Monte Carlo optimisation of correlated wave functions for normal two-electron systems

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ(r₁, r₂) = Σc_mΦ_m(r₁, r₂) with Φ_m(r₁, r₂) = exp[−(r₁ + r₂)]/(br₁₂ + a)^m, where , a, b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.     

Fixed-t partial wave analysis of πN scattering

The last full Karlsruhe PW analysis of πN scattering was finished ca. 20 years ago. After that a huge pile of new accurate πN scattering data has emerged, with which the old analysis is not completely compatible. We are making a highly modernized version of the old analysis to all (recent and old) data, aiming to pay particular attention to the discrepancies between different data sets and to the handling of the experimental errors as well as to the electromagnetic corrections and the effects of isospin breaking.     

Critical currents and the critical state in superconductors with magnetic ions

The critical state model is used to derive equations that relate the additional magnetic moment (ΔM) produced by the flux pinning to the critical current density (J_c) measured in transport measurements. The equations derived for conventional superconductors can be used for superconductors that contain magnetic ions, if ΔM is replaced by ΔM/(1 + χ′(H)) where χ′(H) is the differential susceptibility. In the critical state, the field gradient has contributions from both the macroscopic supercurrents and the Amperian currents from the magnetic ions. Magnetic measurements are sensitive to both contributions. Transport measurements only characterise the macroscopic supercurrents. For superconductors which contain rare-earth elements, the J_c values calculated using hysteretic magnetisation measurements without including the term χ′(H), can be in error by factors of 7.     

An azo-isomerization-induced Freedericksz transition of a nematic liquid crystal

We observed an azo-isomerization-induced Freedericksz transition of the 5CB liquid crystal doped with 1% double-azo. In experiment, we found that the Freedericksz transition threshold occurred at optical intensity level of 0.3 mW/mm² for the 12.5 μm-thickness planar alignment doped 5CB, which is four orders of magnitude lower as that for the pure 5CB. Using optical phase retardation, we measured the relations between the Freedericksz transition threshold and the pump beam polarization. The maximum twist angle of liquid crystal molecules under different pump beam intensity is given. The experiment indicated that trans–cis isomerization plays an important role in the decrease of the Freedericksz transition threshold.     

Characteristic polynomials of random Hermitian matrices and Duistermaat–Heckman localisation on non-compact Kähler manifolds

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N×N random matrix taken from the Gaussian Unitary Ensemble (GUE). Deviating from the standard “supersymmetry” approach, we integrate out Grassmann variables at the early stage and circumvent the use of the Hubbard–Stratonovich transformation in the “bosonic” sector. The method, suggested recently by J.V. Fyodorov [Nucl. Phys. B 621 [PM] (2002) 643], is shown to be capable of calculation when reinforced with a generalisation of the Itzykson–Zuber integral to a non-compact integration manifold. We arrive to such a generalisation by discussing the Duistermaat–Heckman localisation principle for integrals over non-compact homogeneous Kähler manifolds. In the limit of large-N the asymptotic expression for the correlation function reproduces the result outlined earlier by A.V. Andreev and B.D. Simons [Phys. Rev. Lett. 75 (1995) 2304].     

Elliptic Gaudin models and elliptic KZ equations

The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik–Zamolodchikov equations and their solutions are given.     

Globally conformal invariant gauge field theory with rational correlation functions

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_κ(x₁,x₂) of dimension (κ,κ). For a globally conformal invariant (GCI) theory we write down the OPE of V_κ into a series of twist (dimension minus rank) 2κ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field.

We argue that the theory of a GCI hermitian scalar field of dimension 4 in D=4 Minkowski space such that the 3-point functions of a pair of 's and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density .     

Binding energy of an exciton bound to ionized donors in quantum dots

Binding energies for an exciton (X) trapped in the two-dimensional quantum dot by a positive ion located on the z axis at a distance d from the dot plane are calculated by using the method of few-body physics. This configuration is called a barrier (D⁺,X) center. The dependence of the binding energy of the ground state of the barrier (D⁺,X) center on the dot radius for a few values of the distance d between the fixed positive ion on the z axis and the dot plane is obtained. We find that when d<0.2nm the barrier (D⁺,X) center does not form a bound state.     

