The non-Fermi-liquid nature of the metallic states of the Hubbard Hamiltonian

It has long since been argued that the metallic states of the single-band Hubbard Hamiltonian ? in two spatial dimensions (i.e. for d = 2) should be non-Fermi liquid, a possibility that would lead to the understanding of the observed anomalous behaviour of the doped copper-oxide-based superconducting compounds in their normal metallic states. Here we present a formalism which enables us to express, for arbitrary d, the behaviour of the momentum-distribution function nσ(k) pertaining to uniform metallic ground states of ? close to S _F; σ (the Fermi surface of the fermions with spin index σ, σ = ↑, ↓) in terms of a small number of constant parameters which are bound to satisfy certain inequalities implied by the requirement of the stability of the ground state of the system. These inequalities restrict the range of variation in nσ(k) for k infinitesimally inside and outside the Fermi sea pertaining to fermions with spin index σ and consequently the range of variation in the zero-temperature limit of nσ(k) for k on S _F; σ On the basis of some available accurate numerical results for nσ(k) pertaining to the Hubbard and the t-J Hamiltonian, we conclude that, at least in the strong-coupling regime, the metallic ground states of ? for d = 2 cannot be Fermi-liquid nor can they in general be purely Luttinger or marginal Fermi liquids. We further rigorously identify the pseudogap phenomenon, or 'truncation' of the Fermi surface, clearly observed in the normal states of underdoped copper-oxide-based superconductors, as corresponding to a line of resonance energies (i.e. these energies strictly do not relate to quasiparticles) located below the Fermi energy, with a concomitant suppression to zero of the jump in nσ(k) over the 'truncated' parts of the Fermi surface. Our analyses make explicit the singular significance of the non-interacting energy dispersion ε _k underlying ? in determining the low-energy spectral and transport properties of the metallic ground states of ?.     

Electronic states of boron in superconducting MgB2 studied by11B NMR

Nuclear magnetic resonance (NMR) spectra and nuclear spin-lattice relaxation rateT ₁⁻¹ of¹¹B have been measured in superconducting polycrystalline MgB₂ with 7_c^ons = 39.5 K. It is shown that (T ₁T⁻¹ and the Knight shiftK _s are independent of temperature and nearly isotropic aboveT _c. Both of these quantities are decreased gradually in going to the superconducting state. According to NMR data the density of states near the Fermi level is flat at the scale of about 500 K. Some conclusions on the orbital content of the density of states at the Fermi level were drawn and compared with the results of the band structure calculations.     

Quantum groupSU(1, 1) ⋊ Z2 and “super-tensor” products

A quantum analogue of the groupSU(1,1)Z ₂—the normalizer ofSU(1, 1) inSL ₂(C)—is introduced and studied. Although there isno correctly defined tensor product in the category of *-representations of the quantum algebraC[SU(1, 1)] _q of regular functions, some categories of *-representations ofC[SU(1, 1)Z ₂] _q turn out to be endowed with a certainZ ₂-graded structure which can be considered as a super-generalization of the monoidal category structure. This quantum effect may be considered as a step to understanding the concept of quantum topological locally compact group.In fact, there seems to be afamily of quantum groupsSU(1, 1)Z ₂ parameterized by unitary characters T ¹ of the fundamental group of the two-dimensional symplectic leaf ofSU(1, 1)/T, whereT is the subgroup of diagonal matrices.It is shown that thequasi-classical analogues of the results of the paper are connected with the decomposition of Schubert cells of the flag manifoldSL ₂(C)_R/B (whereB is the Borel subgroup of upper-triangular matrices) into symplectic leaves.Supported by the Rosenbaum Fellowship.     

Correlation between fractional independent yields and neutron-to-proton ratio of fission products in low energy fission

Fractional independent yields of fission products in the thermal neutron-induced fission of²³³U,²³⁵U,²³⁹Pu,²⁴¹Pu and in the spontaneous fission of²⁵²Cf have been correlated with the neutron-to-proton ratio of the fission products. The yields of the products from a fissioning system, when plotted as a function of neutron-to-proton (N/Z) ratio of fission preducts, fall on two Gaussian distribution corresponding to light and heavy fission products. The centroids of the distribution or the most probable value of neutron-to-proton ratio is found to be very close to theN/Z of the fissioning nucleus. From the most probable value ofN/Z the various parameters of charge distribution e.g. most probable massA _p, most probable chargeZ _p, the mass dispersionσ _Aand the charge dispersionσ _Zhave been obtained and are in good agreement with the experimental values ofA _pandZ _p.     

