Nonlocal Coulomb interaction in the two-dimensional spin-<Emphasis Type="Bold">1/2</Emphasis> Falicov–Kimball model

The two-dimensional (2D) extended Falicov–Kimball model has been studied to observe the role of nonlocal Coulomb interaction (U _nc) using an exact diagonalization technique. The f-state occupation (n ^f ), the f–d intersite correlation function (c _fd), the specific heat (C), entropy (S) and the specific heat coefficient (γ) have been examined. Nonlocal Coulomb interaction-induced discontinuous insulator-to-metal transition occurs at a critical f-level energy. More ordered state is obtained with the increase of U _nc. In the specific heat curves, two-peak structure as well as a single-peak structure appears. At low-temperature region, a sharp rise in the specific heat coefficient γ is observed. The peak value of γ shifts to the higher temperature region with U _nc.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

Kinematic spin-fluctuation mechanism of high-temperature superconductivity

We study d-wave superconductivity in the extended Hubbard model in the strong correlation limit for a large intersite Coulomb repulsion V. We argue that in the Mott-Hubbard regime with two Hubbard subbands, there emerges a new energy scale for the spin-fluctuation coupling of electrons of the order of the electron kinetic energy W much larger than the exchange energy J. This coupling is induced by the kinematic interaction for the Hubbard operators, which results in the kinematic spin-fluctuation pairing mechanism for V ? W. The theory is based on the Mori projection technique in the equation of motion method for the Green’s functions in terms of the Hubbard operators. The doping dependence of the superconductivity temperature T _c is calculated for various values of U and V.     

On the Identity of Some von Neumann Algebras and Some Consequences

Among von Neumann algebras, the Weyl algebra W{\mathcal{W}} generated by two unitary groups {U(α)} and {V(β)}, the algebra U{\mathcal{U}} generated by a completely non-unitary semigroup of isometries {U ₊(α)} and the Weyl algebra W₊^h{\mathcal{W}_{+}^{h}} pertaining to a semi-bounded space with homogeneous spectrum of the generator of {V(β)}, all share the property that their representations are completely reducible and the irreducible representations are equivalent. We trace this fact to the identity of these algebras, in the sense that any of them contains a representation of any of the remaining two algebras, which in turn contains the original algebra. We prove this statement by explicit construction. The aforementioned results about the representations of the algebras follow immediately from the proof for any of them. Also, by the above construction we prove for W^h₊{\mathcal{W}^{h}_{+}} the analog of a theorem by Sinai for W{\mathcal{W}} : given {V(β)} with semi-bounded homogeneous spectrum, there exists a completely non-unitary semigroup {U ₊(α)} such that {V(β)} and {U ₊(α)} generate W₊^h{\mathcal{W}_{+}^{h}}.     

Fluctuation power spectrum of a Josephson junction

The fluctuation power spectrum of the Josephson junction has been evaluated in the limit of large energy barriers [(U _n ^max−U _n ^min)γ]≫1 and small currents [x≪x _e]. The result is valid for finite capacitance of the junction. The effect of the fluctuating Josephson current on the voltageV(t) across the junction has also been taken into account.     

The Kohn-Luttinger mechanism and phase diagram of the superconducting state in the Shubin-Vonsovsky model

Using the Shubin-Vonsovsky model in the weak-coupling regime W > U > V (W is the bandwidth, U is the Hubbard onsite repulsion, and V is the Coulomb interaction at neighboring sites) based on the Kohn-Luttinger mechanism, we determined the regions of the existence of the superconducting phases with the d _xy , p, s, and $d_{x^2 - y^2 } $ symmetry types of the order parameter. It is shown that the effective interaction in the Cooper channel considerably depends not only on single-site but also on intersite Coulomb correlations. This is demonstrated by the example of the qualitative change and complication of the phase diagram of the superconducting state. The superconducting (SC) phase induction mechanism is determined taking into account polarization contributions in the second-order perturbation theory in the Coulomb interaction. The results obtained for the angular dependence of the superconducting gap in different channels are compared with angule-resolved photoemission spectroscopy (ARPES) results. The influence of long-range hops in the phase diagram and critical superconducting transition temperature in different channels is analyzed. The conditions for the appearance of the Kohn-Luttinger superconductivity with the $d_{x^2 - y^2 } $ symmetry and high critical temperatures T _c ～ 100 K near the half-filling are determined.     

