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).     

Some new four-parameter potentials and their use in the study of vibrational thermodynamical quantities of diatomic molecules

Three four-parameter potentials,U _I,U _II andU _III have been proposed and their accuracy has been demonstrated by finding the mean square deviation from the true RKR potential curve for 15 electronic states of 12 diatomic molecules. Their percentage average mean square deviations from RKR curve have been found to be 1.45, 1.86 and 2.89, respectively. These compare favourably with the value 2.67 for the recently suggested four-parameter potential of Wei Hua which itself yields better results than the commonly employed three-parameter potentials. The superiority of the new potentials (especially ofU _I andU _II has been further established by using these potentials to calculate the molecular constants α_e and ω_ex_e following Dunham’s method. The corresponding percentage average mean deviations, for α_e, turn out to be 3.75, 5.13 and 15.43 and for ω_ex_e 8.73, 17.23 and 27.49, respectively, against the respective values of 7.97 and 18.88 with Wei Hua’s four-parameter potential. Also included are the values of dissociation energy determined with these potentials and these too corroborate the better performance ofU _I andU _II. The relative worth of various potential functions has been further tested by carrying out numerical study of vibrational partition function (evaluated by sum over states method), entropy and thermal capacity for the ground state of 7 molecules and comparing these with the corresponding findings based on the RKR data.     

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.     

A variable electron beam and its irradiation effect on optical and electrical properties of CdS thin films

A low energy electron accelerator has been constructed and tested. The electron beam can operate in low energy mode (100 eV to 10 keV) having a beam diameter of 8–10 mm. Thin films of CdS having thickness of 100 nm deposited on ITO-coated glass substrate by thermal evaporation method have been irradiated by electron beam in the above instrument. The I–V characteristic is found to be nonlinear before electron irradiation and linear after electron irradiation. The TEP measurement confirms the n-type nature of the material. The TEP and I–V measurements also confirm the modification of ITO/CdS interface with electron irradiation.      

Synchronization of high-frequency vibrations of slipping phase centers in a tin whisker under microwave radiation

Current-voltage characteristics of a system with a variable number of slipping phase centers resulting from phase separation in a tin whisker under external microwave field with a frequency Ω/2π≅35–45 GHz have been studied experimentally. Emergence and disappearance of steps with zero slope in a whisker’s current-voltage characteristic at U _m/n =(m/n)U _Ω, where m and n are integers and U _Ω is determined by Josephson’s formula _ℏΩ=2eU _Ω, have been investigated. Microwave field generated by slipping phase centers is nonharmonic, and the system of slipping phase centers permits synchronization of internal oscillations at a microwave frequency by an external field with a frequency which is the n-th harmonic of internal oscillations. The estimated microwave power generated by a whisker is 10⁻⁸ W. Stimulation of superconductivity in a current-carrying whisker has been detected. Zh. éksp. Teor. Fiz. 113, 1364–1375 (April 1998)     

Low concentration of the superconducting phase and thermoelectric power in 90 K superconductors

The thermoelectrical power (TEP) and the electrical resistivity behaviour of three 90 K superconductors viz, Y₁Ba₂Cu₃O_7−x , Sm₁Ba₂Cu₃O_7−x and Gd₁Ba₂Cu₃O_7−x , after the specimens were quenched from the sintering temperature (920°C) to 77 K, are reported. Interestingly the Y₁₂₃ specimen, which has the presence of trace amount of the orthorhombic phase in an otherwise tetragonal phase and does not show a superconducting transition down to 77 K shows zero TEP around 82 K, theT _c for the well oxygenated specimen. The Sm and Gd specimens on the other hand show completely tetragonal structure, semiconducting behaviour in resistivity and no zero TEP up to 77 K. It is argued that the critical concentration of the superconducting phase necessary to make the TEP zero is much smaller than that required for zero resistivity.     

Group theoretical aspects ofU B(6) ⊗U F(20) symmetry limits of IBFM related to theU B(5) andO B(6) limits of IBM

TheU ^B(6)⊗U ^F(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU ^B(6)⊗U ^F(20) related to theU ^B(5) andO ^B(6) limits of sdIBM (U ^B(6)) are analysed. Broadly speaking,U ^B(6)⊗U ^F(20) admitsU ^BF(5)⊗U _s ^F (4), Spin^BF(5)⊗U _k ^F (5) andU ^BF(5)⊗U _s ^F (2) limits withU ^B(5) core and Spin^BF(6),O ^BF(5)⊗U _s ^F (4), Spin^BF(6)⊗U _k ^F (5) andO ^BF(6)⊗U _s ^F (2) limits withO ^B(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU ^B(5) andO ^B(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU ^B(6)⊗U ^F(20) symmetry limits are briefly discussed.     

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.     

Electron screening in backward elastic scattering

Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θ_lab=165° and E _lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σ_R(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σ_R(E,θ)=(1+U_e/E)⁻¹, where U _e is an atomic screening potential energy. The deduced average value, U _e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998     

On scattering of slow particles by a “weak” 2D potential

The problem of elastic scattering of low-energy particles by a “weak” 2D potential U without an axial symmetry is considered. The expression for the scattering amplitude is found in this approximation, and it is shown that at U < 0 it has a pole at the energy E ₀ of the corresponding weakly bound state. An explicit expression in terms of the potential U is derived for the factor refining the known order-of-magnitude estimate for E ₀.     

On the theory of slow-particle scattering in the two-dimensional case

A solution to the problem of elastic scattering of low-energy particles on a “weak” potential U is given. An expression for the amplitude of s-wave scattering is found in this approximation, and it is shown that, for U < 0, it has a pole at the energy E ₀ of the corresponding loosely bound state. An explicit expression in terms of the potential U is obtained for the preexponential factor, which refines the known order-of-magnitude estimate for E ₀.     

