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The most accurate neutron lifetime measurements now use the material or magnetic traps of ultracold neutrons (UCN). The precision of these experiments is determined by the accuracy of estimating the neutron loss rate. In material UCN traps the main source of neutron losses is the absorption by trap walls. In this paper we analyze the standard methods and their approximations for the calculation of UCN absorption rate by the walls of material traps. We emphasize the approximations used both in the standard analytical formulas and in the numerical Monte-Carlo simulations. For the two simplest trap geometries, rectangular and cylindrical, we obtain analytical formulas for this absorption rate provided the UCN velocity distribution is isotropic at trap bottom. Then we perform numerical calculations of UCN velocity distribution and absorption rate taking into account the diffuse elastic UCN reflections by trap walls obeying two different laws: Lambert`s cosine law and isotropic reflection. We compare the results with the standard estimation methods and discuss the differences. We indicate the difference between the UCN number and density velocity distribution. Our results may be useful to resolve the puzzling four-second discrepancy between the magnetic and material-trap measurements of neutron lifetime., Comment: 16 pages, 10 figures

Magnetic quantum oscillations (MQO) are traditionally applied to investigate the electronic structure of metals. In layered quasi-two-dimensional (Q2D) materials the MQO have several qualitative features giving additional useful information, provided their theoretical description is developed. Within the framework of the Kubo formula and the self-consistent Born approximation, we reconsider the phase of beats in the amplitude of Shubnikov oscillations of interlayer conductivity in Q2D metals. We show that the phase shift of beats of the Shubnikov (conductivity) oscillations relative to the de Haas - van Alphen (magnetization) oscillations is larger than expected previously and, under certain conditions, can reach the value of $\pi/2$, as observed experimentally. We explain the phase inversion of MQO during the 3D - 2D crossover and predict the decrease of relative MQO amplitude of interlayer magnetoresistance in a strong magnetic field, larger than the beat frequency., Comment: 13 pages

We develop the theory of magnetoresistance oscillations in layered quasi-two-dimensional (quasi-2D) metals. Using the Kubo-Streda formula, we calculate the Hall intralayer conductivity in a magnetic field perpendicular to conducting layers. The analytical expressions for the amplitudes and phases of magnetic quantum oscillations (MQO) and of the difference or the so-called slow oscillations (SO) are derived as a function of several parameters: magnetic field strength, interlayer transfer integral, temperature, and the electron mean-free time. We calculate the quantum oscillations of the magnetoresistance tensor, because the magnetoresistance rather than conductivity is usually measured. We also discuss the averaging of magnetoresistance oscillations over MQO period due to finite temperature and long-range sample inhomogeneities. The results obtained are useful to analyze experimental data on magnetoresistance oscillations in various quasi-2D metals., Comment: 16 pages, 6 figures

Most high-$T_c$ superconductors are spatially inhomogeneous. Usually, this heterogeneity originates from the interplay of various types of electronic ordering. It affects various superconducting properties, such as the transition temperature, the magnetic upper critical field, the critical current, etc. In this paper, we analyze the parameters of spatial phase segregation during the first-order transition between superconductivity (SC) and a charge- or spin-density wave state in quasi-one-dimensional metals with imperfect nesting, typical of organic superconductors. An external pressure or another driving parameter increases the transfer integrals in electron dispersion, which only slightly affects SC but violates the Fermi surface nesting and suppresses the density wave (DW). At a critical pressure $P_{c}$, the transition from a DW to SC occurs. We estimate the characteristic size of superconducting islands during this phase transition in organic metals in two ways. Using the Ginzburg-Landau expansion, we analytically obtain a lower bound for the size of SC domains. To estimate a more specific interval of the possible size of the superconducting islands in (TMTSF)$_2$PF$_6$ samples, we perform numerical calculations of the percolation probability via SC domains and compare the results with experimental resistivity data. This helps to develop a consistent microscopic description of SC spatial heterogeneity in various organic superconductors., Comment: 11 pages, 3 figures

The interplay between superconductivity (SC) and spin/charge density wave (DW) in organic metals shows many similarities to high-$T_c$ superconductors. It also contains many puzzles, for example, the anisotropic SC onset observed and the severalfold increase of the upper critical field $H_{c2}$ in the coexistence region, as well as the microscopic origin of SC/DW phase separation there. In this paper, by the direct calculation of the Landau expansion for DW free energy, we argue that the phase transition between DW and metallic/SC phase in organic superconductors goes by first order at low enough temperature, which explains the spatial segregation of DW and SC at large length scale, consistent with experimental observations. This first-order phase transition is not directly related to SC and happens even above the SC transition temperature., Comment: 12 pages, 3 figures