Size effects in triplet-triplet annihilation: II. Monte carlo simulations

The dynamics of triplet-triplet annihilation (TTA) is theoretically studied in linear chains and nanoparticles, modeled as 1D, 2D, and 3D regular lattices, as a function of size M, of the rate of excitation migration W, and of the rate of excitation annihilation V in the diffusion-influenced limit (V ≫ W). It is shown that a sum of two exponentials is usually sufficient for fitting experimental phosphorescence and triplet-triplet absorption decays. The first term describes the decay of domains containing initially one triplet, while the second one reflects the disappearance of domains containing initially two triplets. Monte Carlo calculations were carried out to compute the survival probability of an annihilating pair of triplets, yielding expressions for the dependence of the rate constant of TTA on the parameters M, W, and V in one, two, and three dimensions. The text was submitted by the authors in English.     

Electronic structure of TiO<Subscript>2</Subscript> rutile with oxygen vacancies: Ab initio simulations and comparison with the experiment

The electronic structure of TiO₂ rutile with oxygen vacancies, which is a promising insulator, has been analyzed. The ab initio density functional calculations, as well as the comparative analysis of the results obtained in the σ-GGA spin-polarized generalized approximation and those obtained by the σ-GGA + U method with allowance for Coulomb correlations of d electrons titanium atoms in the Hartree-Fock approximation for the Hubbard model, have been performed. It has been found that the effective electron mass in rutile is anisotropic and there are both light (m _e ^* = (0.6–0.8)m ₀, where m ₀ is the free-electron mass) and heavy (m _e ^* > 1m ₀) electrons, whereas holes in rutile are only heavy (m _e ^* ⩾ 2m ₀). It has been shown that the σ-GGA + U method gives a deep occupied level in the band gap and that an oxygen vacancy in rutile is an electron and hole trap.     

Antisite defect types and temporal evolution characteristics of D0<Subscript>22</Subscript>-Ni<Subscript>3</Subscript>V structure: Studied by the microscopic phase field

Microscopic phase field simulation is performed to study antisite defect type and temporal evolution characteristic of D0₂₂-Ni₃V structure in Ni₇₅Al _x V_25−x ternary system. The result demonstrates that two types of antisite defect V_Ni and Ni_V coexist in D0₂₂ structure; however, the amount of Ni_V is far greater than V_Ni; when precipitates transform from D0₂₂ singe phase to two phases mixture of D0₂₂ and L1₂ with enhanced Al:V ratio, the amount of V_Ni has no evident response to the secondary L1₂ phase, while Ni_V exhibits a definitely contrary variation tendency: Ni_V rises without L1₂ structure precipitating from matrix but declines with it; temporal evolution characteristic and temperature dependent antisite defect V_Ni, Ni_V are also studied in this paper: The concentrations of the both defects decline from high antistructure state to equilibrium level with elapsed time but rise with elevated temperature; the ternary alloying element aluminium atom occupies both α and β sublattices of D0₂₂ structure with a strong site preference of substituting α site. Supported by the National Natural Science Foundation of China (Grant Nos. 50671084 and 50875217), the Doctorate Foundation of Northwestern Polytechnical University of China (Grant No. CX200806), the China Postdoctoral Science Foundation Funded Project (Grant No. 20070420218), and the Natural Science Foundation of Shaanxi Province of China     

Unconventional spin-charge phase separation in a model 2D cuprate

In this work, we address a challenging problem of a competition of charge and spin orders for high-T _c cuprates within a simplified 2D spin-pseudospin model which takes into account both conventional Heisenberg Cu²⁺?Cu²⁺ antiferromagnetic spin exchange coupling (J) and the on-site (U) and intersite (V) charge correlations in the CuO₂ planes with the on-site Hilbert space reduced to only three effective charge states (nominally Cu^1+;2+;3+). We performed classical Monte Carlo calculations for large square lattices implying the mobile doped charges and focusing on a case of a small intersite repulsion V ? J. The on-site attraction (U < 0) does suppress the antiferromagnetic ordering and gives rise to a checkerboard charge order with the doped charge distributed randomly over a system in the whole temperature range. However, under the on-site repulsion (U > 0) the homogeneous ground state antiferromagnetic solutions of the doped system found in a mean-field approximation are shown to be unstable with respect to a phase separation with the charge and spin subsystems behaving like immiscible quantum liquids. Puzzlingly, with lowering the temperature one can observe two sequential phase transitions: first, an antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, a charge condensation in the charge droplets. The effects are illustrated by the Monte Carlo calculations of the specific heat and longitudinal magnetic susceptibility.     