Ion impact stopping cross sections for various media (Z = 3–100)

ABSTRACT

Stopping cross sections (SCS) for protons, alphas and Li ions are calculated with a modified form of our earlier work by incorporating a different electron density distribution of target materials; this involves four parameters – two projectile dependent and the rest two remain fixed. The prosed model has been tested for three stripped ion (H⁺, He^{2 +} and Li^{3 +}) projectiles and found that it describes quite satisfactorily the experimental SCS data from low energies with projectile velocities nearing v = Z₁v₀ (with Z₁ as the atomic number and v₀ the Bohr velocity) up to 100.0 MeV over a wide range of stopping media with atomic numbers Z₂ =3–100.     

Electron Spin Resonance and Ground State Wave Functions of Vanadyl Ion in LiNaSO<Subscript>4</Subscript>

Electron spin resonance (ESR) of VO²⁺ doped into LiNaSO₄ has been studied at 300 K on an X-band spectrometer. The ESR powder spectra have been analyzed and spin Hamiltonian parameters have been evaluated. Using the crystal-field approach, a theoretical estimate of the ground state wave functions of VO²⁺ in LiMSO₄ (M = Na, K) has been made from the ESR data. The dipolar hyperfine coupling constant P and Fermi contact parameter K have also been estimated.     

A discrete variational problem related to Ising droplets at low temperatures

We consider a variational problem on thed-dimensional latticeZ ^d which has applications in the study of the meatastable behavior of the stochastic Ising model. The problem, an isoperimetric one, is to find what is the smallest area a finite subset ofZ ^d can have restricted to three classes of subsets ofZ ^d . If is one of these subsets, we define its volume as the number of points in it and its area as the number of pairs of points inZ ^d which are neighbors and such that only one of them belongs to .     

Positron annihilation study for cadmium (electronic structure and enhancement effect)

The three dimensional electron density in momentum space ρ(p) and in wave vector space n(k) was reconstructed for cadmium (Cd). The measurements were performed using the two dimensional angular correlation of annihilation radiation (2D-ACAR) technique. Enhanced contributions in the spectra were observed around 5.5 mrad, discussed in terms of a Kahana-like enhancement effect. From another viewpoint, Fermi radii were analyzed in the (λM K), (ALM) and (AHK) planes, and they showed a maximum deviation of about 4% from the free electron Fermi radius. Moreover, comparisons to a radio-frequency size effect (RFSE) experiment and theoretical band structure calculations (using augmented plane wave (APW), linear combination of atomic orbital (LCAO) and linear muffin tin orbital (LMTO) methods) were examined. The results showed a qualitative agreement with both APW and LCAO calculations. However, a favorable agreement with the APW method was determined via Fermi surface dimensions. The differences of bands' occupation of n(k) between the current work and the APW method were argued in view of positron wave function in Cd.     

Multifaceted asymmetric radiation from the edge along improved confinement mode in LHCD plasmas with graphite limiters on HT-7 tokamak

Multifaceted asymmetric radiation from the edge (MARFE) phenomena during lower hybrid current drive (LHCD) Experiments on the HT-7 superconducting tokamak are summarized in this paper. The best correlation has been found between the total input (ohmic + LHCD) power and the product of the edge line average density and Z _eff. Studies show that the critical density of MARFE onset is observed in the region of Z _eff ^1/2f_GW = 0.6-0.9, where , (here is the maximum line average electron density and n_GW is the Greenwald density). These MARFEs generally appear to have the same characteristics as high f_GW MARFEs and are positionally stable throughout the LHCD pulse. Improved confinement mode induced by a MARFE is observed, and it is maintained for about 65 ms. MARFE cools the plasma edge, and the electron density profile is observed to become more narrow and peaked.     