To increase the storage time of ultracold neutrons (UCN) inside the material traps it is promising to cover the trap walls by liquid 4He, the material which does not absorb neutrons at all. A rough side wall of UCN trap holds the required amount of 4He by the capillary effects, but the edges of wall roughness remain insufficiently coated. Here we propose to apply an electric voltage to these rough side walls of UCN traps to increases the thickness of liquid He on the wall edges and to cover the entire wall surface by sufficiently thick helium films. This completely protects UCN from being absorbed inside the trap walls. We estimate the required electric field and voltage for several possible designs of UCN traps. This improvement may give rise to a new generation of ultracold neutron traps with very long storage time. We also estimate the influence of this electric field on the dispersion of ripplons - the quanta surface waves, which give the main contribution to the inelastic UCN scattering at low temperature., Comment: 7 pages, 6 figures

Mortality patterns at a subnational level or across subpopulations are often used to examine the health of a population. In small populations, however, death counts are erratic. To deal with this problem, demographers have proposed different methods but it is unclear how these methods relate to each other. We aim to provide guidance. First, we review recent demographic small-area methods for mortality schedules. Second, we evaluate three methodological approaches using simulated data. We show that there is considerable variability in the performance across ages and subpopulations/regions and that this performance can depend on the choice of incorporated demographic knowledge.

In highly anisotropic organic superconductor (TMTSF)$_2$ClO$_4$, superconducting (SC) phase coexists with metallic and spin density wave phases in the form of domains. Using the Maxwell-Garnett approximation (MGA), we calculate the volume ratio and estimate the shape of these embedded SC domains from resistivity data at various temperature and anion disorder, controlled by the cooling rate or annealing time of (TMTSF)$_{2}$ClO$_{4}$ samples. We found that the variation of cooling rate and of annealing time affect differently the shape of SC domains. In all cases the SC domains have oblate shape, being the shortest along the interlayer $z$-axis. This contradicts the widely assumed filamentary superconductivity along $z$-axis, used to explain the anisotropic superconductivity onset. We show that anisotropic resistivity drop at the SC transition can be described by the analytical MGA theory with anisotropic background resistance, while the anisotropic $T_c$ can be explained by considering a finite size and flat shape of the samples. Due to a flat/needle sample shape, the probability of percolation via SC domains is the highest along the shortest sample dimension ($z$-axis), and the lowest along the sample length ($x$-axis). Our theory can be applied to other heterogeneous superconductors, where the size $d$ of SC domains is much larger than the SC coherence length $\xi$, e.g. cuprates, iron based or organic superconductors. It is also applicable when the spin/charge-density wave domains are embedded inside a metallic background, or vice versa., Comment: 14 Pages, 6 Figures

We study the coexistence of superconductivity (SC) and density-wave state and reconcile various puzzling experimental data in organic superconductors (TMTSF)$_{2}$PF$_{6}$ and (TMTSF)$_{2}$ClO$_{4}$. The anisotropic resistance drop above $T_c$ is qualitatively described by nascent isolated SC islands within a bulk analytical model. However, the observed anisotropic SC onset is explained only when the finite size and flat needle shape of samples is considered. Our results pave a way to estimate the volume fraction and the typical size of SC islands in far from the sample surface, and apply to many inhomogeneous superconductors, including high-$T_c$ cuprate or Fe-based ones., Comment: 7 pages with Appendix and 5 figures

We calculated electron susceptibility of rare-earth tritelluride compounds RTe$_3$ as a function of temperature, wave vector and electron-dispersion parameters. Comparison of results obtained with the available experimental data on the transition temperature and on the wave vector of a charge-density wave in these compounds allowed us to predict values and the evolution of electron-dispersion parameters with the variation of atomic number of rare-earth element R., Comment: 6 pages, 6 figures

About a half of the Fermi surface in rare-earth tritellurides RT e3 becomes gapped below the transition to a charge-density-wave (CDW) state, as revealed by ARPES data. However, the observed jump in resistivity during the CDW transition is less than 20%. Previously this phenomenon was explained by hypothesizing a very slow evolution of CDW energy gap below transition temperature in RTe3 compounds, which contradicts the X-ray measurements. Here we show that this weak change in resistivity can be explained in the framework of standard mean-field temperature dependence of the CDW energy gap in agreement with X-ray data. The change of resistivity caused by CDW is weak because the decrease in conducting electron density at the Fermi level is almost compensated by the decrease in their scattering rate. We calculate resistivity in RTe3 compounds using the Boltzmann transport equation and the mean-field description of the CDW state, and obtain a good agreement with experimental data., Comment: 6 Pages, 2 Figures, To be published in IOP Journal of Physics Conference Series