Analysis of thermoelectric power of some insulating high-T c superconductors using extended hubbard model

The thermoelectric power (TEP) for a one-dimensional lattice has been studied using the extended Hubbard model in the limitU ≠ ∞, whereU is the on-site Coulomb interaction. A new expression for TEP has been derived in this study. Our study shows that if theV-dependent term in the extended Hubbard model Hamiltonian is considered as attractive, the new expression for TEP could successfully reproduce the TEP results of high-T _c hole-doped insulating systems of Tl₂Ba₂Ca_1−x Y _x Cu₂O_8+y (Tl-2212) and Bi₂Sr₂Ca_−x Y _x Cu₂O_8+y (Bi-2212).     

Non-local matrix generalizations ofW-algebras

There is a standard way to define two symplectic (hamiltonian) structures, the first and second Gelfand-Dikii brackets, on the space of ordinarym ^th-order linear differential opeatorsL=–d ^m +U ₁ d ^m–1+U ₂ d ^m–2+...+U _m . In this paper, I consider in detail the case where theU _k aren×n-matrix-valued functions, with particular emphasis on the (more interesting) second Gelfand-Dikii bracket. Of particular interest is the reduction to the symplectic submanifoldU ₁=0. This reduction gives rise to matrix generalizations of (the classical version of) thenon-linear W _m -algebras, calledV _{n, m} -algebras. The non-commutativity of the matrices leads tonon-local terms in theseV _{n, m} -algebra.s I show that these algebras contain a conformal Virasoro subalgebra and that combinationsW _k of theU _k can be formed that aren×n-matrices of conformally primary fields of spink, in analogy with the scalar casen=1. In general however, theV _{m, n} -algebras have a much richer structure than theW _m -algebras as can be seen on the examples of thenon-linear andnon-local Poisson brackets {(U _2)ab(), (U _2)cd()}, {(U _2)ab(), (W _3)cd()} and {(W _3)ab(), (W _3)cd()} which I work out explicitly for allm andn. A matrix Miura transformations is derived, mapping these complicated (second Gelfand-Dikii) brackets of theU _k to a set of much simpler Poisson brackets, providing the analogoue of the free-field representation of theW _m -algebras.     

A regular potential which is nowhere in L 1

A nonnegative potential V: ℝ^v→ℝ is constructed for which V ∉ L _q (G) for any nonempty open G⊂→^v, q>0, and for which nevertheless W _inf2 ^sup1 ∩ Q(V) is dense in W _inf2 ^sup1 , i.e., is a form core for −1/2Δ in L ₂.     

A Functional-Analytic Theory¶of Vertex (Operator) Algebras, I

This paper is the first in a series of papers developing a functional-analytic theory of vertex (operator) algebras and their representations. For an arbitrary ℤ-graded finitely-generated vertex algebra (V, Y, 1) satisfying the standard grading-restriction axioms, a locally convex topological completion H of V is constructed. By the geometric interpretation of vertex (operator) algebras, there is a canonical linear map from $V⊗V to (the algebraic completion of V) realizing linearly the conformal equivalence class of a genus-zero Riemann surface with analytically parametrized boundary obtained by deleting two ordered disjoint disks from the unit disk and by giving the obvious parametrizations to the boundary components. We extend such a linear map to a linear map from $H\tilde{\otimes} H$ ( being the completed tensor product) to H, and prove the continuity of the extension. For any finitely-generated ℂ-graded V-module (W, Y _W ) satisfying the standard grading-restriction axioms, the same method also gives a topological completion H _W of W and gives the continuous extensions from to H _W of the linear maps from to realizing linearly the above conformal equivalence classes of the genus-zero Riemann surfaces with analytically parametrized boundaries. Received: 15 August 1998 / Accepted: 13 January 1999     

Superconducting state parameters of La<Subscript>100-<Emphasis Type="Italic">C</Emphasis></Subscript>Ga<Subscript><Emphasis Type="Italic">C</Emphasis></Subscript> binary metallic glasses

The theoretical investigations of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _C , isotope effect exponent α and effective interaction strength N _O V of six binary La_100-C Ga _C (C = 16, 20, 22, 24, 26 and 28 at. %) metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential for the first time. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used in the present investigation to study the screening influence on the aforesaid properties. It is observed that the electron-phonon coupling strength λ and the transition temperature T _C are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotential μ*, isotope effect exponent α and effective interaction strength N _O V show weak dependences on the local field correction functions. The T _C obtained from H-local field correction function are found in qualitative agreement with available experimental data and show almost linear nature with the concentration (C) of ‘Ga’ element. A linear T _C equation is proposed by fitting the present outcomes for H-local field correction function, which is in conformity with other results for the experimental data. Also, the present results are found to be in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the metallic glasses.      

