomic basis consists of cluster monomials together with extra elements. We provide explicit expressions for the elements of such bases in every cluster. We prove that the elements of \BB are parameterized by \ZZ^3 via their $\mathbf{g}$--vectors in every cluster. We prove that the denominator vector map in every acyclic seed of \myAA restricts to a bijection between \BB and \ZZ^3. In particular this gives an explicit algorithm to determine the "virtual" canonical decomposition of every element of the root lattice of type $A_2^{(1)}$. We find explicit recurrence relations to express every element of \myAA as linear combinations of elements of \BB.Comment: Latex, 40 pages; Published online in Algebras and Representation Theory, springer, 201

Semi-invariants of symmetric quivers of finite type

Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite quiver without oriented cycles and $\sigma$ is a contravariant involution on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall call the representation orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover we can define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. For symmetric quivers of finite type, we prove that the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, in the case when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$

Influence of the confinement geometry on surface superconductivity

The nucleation field for surface superconductivity, $H_{c3}$, depends on the geometrical shape of the mesoscopic superconducting sample and is substantially enhanced with decreasing sample size. As an example we studied circular, square, triangular and wedge shaped disks. For the wedge the nucleation field diverges as $H_{c3}/H_{c2}=\sqrt{3}/\alpha$ with decreasing angle ($\alpha$) of the wedge, where $H_{c2}$ is the bulk upper critical field.Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev.

An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure

The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for the traveling salesman problem in an n-vertex graph with maximum degree 3. This improves the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and O^*(1.260^n) by Eppstein. Our algorithm is a simple branch-and-search algorithm. The only branch rule is designed on a cut-circuit structure of a graph induced by unprocessed edges. To improve a time bound by a simple analysis on measure and conquer, we introduce an amortization scheme over the cut-circuit structure by defining the measure of an instance to be the sum of not only weights of vertices but also weights of connected components of the induced graph.Comment: 24 pages and 4 figure

Low temperature mixed spin state of Co3+ in LaCoO3 evidenced from Jahn-Teller lattice distortions

One- and multi-phonon excitations of the single crystalline LaCoO3 were studied using Raman spectroscopy in the temperature region of 5 K - 300 K. First-order Raman spectra show a larger number of phonon modes than allowed for the rhombohedral structure. Additional phonon modes are interpreted in terms of activated modes due to lattice distortions, arising from the Jahn-Teller (JT) activity of the intermediate-spin (IS) state of Co3+ ions. In particular, the 608-cm-1 stretching-type mode shows anomalous behavior in peak energy and scattering intensity as a function of temperature. The anomalous temperature dependence of the second-order phonon excitations spectra is in accordance with the Franck-Condon mechanism that is characteristic for a JT orbital order.Comment: 11 pages, 9 figures, to be published in J. Low. Temp. Physic