Kondo lattice model: Unitary transformations, spin dynamics, strongly correlated charged modes, and vacuum instability

Using unitary transformations, we express the Kondo lattice Hamiltonian in terms of fermionic operators that annihilate the ground state of the interacting system and that represent the best possible approximations to the actual charged excitations. In this way, we obtain an effective Hamiltonian which, for small couplings, consists in a kinetic term for conduction electrons and holes, an RKKY-like term, and a renormalized Kondo interaction. The physical picture of the system implied by this formalism is that of a vacuum state consisting in a background of RKKY-induced spin correlations, where two kinds of elementary modes can be excited: Soft neutral modes associated with deformations of the spin liquid, which lead to very large low-temperature values of the heat capacity and magnetic susceptibility, and charged modes corresponding to the excitation of electrons and holes in the system. Using the translational and spin rotational symmetries, we construct a simple ansatz to determine the charged excitations neglecting the effects of the spin correlations. Apart from the `normal', uncorrelated states, we find strongly correlated charged modes involving soft electrons (or holes) and spin fluctuations, which strongly renormalize the low-energy charged spectrum, and whose energy becomes negative beyond a critical coupling, signaling a vacuum instability and a transition to a new phase.Comment: 35 pages, revtex 3.

Resonant magnetic mode in superconducting 2-leg ladders

The spin dynamics of a doped 2-leg spin ladder is investigated by numerical techniques. We show that a hole pair-magnon boundstate evolves at finite hole doping into a sharp magnetic excitation below the two-particle continuum. This is supported by a field theory argument based on a SO(6)-symmetric ladder. Similarities and differences with the resonant mode of the high-T$_c$ cuprates are discussed.Comment: 5 pages, 5 figure

Enhanced Bound State Formation in Two Dimensions via Stripe-Like Hopping Anisotropies

We have investigated two-electron bound state formation in a square two-dimensional t-J-U model with hopping anisotropies for zero electron density; these anisotropies are introduced to mimic the hopping energies similar to those expected in stripe-like arrangements of holes and spins found in various transition metal oxides. In this report we provide analytical solutions to this problem, and thus demonstrate that bound-state formation occurs at a critical exchange coupling, J_c, that decreases to zero in the limit of extreme hopping anisotropy t_y/t_x -> 0. This result should be contrasted with J_c/t = 2 for either a one-dimensional chain, or a two-dimensional plane with isotropic hopping. Most importantly, this behaviour is found to be qualitatively similar to that of two electrons on the two-leg ladder problem in the limit of t_interchain/t_intrachain -> 0. Using the latter result as guidance, we have evaluated the pair correlation function, thus determining that the bound state corresponds to one electron moving along one chain, with the second electron moving along the opposite chain, similar to two electrons confined to move along parallel, neighbouring, metallic stripes. We emphasize that the above results are not restricted to the zero density limit - we have completed an exact diagonalization study of two holes in a 12 X 2 two-leg ladder described by the t-J model and have found that the above-mentioned lowering of the binding energy with hopping anisotropy persists near half filling.Comment: 6 pages, 3 eps figure

From Majorana theory of atomic autoionization to Feshbach resonances in high temperature superconductors

The Ettore Majorana paper - Theory of incomplete P triplets- published in 1931, focuses on the role of selection rules for the non-radiative decay of two electron excitations in atomic spectra, involving the configuration interaction between discrete and continuum channels. This work is a key step for understanding the 1935 work of Ugo Fano on the asymmetric lineshape of two electron excitations and the 1958 Herman Feshbach paper on the shape resonances in nuclear scattering arising from configuration interaction between many different scattering channels. The Feshbach resonances are today of high scientific interest in many different fields and in particular for ultracold gases and high Tc superconductivity.Comment: 13 pages, 7 figures. Journal of Superconductivity and Novel Magnetism to be publishe

Dynamics of earthquake nucleation process represented by the Burridge-Knopoff model

Dynamics of earthquake nucleation process is studied on the basis of the one-dimensional Burridge-Knopoff (BK) model obeying the rate- and state-dependent friction (RSF) law. We investigate the properties of the model at each stage of the nucleation process, including the quasi-static initial phase, the unstable acceleration phase and the high-speed rupture phase or a mainshock. Two kinds of nucleation lengths L_sc and L_c are identified and investigated. The nucleation length L_sc and the initial phase exist only for a weak frictional instability regime, while the nucleation length L_c and the acceleration phase exist for both weak and strong instability regimes. Both L_sc and L_c are found to be determined by the model parameters, the frictional weakening parameter and the elastic stiffness parameter, hardly dependent on the size of an ensuing mainshock. The sliding velocity is extremely slow in the initial phase up to L_sc, of order the pulling speed of the plate, while it reaches a detectable level at a certain stage of the acceleration phase. The continuum limits of the results are discussed. The continuum limit of the BK model lies in the weak frictional instability regime so that a mature homogeneous fault under the RSF law always accompanies the quasi-static nucleation process. Duration times of each stage of the nucleation process are examined. The relation to the elastic continuum model and implications to real seismicity are discussed.Comment: Title changed. Changes mainly in abstract and in section 1. To appear in European Physical Journal