Superconducting state parameters of CuCZr100-C metallic glasses

The theoretical investigation of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _c, isotope effect exponent α and effective interaction strength N ₀ V of ten Cu _C Zr_100−C metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential. Three local field correction functions proposed by Hartree (H), Taylor (T) and Ichimaru-Utsumi (IU) are used in the current investigation to study the screening influence on the aforesaid properties. It is observed that the electron-phonon coupling strength λ and the transition temperature T _C are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotential μ*, isotope effect exponent α and effective interaction strength N ₀ V show weak dependences on local field correction functions. The T _c obtained from IU-local field correction function are found an excellent agreement with available theoretical or experimental data. Also, the present results are found in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in metallic glasses.      

Semiclassical Limit for the Schrödinger Equation¶with a Short Scale Periodic Potential

We consider the dynamics generated by the Schr?dinger operator H=−?Δ+V(x)+W(ɛx), where V is a lattice periodic potential and W an external potential which varies slowly on the scale set by the lattice spacing. We prove that in the limit ɛ→ 0 the time dependent position operator and, more generally, semiclassical observables converge strongly to a limit which is determined by the semiclassical dynamics. Received: 7 February 2000 / Accepted: 7 July 2000     

Re-evaluation of the LHC potential for the measurement of <Emphasis Type="Italic">m</Emphasis><Subscript><Emphasis Type="Italic">W</Emphasis></Subscript>

We present a study of the LHC sensitivity to the W boson mass based on simulation studies. We find that both experimental and phenomenological sources of systematic uncertainties can be strongly constrained with Z measurements: the lineshape, dσ _Z /dm, is robustly predicted, and its analysis provides an accurate measurement of the detector resolution and absolute scale, while the differential cross-section analysis, d² σ _Z /dydp _T , absorbs the strong interaction uncertainties. A sensitivity δ m _W ∼7 MeV for each decay channel (W→e ν, W→μ ν), and for an integrated luminosity of 10 fb⁻¹, appears as a reasonable goal.     

Formation of heavy quasiparticles and singlet superconductivity in the periodic Anderson model

The periodic Anderson model is investigated by the method of equations of motion for the symmetric case. The narrowing of the central peak in the density of states with an increase of Coulomb correlation energyU is derived and the resulting enhancement of the effective mass is scaled by the hybridization strength asV ^–4. An intersite pairing is allowed forf electrons and a Green function for the superconducting state is calculated. One can conclude that the conduction electron mediatedf-f interaction, which manifests itself as an effective pairing mechanism, supports singlet superconductivity off electrons.Supported by Polish Academy of Sciences, CPBP, 01.12     

Statistics of inter-particle distances and angles in plasmas

Accurate treatment of the plasma density effects requires a detailed knowledge of the spatial distribution of individual ions around a test ion. In the present work, rigorous expressions are derived for the main 2- and 3-particle spatial distribution functions involving the nearest neighbor (NN) and the next-nearest neighbor (NNN) ions. These expressions, valid for both ideal and nonideal plasmas, present the distributions as functionals of the potentials U _NN and U _NNN at the nearest and next-nearest ion locations. All of the distribution functions except one are derived and discussed in the present work for the first time ever. For utilization of our results in practical calculations, we suggest semi-empirical expressions for U _NN and U _NNN in the ion-ion coupling parameter range 0 ?Γ < 1. In order to test the accuracy of our expressions for U _NN and U _NNN we conduct Molecular Dynamics (MD) simulations. The simulations utilize the pure Coulomb particle-particle interaction potentials, regularized at close range to avoid classical Coulomb collapse, and are free from the assumptions made to find U _NN and U _NNN. Thus, the results of the MD simulations provide an independent test of our theoretical results. Excellent agreement has been found between the results of the theory and of the MD simulations. Finally, we outline the implications of the present findings on the problem of tunneling and charge exchange in dense plasmas. Received 27 October 2000 and Received in final form 30 January 2001