Three-body analysis of<Superscript>11</Superscript>Li and its<Emphasis Type="Italic">β</Emphasis>-decay to deuteron channel and to halo analog state<Superscript>11</Superscript>Be* (18.3 MeV)

The ground state wave function of¹¹Li obtained in a three-body model proposed earlier (S Kumar and V S Bhasin,Phys. Rev. C65, 034007 (2002)) has been employed to study the probability distributions, momentum distributions and n−n correlation. Complex scaling method has been used to find the energy positions and widths of the three resonant states of¹¹Li above the breakup threshold. The formalism is extended further to study the β-decay of¹¹Li to two channels. One is the β-transition of¹¹Li into a high lying excited state of¹¹Be at 18.3 MeV, i.e.,¹¹Be* and the second is the decay to deuteron +⁹Li channel. The¹¹Be* state has been considered as a halo analog state identified as a bound three-body (⁹Li + n + p) system. The n-⁹Li interaction incorporates both the virtual state and the p-wave resonance observed experimentally. For p-⁹Li interaction, a Coulomb corrected separable interaction is constructed using charge indepedendence for strong interaction part. The n-p interaction is operative only in³S₁ state corresponding to the isotopic spin T^h =0. As a result the¹¹Be* state has the same isotopic spin as that of⁹Li core, i.e.,T = 3/2. Using these realistic parameters as input and without invoking any other free parameter, the model has been used to predict the strength of the Gamow-Teller β-decay of¹¹Li to¹¹Be*, i.e.,Bgt = 1.5 and the value of the branching ratio to⁹Li + deuteron channel to be 1.3 × 10^-4. These results are found to be in rather good agreement with the recent experimental findings.     

de Haas-van Alphen effect and the Fermi surface of PrNi5

The Fermi surface of PrNi₅ has been studied by the measurements of the de Haas-van Alphen (dHvA) effect at temperatures between 0.3 and in magnetic fields up to 12 T. Two dHvA frequencies have been obtained. The electronic structure of PrNi₅ was calculated using the full potential linearized augmented plane wave method. Five sheets of the Fermi surface and the multiple extremal cross sections were determined. First and second sheet have a hole-like structure. The agreement between theory and experiment is obtained by a small downward shift ( 0.1 eV) of the Fermi energy which is probably due to an underestimation of the role of 4 f electrons. Received 9 May 2000 and Received in final form 20 September 2000     

Effect of frequency on acoustic parameters in a binary mixture of polar liquids

The densities (α) and ultrasonic velocities (C) of binary mixtures of a polar liquid like acetone and toluene have been measured at different frequencies (lMHz, 3MHz and 5MHz) over the entire range of mole fraction of acetone at temperature 303.16k. The intermolecular free length (L _f ), isentropic compressibility (β), acoustic impedance (Z), excess values of isentropic compressibility (β ^E ) and acoustic impedance (Z ^E ) have been computed using values of ultrasonic velocity (C) and density (α). The ultrasonic velocity (C), intermolecular free length (L _f ) and excess values of isentropic compressibility are positive whereas excess values of acoustic impedance is negative for the entire composition range which indicates the specific interaction between unlike molecules. The results are discussed in the light of intermolecular interactions occurring in the solutions.     

Optical and electron spin resonance spectra ofZ 2(Eu) centers in alkali halide crystals

The ESR spectra ofZ ₂(Eu)-centers in KBr and KCl are presented and correlated to the optical absorption and the electron spin resonance of the Europium vacancy complex. The fine structure of theZ ₂ spectra can be described by a Spin-Hamiltonian with an axialb ₂ ⁰ -parameter only. At room temperature it amounts to 1,761 10^–4 cm^–1 for KBr, 1,854 10^–4 cm^–1 for KCl and 1,453 10^–4 cm^–1 for RbCl. Accordingly theZ ₂(Eu)-center must posses a strict axial 100-symmetry in these crystals.     

Coherent backscattering of electromagnetic waves in a magnetised plasma

Summary A microwave coherent backscattering experiment has been carried out on Mirabelle, a weakly ionised plasma device, with the objective of measuring the electron density fluctuation level. The experiment is a preliminary step in order to prepare the detection system for a microwave stimulated backscattering experiment. The incident electromagnetic wave is focused in front of a plane grid which excites ion acoustic or electron Bernstein waves inducing fluctuations in the plasma. The backscattering signal is collected by the launching circuit and detected by homodyne mixing. The typical ratio of the scattered power to the incident power is about 10⁻¹² and the relative density fluctuations are of the order of δn _e/n _e=10⁻³ against a background electron density ofn _e=1–5·10⁹ cm⁻³. The backscattering measurement is compared with Langmuir probe measurements. The spectral width of the backscattered signal has also been studied, by taking into account effects due to the incident wave focusing and plasma wave damping. The authors of this paper have agreed to not receive the proofs for correction     