Using the self-consistent approximation we calculate conductivity in an anisotropic heterogeneous media with superconducting inclusions and compare the results with those obtained previously using the Maxwell approximation and with available experimental data on excess conductivity above $ T_c= $~8K in FeSe. Advantages and drawbacks of these two approximations are discussed. The obtained analytical formulas can be applied to various other anisotropic heterogeneous superconductors, including high-Tc layered superconductors., Comment: 6 pages, 4 figures; the work presented at the IV International Conference LaPlas-2018; to be published in the Journal of Physics: Conference Series (in press)

We report measurements of the magnetoresistance in the charge density wave (CDW) state of rare-earth tritellurides, namely TbTe$_3$ and HoTe$_3$. The magnetic field dependence of magnetoresistance exhibits a temperature dependent crossover between a conventional quadratic law at high $T$ and low $B$ and an unusual linear dependence at low $T$ and high $B$. We present a quite general model to explain the linear magnetoresistance taking into account the strong scattering of quasiparticles on CDW fluctuations in the vicinity of "hot spots" of the Fermi surface (FS) where the FS reconstruction is the strongest., Comment: 6 pages, 5 figures

The magnetic oscillations in YBCO high-temperature superconductors have been widely studied over the last decade and consist of three equidistant low frequencies with a central frequency several times more intense than its two shoulders. This remains a puzzle in spite of numerous attempts to explain the corresponding small Fermi-surface pockets. Furthermore the ARPES data indicate only four Fermi-arcs with bilayer splitting, and show no sign of such small areas in the Fermi surface. Here we argue that the magnetic oscillations measured in under-doped bilayer high temperature superconductors, in particular YBa$_{2}$Cu$_{3}$O$_{6+\delta }$, provide a measure of the interplanar electronic coupling rather than the areas of fine-grain reconstruction of the Fermi surfaces coming from induced charge density waves. This identification is based on the relative intensities of the different peaks, as well as their angular dependence, which points to an effective Fermi surface that is larger than the oscillation frequencies, and is compatible with several indications from ARPES. The dominance of such frequencies with respect to the fundamental frequencies from the Fermi surface is natural for a strongly correlated quasi-two dimensional electronic systems where non-linear mixings of frequencies are more resistant to sample inhomogeneity., Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1606.03942

Slow oscillations (SlO) of the in-plane magnetoresistance with a frequency less than 4 T are observed in the rare-earth tritellurides and proposed as an effective tool to explore the electronic structure in various strongly anisotropic quasi-two-dimensional compounds. Contrary to the usual Shubnikov-de-Haas oscillations, SlO originate not from small Fermi-surface pockets, but from the entanglement of close frequencies due to a finite interlayer transfer integral, either between the two Te planes forming a bilayer or between two adjacent bilayers. From the observed angular dependence of the frequency and the phase of SlO we argue that they originate from the bilayer splitting rather than from the Fermi-surface warping. The SlO frequency gives the value of the interlayer transfer integral $\approx 1$ meV for TbTe$_3$ and GdTe$_3$., Comment: 10 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1504.06064

The Fourier transform of the observed magnetic quantum oscillations (MQO) in YBa$_{2}$Cu$_{3}$O$_{6+\delta }$ high-temperature superconductors has a prominent low-frequency peak with two smaller neighbouring peaks. The separation and positions of these three peaks are almost independent of doping. This pattern has been explained previously by rather special, exquisitely detailed, Fermi-surface reconstruction. We propose that these MQO have a different origin, and their frequencies are related to the bilayer and inter-bilayer electron hopping rather than directly to the areas of tiny Fermi-surface pockets. Such so-called "slow oscillations" explain more naturally many features of the observed oscillations and allow us to estimate the inter-layer transfer integrals and in-plane Fermi momentum., Comment: 6 pages

An example of trigonometric polynomials with extremely small uniform norm is given. This example demonstrates the potential limits for extension of Sidon's inequality for lacunary polynomials in a certain direction.

A decoupling type inequality for a sum of functions of Guassian vectors is established.

