Repulsion-Sustained Supercurrent and Flux Quantization in Rings of Symmetric Hubbard Clusters

We test the response to a threading magnetic field of rings of 5-site $C_{4v}$-symmetric repulsive Hubbard clusters connected by weak intercell links; each 5-site unit has the topology of a CuO$_{4}$ cluster and a repulsive interaction is included on every site. In a numerical study of the three-unit ring with 8 particles, we take advantage of a novel exact-diagonalization technique which can be generally applied to many-fermion problems. For O-O hopping we find Superconducting Flux Quantization (SFQ), but for purely Cu-Cu links bound pair propagation is hindered by symmetry. The results agree with W=0 pairing theory.Comment: 4 pages, 2 figure

W=0 Pairing in (N,N)(N,N) Carbon Nanotubes away from Half Filling

We use the Hubbard Hamiltonian $H$ on the honeycomb lattice to represent the valence bands of carbon single-wall $(N,N)$ nanotubes. A detailed symmetry analysis shows that the model allows W=0 pairs which we define as two-body singlet eigenstates of $H$ with vanishing on-site repulsion. By means of a non-perturbative canonical transformation we calculate the effective interaction between the electrons of a W=0 pair added to the interacting ground state. We show that the dressed W=0 pair is a bound state for resonable parameter values away from half filling. Exact diagonalization results for the (1,1) nanotube confirm the expectations. For $(N,N)$ nanotubes of length $l$, the binding energy of the pair depends strongly on the filling and decreases towards a small but nonzero value as $l \to \infty$. We observe the existence of an optimal doping when the number of electrons per C atom is in the range 1.2$\div$1.3, and the binding energy is of the order of 0.1 $\div$ 1 meV.Comment: 16 pages, 6 figure

W=0 pairing in Hubbard and related models of low-dimensional superconductors

Lattice Hamiltonians with on-site interaction $W$ have W=0 solutions, that is, many-body {\em singlet} eigenstates without double occupation. In particular, W=0 pairs give a clue to understand the pairing force in repulsive Hubbard models. These eigenstates are found in systems with high enough symmetry, like the square, hexagonal or triangular lattices. By a general theorem, we propose a systematic way to construct all the W=0 pairs of a given Hamiltonian. We also introduce a canonical transformation to calculate the effective interaction between the particles of such pairs. In geometries appropriate for the CuO$_{2}$ planes of cuprate superconductors, armchair Carbon nanotubes or Cobalt Oxides planes, the dressed pair becomes a bound state in a physically relevant range of parameters. We also show that W=0 pairs quantize the magnetic flux like superconducting pairs do. The pairing mechanism breaks down in the presence of strong distortions. The W=0 pairs are also the building blocks for the antiferromagnetic ground state of the half-filled Hubbard model at weak coupling. Our analytical results for the $4\times 4$ Hubbard square lattice, compared to available numerical data, demonstrate that the method, besides providing intuitive grasp on pairing, also has quantitative predictive power. We also consider including phonon effects in this scenario. Preliminary calculations with small clusters indicate that vector phonons hinder pairing while half-breathing modes are synergic with the W=0 pairing mechanism both at weak coupling and in the polaronic regime.Comment: 42 pages, Topical Review to appear in Journal of Physics C: Condensed Matte

On the half-life of 44Ti by results in meteorites

Measurements of the 44Ti half-life display a large spread ranging from 46.4 to 66.6 years. The activity of this radioisotope measured in eight meteorites (chondrites) fell in the time interval 1883-1992 and calculated at the time of fall by the different values of T1O2 shows that the shorter values are not reliable, if it is assumed that the average cosmic-ray intensity has remained the same during the past two centuries. The low activity of the cosmogenic isotope 44Ti has been determined by means of a selective Ge-NaI (Tl) g-spectrometer with a very low background (about 1 count per day in the g-peak at 1157 keV of 44Sc in equilibrium with its parent 44Ti). The high stability of this system allows long-lasting runs (A107 s ), in order to achieve the standard deviation of counting up to A10%. PACS 94.40.Vf – Cosmic-ray effects in meteorites and terrestrial matter

Neighbor Balanced Block Designs for Two Factors

The concept of Neighbor Balanced Block (NBB) designs is defined for the experimental situation where the treatments are combinations of levels of two factors and only one of the factors exhibits a neighbor effect. Methods of constructing complete NBB designs for two factors in a plot that is strongly neighbor balanced for one factor are obtained. These designs are variance balanced for estimating the direct effects of contrasts pertaining to combinations of levels of both the factors. An incomplete NBB design for two factors is also presented and is found to be partially variance balanced with three associate classes

Field theoretic formulation of a mode-coupling equation for colloids

The only available quantitative description of the slowing down of the dynamics upon approaching the glass transition has been, so far, the mode-coupling theory, developed in the 80's by G\"otze and collaborators. The standard derivation of this theory does not result from a systematic expansion. We present a field theoretic formulation that arrives at very similar mode-coupling equation but which is based on a variational principle and on a controlled expansion in a small dimensioneless parameter. Our approach applies to such physical systems as colloids interacting via a mildly repulsive potential. It can in principle, with moderate efforts, be extended to higher orders and to multipoint correlation functions

One Dimensional Kondo Lattice Model Studied by the Density Matrix Renormalization Group Method