Oxygen nonstoichiometry and phase transitions of the neodymium-rich Nd1+xBa2−xCu3Oz solid solution

On the basis of chemical, thermal analysis and Cu K-edge X-ray absorption measurements, oxygen content in the Nd_1+xBa_2−xCu₃O_z solid solution was determined between 1000°C in air and 400°C in oxygen for x=0.05–0.9 compositions. It has been observed that the oxygen nonstoichiometry Δz of the Nd_1+xBa_2−xCu₃O_7+x/2−Δz solid solution decreases 2–2.5 times for a large substitution (Δz≈0.3–0.33 for x=0.9), despite of the acclaimed higher total oxygen content. The difference in nonstoichiometry is explained by a higher average value of the copper oxidation state (ACV), which is vital for the solid solution with large x even at elevated temperatures (ACV≈2–2.05 for x>0.3 at 1000°C, PO₂=0.21 atm). On the contrary, the ACV after complete oxygenation is almost constant (about 2.25–2.3) for the whole series. The x-dependence of the oxygen content is not monotonous and structural phase transitions can be observed at x=0.3 and x=0.6, as confirmed by the X-ray diffraction and the Raman scattering spectroscopy. The first well-known transition is connected with the oxygen disorder due to the Nd substitution for Ba at random Ba-sites. In the present work, it is proved by the apical oxygen mode broadening in Raman spectra. Ordering of the Nd and Ba atoms with a subsequent orthorhombic distortion of the lattice may occur even at 1000°C in air due to the second transformation at x≈0.6. The invariable orthorhombicity of the Nd-rich solid solution with x>0.6 is not caused by the oxygen absorption as in the x=0.05 case. Existence of high- and low-temperature orthorhombic modifications of this solid solution has been observed for the first time. Finally, a tentative 3D (z–x–T) diagram is suggested for the Nd_1+xBa_2−xCu₃O_z solid solution up to 1000°C in air, including the new x=0.6–0.9 region.     

Structural and optical properties of thermally evaporated Bi2Te3 films

Bi₂Te₃ films were prepared by thermal evaporation technique. X-ray diffraction analysis for as-deposited and annealed films in vacuum at 150 °C were polycrystalline with rhombohedral structure. The crystallite size is found to increase as the film thickness increases and has values in the range 67–162 nm. The optical constants (the refractive index, n, and absorption index, k) were determined using transmittance and reflectance data in the spectral range 2.5–10 μm for Bi₂Te₃ films with different thicknesses (25–99.5 nm). Both n and k are independent on the film thickness in the investigated range. It was also found that Bi₂Te₃ is a high refractive index material (n has values of 4.7–8.8 in the wavelength range 2.5–10 μm). The allowed optical transitions were found to be direct optical transitions with energy gap  eV. The optical conductivities σ₁ = ƒ(hν) and σ₂ = f(hν) show distinct peaks at about 0.13 and 0.3 eV, respectively. These two peaks can be attributed to optical interband transitions.     

Non-Fermi liquid regimes in U1−xMxPd2Al3(M=Y,Th)

The temperature-composition (T–x) phase diagram and NFL characteristics in the electrical resistivity ρ(T), specific heat C(T), and magnetic susceptibility χ(T) at low temperatures for the systems U_1−xM_xPd₂Al₃ (M=Y,Th) are described. The T–x phase diagram, the NFL characteristics, and the underlying mechanism for the NFL behavior are distinctly different for M=Y³⁺ and Th⁴⁺, apparently reflecting the difference in valence of the M atom substituents, and suggesting that U is tetravalent in these two systems.     

The relationship between crystal structure and electrical conductivity in the LaY1−xInxO3 (x=0.0–0.7) system

The electrical conductivity of the LaY_1−xIn_xO₃ (x=0.0–0.7) system has been studied from the viewpoint of crystal chemistry. The high temperature form of LaYO₃ (x=0.0) was ascertained to be the Sm₂O₃-type (B-type rare earth) structure, not perovskite-type one. The X-ray diffraction (XRD) experiments revealed that the samples with x=0.05 and 0.10 were the mixed phase of Sm₂O₃-type and perovskite-type structure, and changed to perovskite phase in the range of x0.20. From oxygen partial pressure dependence of the electrical conductivity, it was found that both the Sm₂O₃-type and the perovskite-type single phases showed hole conduction, but the mixed phase did oxide-ion one. The electrical conductivity of the LaY_1−xIn_xO₃ (x=0.0–0.7) system increased with increasing x, and showed the maximum value in the range of x=0.05–0.10, and then decreased with increasing x. The occurrence of oxide-ion conduction was discussed from the viewpoint of lattice distortion in the mixed phase.     