We investigate the monotonic growth of longitudinal interlayer magnetoresistance $\bar{R}_{zz}(B_z) $, analytically and numerically in the self-consistent Born approximation. We show that in a weak magnetic field the monotonic part of $\bar{R}_{zz}(B_z)$ is almost constant and starts to grow only above the crossover field $B_{c}$, when the Landau levels (LL) become isolated, i.e. when the LL separation becomes greater than the LL broadening. In higher field $B_{z}>>B_{c}$, $\bar{R}_{zz}(B_{z}) \propto B_{z}^{1/2}$ in agreement with previous works., Comment: 5 pages, 3 figures

We present the quantum-mechanical calculations of the angular dependence of interlayer conductivity $\sigma _{zz}(\theta )$ in a tilted magnetic field in quasi-2D layered metals. Our calculation shows that the LL shape is important for this angular dependence. In particular, the amplitude of angular magnetoresistance oscillations (AMRO) is much stronger for the Gaussian LL shape than for the Lorentzian. The ratio $\sigma_{zz}(\theta =0)/ \sigma_{zz}(\theta ->\pm 90^{\circ})$ is also several times larger for the Gaussian LL shape. AMRO and Zeeman energy splitting lead to a spin current. For typical organic metals and for a medium magnetic field 10T this spin current is only a few percent of the charge current, but its value may almost reach the charge current for special tilt angles of magnetic field. The spin current has strong angular oscillations, which are phase-shifted as compared to the usual AMRO., Comment: 8 pages, 3 figures

It is shown that in rather strong magnetic field the interlayer electron conductivity is exponentially damped by the Coulomb barrier arising from the formation of polaron around each localized electron state. The theoretical model is developed to describe this effect, and the calculation of the temperature and field dependence of interlayer magnetoresistance is performed. The results obtained agree well with the experimental data in GaAs/AlGaAs heterostructures and in strongly anisotropic organic metals. The proposed theory allows to use the experiments on interlayer magnetoresistance to investigate the electron states, localized by magnetic field and disorder., Comment: 6 pages, 3 figures

We investigate the conductivity in layered metals in magnetic field in the weakly incoherent limit, when the interlayer transfer integral is smaller than the Landau level broadening due to the impurity potential, but the interlayer electron tunnelling conserves the intralayer momentum. It is shown that the impurity potential has much stronger effect in this regime, than in the quasi-2D metals in the coherent limit. The weakly incoherent regime has several new qualitative features, not found in the previous theoretical approaches. The background interlayer magnetoresistance in this regime monotonically grows with increasing of magnetic field perpendicular to the conducting layers. The effective electron mean free time is considerably shorter than in the coherent regime and decreases with magnetic field. This enhances the role of higher harmonics in the angular magnetoresistance oscillations and increases the Dingle temperature, which damps the magnetic quantum oscillations., Comment: 10 pages, 5 figures

In the paper I study properties of random polynomials with respect to a general system of functions. Some lower bounds for the mathematical expectation of the uniform and recently introduced integral-uniform norms of random polynomials are established. {\sc Key words and phrases:} Random polynomial, estimates for maximum of random process, integral-uniform norm., Comment: To be puslished in Mathematical Notes

This paper contains some estimates for the {\it integral-uniform} norm and the uniform norm of a wide class of random polynomials. The family of integral-uniform norms introduced by Kasin and Tzafriri is a natural generalization of the maximum norm taken over a net. We prove some properties of the integral-uniform norms. The given application of the established estimates demonstrates that the integral-uniform norms may be useful whenever one is interested in the properties of a function distribution. Key words: integral-uniform norm; random polynomials with respect to a general function system; trigonometric polynomials with random coefficients., Comment: Almost the same text was published in East J. Approximation 2001 v. 7 no. 4 pp. 445--469

The de Haas - van Alphen effect in quasi-two-dimensional metals is studied at arbitrary parameters. The oscillations of the chemical potential may substantially change the temperature dependence of harmonic amplitudes that is usually used to determine the effective electron mass. Hence, the processing of the experimental data using the standard Lifshitz-Kosevich formula (that assumes the chemical potential to be constant) may lead to substantial errors even in the limit of strong harmonic damping. This fact may explain the difference between the effective electron masses, determined from the de Haas - van Alphen effect and the cyclotron resonance measurements. The oscillations of the chemical potential and the deviations from the Lifshitz-Kosevich formula depend on the reservoir density of states, that exists in organic metals due to open sheets of Fermi surface. This dependence can be used to determine the density of electron states on open sheets of Fermi surface. We present the analytical results of the calculations of harmonic amplitudes in some limiting cases that show the importance of the oscillations of the chemical potential. The algorithm of the simple numerical calculation of the harmonic amplitudes at arbitrary reservoir density of states, arbitrary warping, spin-splitting, temperature and Dingle temperature is also described., Comment: 8 pages, 1 figure