Recent developments of the theoretical investigations on the one-dimensional Kondo lattice model by using the density matrix renormalization group (DMRG) method are discussed in this review. Short summaries are given for the zero-temperature DMRG, the finite-temperature DMRG, and also its application to dynamic quantities. Away from half-filling, the paramagnetic metallic state is shown to be a Tomonaga-Luttinger liquid with the large Fermi surface. For the large Fermi surface its size is determined by the sum of the densities of the conduction electrons and the localized spins. The correlation exponent K_rho of this metallic phase is smaller than 1/2. At half-filling the ground state is insulating. Excitation gaps are different depending on channels, the spin gap, the charge gap and the quasiparticle gap. Temperature dependence of the spin and charge susceptibilities and specific heat are discussed. Particularly interesting is the temperature dependence of various excitation spectra, which show unusual properties of the Kondo insulators.Comment: 18 pages, 23 Postscript figures, REVTe

Heavy Meson Electromagnetic Mass Differences from QCD

We compute the electromagnetic mass differences of mesons containing a single heavy quark in terms of measurable data using QCD-based arguments in heavy-quark effective theory. We derive an unsubtracted dispersion relation that shows that the mass differences are calculable in terms of the properties of the lowest-lying physical intermediate states. We then consider the problem in the large-$N$ limit, where $N$ is the number of QCD colors. In this limit, we can write a kind of double-dispersion relation for the amplitude required to determine the electromagnetic mass difference. We use this to derive analogs of the Weinberg sum rules for heavy meson matrix elements valid to leading order in $1/N$ and to $O(1/m_Q)$ in the heavy quark expansion. In order to obtain our final result, we assume that the electromagnetic mass differences and sum rules are dominated by the lowest-lying states in analogy with the situation for the $\pi^+$--$\pi^0$ mass difference. Despite the fact that some of the matrix elements appearing in our final result have not yet been accurately measured, we can obtain useful numerical estimates: for example, we obtain (M_{B^+} - M_{B^0})^{EM} \simeq +1.8 \MeV. We argue that our results are accurate to about $30\%$.Comment: 20 pages, plain TeX, 1 uuencoded postscript figur

Intermediate-statistics spin waves

In this paper, we show that spin waves, the elementary excitation of the Heisenberg magnetic system, obey a kind of intermediate statistics with a finite maximum occupation number n. We construct an operator realization for the intermediate statistics obeyed by magnons, the quantized spin waves, and then construct a corresponding intermediate-statistics realization for the angular momentum algebra in terms of the creation and annihilation operators of the magnons. In other words, instead of the Holstein-Primakoff representation, a bosonic representation subject to a constraint on the occupation number, we present an intermediate-statistics representation with no constraints. In this realization, the maximum occupation number is naturally embodied in the commutation relation of creation and annihilation operators, while the Holstein-Primakoff representation is a bosonic operator relation with an additional putting-in-by-hand restriction on the occupation number. We deduce the intermediate-statistics distribution function for magnons. On the basis of these results, we calculate the dispersion relations for ferromagnetic and antiferromagnetic spin waves. The relations between the intermediate statistics that magnons obey and the other two important kinds of intermediate statistics, Haldane-Wu statistics and the fractional statistics of anyons, are discussed. We also compare the spectrum of the intermediate-statistics spin wave with the exact solution of the one-dimensional s = 1/2 Heisenberg model, which is obtained by the Bethe ansatz method. For ferromagnets, we take the contributions from the interaction between magnons (the quartic contribution), the next-to-nearest neighbor interaction, and the dipolar interaction into account for comparison with the experiment.Comment: 22 pages, 2 figure

Irrigation application efficiency and uniformity of water distribution using multi-outlet pipe and resource conservation technologies

Irrigation experiments were conducted during November to April under wheat crop in the winter season of 2012-13 and 2013-14 in the farmer’s field at Galibkhedi village located in Karnal District, Haryana State, India. In the study, collapsible multi-outlet pipe (MOP) along with single outlets pipe (SOP) was tested in farmer’s field under wheat cultivation. Irrigation was carried out in five treatments including tillage (T) with SOP and MOP; zero-tillage (ZT) with SOP and MOP, and furrow irrigation with raised bed (FIRB). Iso-time profile of waterfront spreading and advance indicated that irrigation water distribution was uniform under the plot irrigated using MOP as compared to plot irrigated using SOP. In addition, water distribution was uniform under zero tilled plots as compared to tilled plot. Results implied that MOP has several advantages over SOP in terms of application efficiency (AE) and uniformity of water distribution. Average application efficiency for the first study year was found to be in the order of ZT-MOP (82.41%) > FIRB (76.79%) > ZT-SOP (75.25%) > T-MOP (74.85%) > T-SOP (69.79%). Average application efficiency for the second study year was found to be in the same order as first year with some deviation in values. In the second year values of mean application efficiencies were ZT-MOP (82.58%) > FIRB (77.13%) > ZT-SOP (73.04%) > T-MOP (69.65%) > T-SOP (66.13%). Overall, this study concludes that irrigation under wheat crop using collapsible multi-outlet pipe (MOP) with zero tillage practices is a suitable option for surface irrigation that accomplishes uniform distribution of water with higher application efficiency