Exchange and correlation in finite-temperature TDDFT

We discuss the finite-temperature generalization of time-dependent density functional theory (TDDFT). The theory is directly analogous to that at temperature T = 0. For example, the finite-T TDDFT exchange-correlation kernel f_xc(T, n) in the local density approximation can again be expressed as a density derivative of the exchange correlation potential f_xc(T, n) = [?v_xc(T, n)∕?n]δ(r ? r′), where n = N∕V is the electron number density. An approximation for the kernel f_xc(T, n) is obtained from the finite-T generalization of the retarded cumulant expansion applied to the homogeneous electron gas. Results for f_xc and the loss function are presented for a wide range of temperatures and densities including the warm dense matter regime, where T ≈ T_F, the electron degeneracy temperature. The theory also permits a physical interpretation of the exchange and correlation contributions to the theory.     

Dependence of structure factor and correlation energy on the width of electron wires

The structure factor and correlation energy of a quantum wire of thickness b ? a _B are studied in random phase approximation (RPA) and for the less investigated region r _s < 1. Using the single-loop approximation, analytical expressions of the structure factor are obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy in RPA is found to be represented by ? _c (b, r _s ) = α(r _s )/b + β(r _s ) ln(b) + η(r _s ), for small b and high densities. For a pragmatic width of the wire, the correlation energy is in agreement with the quantum Monte Carlo simulation data.     

Volume charge density and radial electric field <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">r</Emphasis></Subscript>(<Emphasis Type="Italic">r</Emphasis>) in a moving tokamak plasma

Electric field E _r transverse to the current in a moving quasi-neutral plasma can (and should) be considered using Poisson equations and densities of volume charges emerging in the plasma. In the general case, E _r becomes nonlocal; i.e., remote volume charge densities are not screened but affect the formation of E _r at the points under investigation. This approach is used for describing a phenomenological theory of radial electric field E _r (r) and velocity of toroidal rotation of the plasma in the tokamak. Examples of application of this theory to actual experiments are considered.     

Aussagen der Theorie von Kraichnan für die isotrope hydromagnetische Turbulenz

The theory ofKraichnan is applied to quasi-stationary isotropic hydromagnetic turbulence. The average infinitesimal-impulse-response functionsg(k, τ), g _m (k, τ) and the time-correlationsr(k, τ), r _m (k, τ) are evaluated by the non-local direct-interaction approximation within the inertial range. For the range of ohmic but no viscous dissipation it is found that the magnetic energy spectrumE _m (k) obeys aE(k)k ^?2-law in accordance with results ofGolitsyn andMoffatt.     

Statistical mechanics of rotating systems

A microcanonical distribution function depending on the total energyE and thez-componentM of the total angular momentum of a rotating system is examined. ForM=0 the generalized microcanonical ensemble is found to give the same entropy as the usual microcanonical ensemble. The moment of inertia of a rotating gas is calculated, and the kinetic energy of rotation is given as a power series in the small parameterM ²/2I ₀E_int, whereI ₀ is the moment of inertia of the gas at rest andE _int the internal energy.     

Josephson effects in unconventional heavy fermion superconductors

We discuss the Josephson effect for pairing states which break crystal symmetries in addition to gauge symmetry. We consider theE _1g andE _2u models for the low-temperature phase ofUPt ₃, with order parameters Δ(E _1g )～p _z (p _x +ip _y ) and Δ(E _2u )～p _z (p _x +ip _y )². We report calculations of Josephson critical currents, taking into account the effects of depairing at the interface. For singlet-triplet junctions the critical current is non-zero only for spin-orbit, spin-flip tunneling, and is found to be much smaller than the Ambegaokar-Baratoff value even when the spin-orbit tunneling amplitude is comparable to the spin-independent amplitude.     

Spectra and mean energies of prompt neutrons from <Superscript>238</Superscript>U fission induced by primary neutrons of energy in the region <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><20 MeV

The time-of-flight technique is used to measure the ratios R(E, E _n )=N(E, E _n )/N_Cf(E) of the normalized (to unity) spectra N(E, E _n ) of neutrons accompanying the neutron-induced fission of ²³⁸U at primary-neutron energies of E _n =6.0 and 7.0 MeV to the spectrum N_Cf(E) neutrons from the spontaneous fission of ²⁵²Cf. These experimental data and the results of their analysis are discussed together with data that were previously obtained for the neutron-induced fission of ²³⁸U at the primary energies of E _n =2.9, 5.0, 13.2, 14.7, 16.0, and 17.7 MeV.     