Stopping of swift hydrogen diclusters: oscillator model

Enhanced stopping of swift hydrogen diclusters has been analysed theoretically. The target has been modeled as a gas of harmonic-oscillator atoms of variable density. This model predicts a proximity effect, i.e., enhanced stopping at high beam energy, and an oscillatory behavior at low energy. Both features get less pronounced with increasing target density due to increased screening of the ion-target interaction by polarization of the medium. Static screening by electrons accompanying the cluster likewise reduces the proximity effect. The Barkas-Andersen correction has been estimated in the Z₁³Z_1^3 limit. Our findings are in contrast with measurements on SiO₂ [S.M. Shubeita et al., Phys. Rev. B 77, 115327 (2008)] which showed a pronounced step in the energy dependence of the proximity effect.     

Magnetic field alignment of high-T c superconductorsRBa2Cu3O7–δ (R=rare earth)

Finely ground powders ofRBa₂Cu₃O_{7 –} (R=Y, Nd, Sm, Eu, Dy, Ho, Er, Tm, Yb) have been mixed at dilute 3%-by-volume concentrations into epoxy matrices which were then allowed to harden in applied magnetic fieldsH _A=18 kOe. X-ray diffractometry studies and 4.3 K measurements of supercurrent-induced magnetization hysteresisM are interpreted as indicating at least partial alignment of single-crystal-grain c-axes (1) parallel toH _A forR=Y, Nd, Sm, Dy, Ho (as earlier found by Farrell et al. forR=Y), and (2) perpendicular toH _A forR=Eu, Er, Tm, Yb. With a few exceptions (Y, Sm, Eu) the alignment direction correlates with the sign of the second-order Stevens factor _J of the crystalline electric field Hamiltonian in the manner suggested by Livingston et al. For the best aligned specimens (Ho, Dy) critical current densitiesJ _c (4.3 K, 5 kOe) for individual grains are estimated fromM and the Bean model to be of order 10⁷ A/cm² for the measuring fieldH parallel to the original alignment fieldH _A, and of order 10⁶ A/cm² forH perpendicular toH _A.     

Observation of a degenerate Fermi gas confined by a standing electromagnetic wave

We have observed a gas of Fermi atoms confined in the antinodes of a standing electromagnetic wave. The standing wave is formed by two counter-propagating beams with the wavelength of 10.6 μm focused on the same spot. Each antinode confines a pancake-shaped cloud of 7500 lithium-6 atoms in two equally populated spin states at the temperature T = 0.1E _F, where E _F is the Fermi energy. The system is in the regime beyond the local density approximation: Only the 3 lowest energy states of the axial motion are populated. The system may become an instrument for the study of 2D Fermi physics and 3D effects beyond the local density approximation.     

Spherical harmonics and cartesian tensor scalar product expansions of the distribution function

On the basis of the expansion of the distribution function in a sum of the spherical harmonics, the distribution functionf(v, r, t) is expanded in a series of scalar products of two Cartesian tensors term by term, i.e. The tensors and ^(l) (l=2, 3) are constructed in dependence on the spherical harmonic expansion coefficients (the tensors and ^(l) (l=0, 1) have been constructed by Jancel and Kahan [3]). On the basis of the knowledge of the analytic form off ₂ andf ₃ the equations forf ₁ f ₂ andf ₃ for the case of the Boltzmann's equation are determined.Technická 2, Praha 6, Czechoslovakia.     

Iterated networks and the spectra of renormalizable electromechanical systems

Beginning with anLRC network with impedance functionZ(), a sequence of iterated networksN _k with impedance functionsZ ^k(), k= 1, 2, 3,..., is introduced. The asymptotic comportment ofZ ^k() and the spectra ofN _k are analyzed in terms of the Julia set ofZ. An example is given of an iterated network associated with a cascade of period-doubling bifurcations.     

The nuclear magnetic moment of theI=2 80.56 keV Mössbauer level of166Er

A value for the nuclear magnetic moment of theI=2 (80.56 keV) level of¹⁶⁶Er has been obtained by comparing measurements made by the Mössbauer effect on¹⁶⁶Er with NMR measurements on the ground state of¹⁶⁷Er in the same matrix. From measurements on ErFe₂, ErAl₂ and ErZn we obtain the value _N (¹⁶⁶Er; 80.56 keV)=0.650±0.010 n.m. This result is slightly higher than previously proposed values.