Oxygen tracer diffusion in La1 − xSrxCoO3

Tracer diffusion of ¹⁸O in dense, polycrystalline La_1−xSr_xCoO₃ for x = 0.1 has been measured in the temperature range 400 to 600 °C and at 500 °C for x = 0.2 at an oxygen partial pressure of 1 × 10⁵ Pa. Depth profiles were obtained by secondary ion mass spectrometry. The diffusion coefficient for La_0.9Sr_0.1CoO₃ is given by D = (17–247) exp[(−232 ± 8 kJ/mole)/RT] cm²/s. This value is several orders of magnitude lower than D extrapolated from the results for x = 0.2 measured in the 700–900 °C temperature range. One possible explanation for the discrepancy is that the two measurements reflect different diffusion paths. As expected, La_0.8Sr_0.2CoO₃ exhibits a higher diffusivity at 500 °C than does La_0.9Sr_0.1CoO₃.     

On the barrier inhomogeneities of polyaniline/p-Si/Al structure at low temperature

The current–voltage (I–V) characteristics of Au/polyaniline(PANI)/p-Si/Al structures were determined at various temperatures in the range of 90–300 K. The evaluation of the experimental I–V data reveals a decrease of the zero-bias barrier height (BH) and an increase of the ideality factor (n) with decreasing temperature. It was shown that the occurrence of a Gaussian distribution of then BHs is responsible for the decrease of the apparent BH, increase of the ideality factor n due to barrier height imhomogeneities that prevail at the interface. A Φ_b0 versus 1/T plot has been drawn for evidence of the Gaussian distribution of the barrier height, and and σ₀ = 0.0943 V for the mean barrier height and zero-bias standard deviation, respectively, have been obtained from this plot. Thus, a modified versus 1/T plot gives and A^* as 0.885 eV and A^* = 55.80 A/K² cm², respectively. Hence, it can be concluded that Au/PANI/p-Si/Al structure has a good rectifying contact and the temperature dependence of I–V characteristics of the rectifying contact on p-Si successfully have been explained on the basis of TE mechanism with Gaussian distribution of the barrier heights.     

Oxygen diffusion and surface exchange in La1−xSrxFe0.8Cr0.2O3−δ (x=0.2, 0.4 and 0.6)

Oxygen tracer diffusion (D*) and surface exchange rate constant (k*) have been measured, using isotopic exchange and depth profiling by secondary ion mass spectrometry (SIMS), in La_1−xSr_xFe_0.8Cr_0.2O_3−δ (x=0.2, 0.4 and 0.6). Measurements were made as a function of temperature (700–1000 °C) and oxygen partial pressure (0.21–10⁻²¹ atm) in dry oxygen, water vapour and water vapour/hydrogen/nitrogen mixtures. At high oxygen activity, D* was found to increase with increasing temperature and Sr content. The activation energies for D* in air are 2.13 eV (x=0.2), 1.53 eV (x=0.4) and 1.21 eV (x=0.6). As the oxygen activity decreases, D* increases as expected qualitatively from the increase in oxygen vacancy concentration. Under strongly reducing conditions, the measured values of D* at 1000 °C range from 10⁻⁸ cm² s⁻¹ for x=0.2 to 10⁻⁷ cm² s⁻¹ for x=0.4 and 0.6. The activation energies determined at constant H₂O/H₂ ratio are 1.21 eV (x=0.2), 1.59 eV (x=0.4) and 0.82 eV (x=0.6).

The surface exchange rate constant of oxygen for the H₂O molecule is similar in magnitude to that for the O₂ molecule and both increase with increasing Sr concentration.     