Electron paramagnetic resonance of Cr<Superscript>3+</Superscript>-Li<Superscript>+</Superscript> centers in (Cr,Li): Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript> synthetic forsterite

Synthetic single crystals of chromium-and lithium-doped forsterite, namely, (Cr,Li): Mg₂SiO₄, are studied using electron paramagnetic resonance spectroscopy. It is revealed that, apart from the known centers Cr³⁺(M1) and Cr³⁺(M2) (with local symmetries C_i and C_s, respectively), these crystals involve two new types of centers with C₁ symmetry, namely, Cr³⁺(M1)′ and Cr³⁺(M2)′ centers. The standard parameters D and E in a zero magnetic field [zero-field splitting (ZFS) parameters expressed in GHz] and principal components of the g tensor are determined as follows: D=31.35, E=8.28, and g=(1.9797, 1.9801, 1.9759) for Cr³⁺(M1)′ centers and D=15.171, E=2.283, and g=(1.9747, 1.9769, 1.9710) for Cr³⁺(M2)′ centers. It is found that the lowsymmetric effect of misalignment of the principal axes of the ZFS and g tensors most clearly manifests itself (i.e., its magnitude reaches 19°) in the case of Cr³⁺(M2)′ centers. The structural models Cr³⁺(M1)-Li⁺(M2) and Cr³⁺(M2)-Li⁺(M1) are proposed for the Cr³⁺(M1)′ and Cr³⁺(M2)′ centers, respectively. The concentrations of both centers are determined. It is demonstrated that, upon the formation of Cr³⁺-Li⁺ ion pairs, the M1 position for chromium appears to be two times more preferable than the M2 position. Reasoning from the results obtained, the R₁ line (the ²E → ⁴A₂ transition) observed in the luminescence spectra of (Cr,Li): Mg₂SiO₄ crystals in the vicinity of 699.6 nm is assigned to the Cr³⁺(M1)′ center.     

Zum Energiespektrum der isotropen hydromagnetischen Turbulenz

The physical consequences emerging from a theory stated byKraichnan are considered with regard to isotropic hydromagnetic turbulence. This theory involves the direct-interaction approximation retaining the phase correlation within each triad of Fourier amplitudes. These interactions are suggested to be very important in hydromagnetic turbulence. Hydrodynamic as well as magnetic impulse-response function and time-correlation are unequivocally the same. This result suggests the existence of a universal equilibrium range. Within the inertial range the total energy spectrumE _g (k)=E(k)+E _m (k) obeys the same law as in hydrodynamic turbulenceE(k). The valueE _m (k)≈E(k) corresponds roughly to maximum energy flux through this range. The magnetic energy flux decreases rapidly for eddies with larger wave-numbers within the range of ohmic ? viscous dissipation.     

On a modified separation method for nuclear potentials

In order to obtain a regular but energy-dependent nuclear potential, the following modification of the separation method ofMoszkowski andScott is used: we replace the nuclear potentialv _c (r) by a long-range potentialv _l (r)=v _c (r) Θ(r? d ₀) together with a short-range energy dependent repulsionv _s =h(k) Θ(r _c ?r), whered ₀ is the separation distance for vanishing energy andr _c is the hard-core radius. The potentialv=v _s +v _l (r) is fitted to theS-wave scattering data and the binding energy of the deuteron.h(k) turns out to be almost proportional to the scattering energyE _rel for energiesE _rel<150 MeV.     

Light-Front Quantization of the Restricted Gauge Theory of QCD2

In this talk we study the light-front quantization of the restricted gauge theory of QCD₂à la Cho et al.     