Independent osteoarthritis risk-conferring alleles mediate the same epigenetic and transcriptional effect on a shared target gene, COLGALT2

Objective Over 100 DNA variants have been associated with osteoarthritis (OA), including rs1046934, located within a linkage disequilibrium block encompassing part of COLGALT2 and TSEN15. Here, we used human foetal cartilage, cartilage from arthroplasty patients, and a chondrocyte cell model to determine the target gene(s) at the locus and the mechanism of action. Methods Genotyping and methylation array data of cartilage DNA (n=87) were used to determine if rs1046934 genotype associated with differential DNA methylation at proximal CpGs. Results were replicated in arthroplasty (n=132) and foetal (n=77) cartilage DNA using pyrosequencing. Allelic expression imbalance (AEI) measured effect of genotype upon COLGALT2 and TSEN15 expression. Reporter gene assays and epigenetic editing determined the functional role of regions harbouring differentially methylated CpGs. In silico analyses complemented these experiments. Results Three differentially methylated CpGs residing within regulatory regions were detected, two of which replicated. AEI was detected for COLGALT2 and TSEN15, with associations between expression and methylation for COLGALT2. Reporter assays confirmed that the CpGs are in chondrocyte enhancers with epigenetic editing directly linking methylation with COLGALT2 expression. Conclusion COLGALT2 is a target of this OA locus. We previously characterised another OA locus, marked by rs11583641, that independently targets COLGALT2. rs1046934, like rs11583641, mediates its effect by modulating expression of COLGALT2 via methylation changes to CpGs located in enhancers. The SNPs, CpGs and enhancers are distinct between the loci but the effect on COLGALT2 is the same. COLGALT2 is the target of independent OA risk loci sharing a common mechanism of action

Osteoarthritis genetic risk acting on the galactosyltransferase gene COLGALT2 has opposing functional effects in articulating joint tissues

Background Investigation of cartilage and chondrocytes has revealed that the osteoarthritis risk marked by the independent DNA variants rs11583641 and rs1046934 mediate their effects by decreasing the methylation status of CpG dinucleotides in enhancers and increasing the expression of shared target gene COLGALT2. We set out to investigate if these functional effects operate in a non-cartilaginous joint tissue. Methods Nucleic acids were extracted from the synovium of osteoarthritis patients. Samples were genotyped, and DNA methylation was quantified by pyrosequencing at CpGs within the COLGALT2 enhancers. CpGs were tested for enhancer effects using a synovial cell line and a reporter gene assay. DNA methylation was altered using epigenetic editing, with the impact on gene expression determined using quantitative polymerase chain reaction. In silico analysis complemented laboratory experiments. Results The rs1046934 genotype did not associate with DNA methylation or COLGALT2 expression in the synovium, whereas the rs11583641 genotype did. Surprisingly, the effects for rs11583641 were opposite to those previously observed in cartilage. Epigenetic editing in synovial cells revealed that enhancer methylation is causally linked to COLGALT2 expression. Conclusions This is the first direct demonstration for osteoarthritis genetic risk of a functional link between DNA methylation and gene expression operating in opposite directions between articular joint tissues. It highlights pleiotropy in the action of osteoarthritis risk and provides a cautionary note in the application of future genetically based osteoarthritis therapies: an intervention that decreases the detrimental effect of a risk allele in one joint tissue may inadvertently increase its detrimental effect in another joint tissue

Absolute Calibration of a 200 MeV Proton Polarimeter for Use with the Brookhaven Linac

This work was supported by the National Science Foundation Grant NSF PHY 81-14339 and by Indiana Universit

Triplet superconductivity in a one-dimensional ferromagnetic t-J model

In this paper we study the ground state phase diagram of a one-dimensional $t-U-J$ model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting ($TS$) and spin density wave ($SDW^{z}$) instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin-1/2 XY model takes place. In the case of weakly anisotropic antiferromagnetic exchange the system shows a long range dimerized (Peierls) ordering in the ground state. The complete weak-coupling phase diagram of the model, including effects of the on-site Hubbard interaction, is obtained

Arithmetical properties of Multiple Ramanujan sums

In the present paper, we introduce a multiple Ramanujan sum for arithmetic functions, which gives a multivariable extension of the generalized Ramanujan sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental arithmetic properties of the multiple Ramanujan sum and study several types of Dirichlet series involving the multiple Ramanujan sum. As an application, we evaluate higher-dimensional determinants of higher-dimensional matrices, the entries of which are given by values of the multiple Ramanujan sum.Comment: 19 page