Measurement of the 45Ca β spectrum in search of deviations from the theoretical shape

The ⁴⁵Ca β spectrum has been measured with a Si(Li) detector. New limits on the mixing parameter (|U _eH |²≤0.005) for a neutrino with mass in the interval 75–100 keV are obtained. The possibility of a monochromatic peak appearing at the end of the β spectrum is analyzed. Fiz. Tverd. Tela (St. Petersburg) 66, No. 2, 81–84 (25 July 1997)     

Quantum creation of the universe with a minimum scalar-field energy

The quantum creation of a closed Friedmann universe is studied on the basis of a Wheeler-DeWitt equation with two arguments — a scale factor and a scalar-field potential. In the quasiclassical approximation the wave function of the universe (WF) starts to evolve at a zero scalar field. A near-Planckian energy density of the field arises as a result of tunneling through a potential barrier. In our opinion, this variant of the scenario most closely resembles creation ex nihilo. The only parameter controlling quantum evolution is the mass of a quantum of the scalar field. In the paper by Khalatnikov and Schiller [JETP Lett. 57,1 (1993)], tunneling through the classically inaccessible region of the superpotential U(a,φ) is calculated by the instanton method. However, this method requires that the potential U(a,φ) satisfy special conditions in the space (a,φ). For this reason, in the present paper the tunneling calculation is performed by the method of characteristics for the quasiclassical approximation of the Wheeler-DeWitt equation under the barrier. The WKB theory, which has been well-developed for one-dimensional problems, is employed along each characteristic. It is shown that the corresponding turning points are also points where U(a, φ)=0. The total barrier penetrability is obtained by averaging over a bundle of characteristics. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 305–308 (10 September 1996)     

Role of the volume and surface breakdown in a formation of microdischarges in a steady-state DBD

The results of an experimental study on a spatial-time behavior of microdischarges (MDs) in steady-state dielectric barrier discharge (DBD) are presented. MDs of DBD have a spatial “memory”, i.e. every subsequent MD appears exactly at the same place that was occupied by the preceding MD. In most cases each MD appears at its fixed place only once by every half-period (HP). Spatial “memory” is derived from slow recombination of plasma in the MDs channels for a period between two neighbor HPs. In steady-state DBD each plasma column was formed only one-time due to local avalanche-streamer breakdown in the very first (initial) gas gap breakdown under inception voltage U^*U^*. After that DBD is sustained under voltage lower than U^*U^*. For the plane-to-plane DBD having the restricted electrode area there is a critical voltage U ₁: DBD is in a steady-state if U > U ₁ but the DBD decays slowly at voltages below U ₁. The decay takes many HPs and occurs due to decreasing the number of MDs inside the gap because of their Brownian motion from central region to the outside of the discharge area. In steady-state DBD there is no correlation between an appearance of alone MD and phase of the applied voltage – each MD has a great scatter in its appearance at the HP. This scatter is attributed to the dispersion in a threshold voltage for local surface breakdowns around the MD base. So, in steady-state DBD the MD volume plasma is responsible for an existence of spatial “memory” (i.e. where the MD appears) but the surface charge distribution around MD is responsible for MD time dispersion (i.e. when the MD appears).     

New approach in theory of Clebsch-Gordan coefficients foru(n) andU q(u(n))

A new method for calculation of Clebsch-Gordan coefficients (CGCs) of the Lie algebrau(n) and its quantum analogU _q(u(n)) is developed. The method is based on the projection operator method in combination with the Wigner-Racah calculus for the subalgebrau(n−1) (U _q(u(n−1))). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form of the projection operator ofu(n) andU _q(u(n)). It is shown that theU _q(u(n)) CGCs can be presented in terms of theU _q(u)(n−1)) q−9j-symbols. Presented at the 9th International Colloquium: “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. Supported by Russian Foundation for Fundamental Research, grant 99-01-01163. Supported in part by the U.S. National Science Foundation under Grant PHY-9970769 and Cooperative Agreement EPS-9720652 that includes matching from the Louisiana Board of Regents Support Fund.     

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.     

Spectral Measures of Small Index Principal Graphs

The principal graph X of a subfactor with finite Jones index is one of the important algebraic invariants of the subfactor. If Δ is the adjacency matrix of X we consider the equation Δ = U + U ⁻¹. When X has square norm ≤ 4 the spectral measure of U can be averaged by using the map u→ u ⁻¹, and we get a probability measure on the unit circle which does not depend on U. We find explicit formulae for this measure for the principal graphs of subfactors with index ≤ 4, the (extended) Coxeter-Dynkin graphs of type A, D and E. The moment generating function of is closely related to Jones’ Θ-series.D.B. was supported by NSF under Grant No. DMS-0301173.     

Dissociation energy of diatomic molecules

The dissociation energy of twelve diatomic molecules has been determined by fitting four-parameter potential functionU(r)=D _e[[1−exp{−b(r−r _e)}]/ [1−Cexp{−b(r−r _e)}]]² to the true Rydberg-Klein-Rees (RKR) curves for their fifteen electronic states using the mean square deviation as the criterion for the selection of the best fit. Average deviation ofD _e has been found to be 2.7% as compared to 20.5% obtained with Lippincott’s potential function for these molecules. In addition the anharmonocity constantω _ex_e has also been calculated for the same electronic states yielding average mean deviation 8.9%.     

Cohomologies and peripheric chains

The deformation properties of Lie subalgebrasLεg that are carriers for twistsF : U(g)→UF(g) are tightly connected with the possibility to apply additional twisting deformationsFR andFJ┴ toUF(g) and quantize new sets ofγ-matrices. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. This work has been partially supported by the Russian Foundation for Fundamental Research under the grant N 00-01-00500.