Synthesis and characterization of HgBa2Can−1CunO2n+2+δ (n = 1, 2, and 3)

We have successfully prepared the first three members of the mercury-based superconducting compounds Hg--- Ba₂Ca_n−1Cu_nO_2n+2+δ, namely Hg---1201, Hg---1212 and Hg---1223 with high purity and very good quality. T he influence of the synthesis parameters is studied in detail. Using the sealed quartz tube method, very simple procedures are found to ensure a 100% reproducibility of nearly 100% pure Hg---1201 and 85–90% Hg---1212 and Hg---1223. Oxygen annealing of the sample Hg---1201 at 300°C for 18 h results in an enhancement of its critical temperature up to 97 K. The symmetry of the first and second members is tetragonal with lattice parameters a = 3.8831 (1) Å, C = 9.5357 (2) Å, and A = 3.8624 (1) Å, C = 12.7045 (2) Å, respectively. X-ray diffraction lines of Hg---1223 can be indexed in a tetragonal cell with a = 3.8564 (1) Å and C = 15.8564 (9) Å as well as in an orthorhombic cell with lattice parameters a = 5.4537 (1) Å, B = 5.4247 (1) Å, and C = 15.8505 (7) Å.     

N=2 6-dimensional supersymmetric E6 breaking

We study the N=2 supersymmetric E₆ models on the 6-dimensional space–time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space–time M⁴×S¹/(Z₂×Z₂′)×S¹/(Z₂×Z₂′), for the zero modes, we obtain the 4-dimensional N=1 supersymmetric models with gauge groups SU(3)×SU(2)×SU(2)×U(1)², SU(4)×SU(2)×SU(2)×U(1), and SU(3)×SU(2)×U(1)³ with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus A² and disc D², we list all the constraints on constructing the 4-dimensional N=1 supersymmetric SU(3)×SU(2)×U(1)³ models for the zero modes, and give the simplest model with Z₉ symmetry. We also comment on the extra gauge symmetry breaking and its generalization.     

The dependence of I–V and C–V characteristics on temperature in the H-terminated Pb/p-Si(1 0 0) Schottky barrier diodes

The current–voltage (I–V) and capacitance–voltage (C–V) characteristics of H-terminated Pb/p-Si/Al contacts fabricated by us have been measured in the temperature range of 77–300 K. The experimental values of the barrier height (BH) Φ_bo and the ideality factor n for the device range from 0.674 and 1.072 eV (at 300 K) to 0.352 and 2.452 eV (at 77 K), respectively. The ideality factors become larger with lowering temperature while the barrier height decreases. The Φ_bo(n) plot shows a linear dependence in the temperature range of 77–300 K that can be explained by the barrier inhomogeneity at the metal/semiconductor interface. The extrapolation of the linear Φ_bo(n) plot to n = 1 has given a homogeneous barrier height of approximately 0.713 eV for the Pb/p-Si(1 0 0) contact. A Φ_bo versus 1/T plot was drawn to obtain evidence of a Gaussian distribution of the BHs, and values of and σ_s = 80.5 mV for the mean BH and zero-bias standard deviation have been obtained from this plot, respectively. Then, a modified versus 1/T plot gives and A^* as 0.828 eV and 54.89 A/cm² K², respectively. Furthermore, an average value of −0.687 meV/K for the temperature coefficient has been obtained, the value of −0.687 meV/K for hydrogen terminated p-type Si differs from those given for p-type Si without hydrogen termination in the literature.     

Sphaleron glueballs in NBI theory with symmetrized trace

We derive a closed expression for the SU(2) Born–Infeld action with the symmetrized trace for static spherically symmetric purely magnetic configurations. The lagrangian is obtained in terms of elementary functions. Using it, we investigate glueball solutions to the flat space NBI theory and their self-gravitating counterparts. Such solutions, found previously in the NBI model with the “square root–ordinary trace” lagrangian, are shown to persist in the theory with the symmetrized trace lagrangian as well. Although the symmetrized trace NBI equations differ substantially from those of the theory with the ordinary trace, a qualitative picture of glueballs remains essentially the same. Gravity further reduces the difference between solutions in these two models, and, for sufficiently large values of the effective gravitational coupling, solutions tends to the same limiting form. The black holes in the NBI theory with the symmetrized trace are also discussed.