Extended <Emphasis Type="Italic">E</Emphasis>(5) and <Emphasis Type="Italic">X</Emphasis>(5) symmetries: Series of models providing parameter-independent predictions

The E(5) symmetry describes nuclei related to the U(5)-SO(6) phase transition, while the X(5) symmetry is related to the U(5)-SU(3) phase transition. First, a chain of potentials interpolating between the U(5) symmetry of the five-dimensional harmonic oscillator and the E(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ = E(4)/E(2) ratios of 2.093, 2.135, and 2.157 (compared to the ratio of 2.000 of the U(5) case and the ratio of 2.199 of the E(5) case) are derived numerically and compared to existing experimental data, suggesting several new experiments. TheX(5) symmetry describes nuclei characterized byR₄=2.904.Using the same separation of variables of the original Bohr Hamiltonian as in X(5), an exactly soluble model with R₄=2.646 is constructed and its parameter-independent predictions are compared to existing spectra and B(E2) values. In addition, a chain of potentials interpolating between this new model and the X(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ ratios of 2.769, 2.824, and 2.852 are derived numerically and compared to existing experimental data, suggesting several new experiments.     

Thermal annealing effect on structural and optical properties of 2,9-Bis [2-(4-chlorophenyl)ethyl] anthrax [2,1,9-def:6,5,10-d′e′f′] diisoquinoline-1,3,8,10 (2H,9H) tetrone (Ch-diisoQ) thin films

Thin films of 2,9-Bis [2-(4-chlorophenyl)ethyl] anthrax [2,1,9-def:6,5,10-d′e′f′] diisoquinoline-1,3,8,10 (2H,9H) tetrone (Ch-diisoQ) were prepared by thermal evaporation technique. Structural properties of these (as-prepared and annealed at 373, 423, 473 and 523 K) films were determined by X-ray diffraction and scanning electron microscopy, which showed that the grain sizes increasing by the annealing effect. The transmittance and reflectance of all Ch-diisoQ thin films were measured in the range 200–2500 nm. Some optical constants such as optical band gap (E _g ), dispersion energy (E _d ), single oscillator energy (E _o ) and optical dielectric constant at a higher frequency (ε _∞ ) were calculated at different annealing temperatures. The optical band gap of the samples is decreased with the increase of annealing temperatures due to the increasing of the π-dislocation. Finally, the values of the optical susceptibility, χ⁽³⁾, were found to be annealing dependence.     

Treatment of pairing in small systems by Green functions

A finite system of fermions with pairing interaction is treated by the Green function method. It is shown that a finite number of “bound pairs” must be assumed to get the correct properties of the system in that region of the interaction strength where the BCS-solution is incorrect. Also the difference betweenE ₀(N+2)?E ₀(N) andE ₀(N)?E ₀(N?2),E ₀(N) being the ground state energy of theN-particle system, has to be considered. The formulae derived give an interpolation between the region where perturbation theory applies and the region of validity of the BCS-equations.     

Correlation of the piezoelectric and dielectric properties of soft ferroelectric ceramics

The dependences of the piezoelectric (g ₃₃) and electrostriction (Q ₃₃) coefficients of nonpolarized soft relaxor ferroelectric ceramics of the PbMg_1/3Nb_2/3O₃-PbTiO₃ system on electric field E ₃ are calculated and interpreted. The nonmonotonic g ₃₃(E ₃) dependence and negative values of Q ₃₃ were revealed in strong electric fields. These features are shown to be the manifestation of correlation between the piezoelectric and dielectric properties.     

An Analysis of Charged Anisotropic Star with de Sitter Spacetime

We propose a model for charged anisotropic star in de Sitter spacetime. We have taken Krori and Barua (J. Phys. A, Math. Gen. 8, 508, 1975) metric in de Sitter spacetime with non-zero cosmological constant. The model is free from singularity. We incorporate the existence of the cosmological constant on a small scale to study the structure of anisotropic charged star. To solve the Einstein-Maxwell field equations we assume the relation between the radial and transverse pressure as p _t ?p _r =g q(r)² r ² (where g is a non-zero positive constant). The physical conditions inside the stellar model are also discussed.     

On a Semiclassical Formula for Non-Diagonal Matrix Elements

Let H(?)=?? ²d²/dx ²+V(x) be a Schrödinger operator on the real line, W(x) be a bounded observable depending only on the coordinate and k be a fixed integer. Suppose that an energy level E intersects the potential V(x) in exactly two turning points and lies below V _∞=lim?inf?_|x|→∞ V(x). We consider the semiclassical limit n→∞, ?=? _n →0 and E _n =E where E _n is the nth eigenenergy of H(?). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(?), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.     

Fine Structure of Beta Decay Strength Function and Anisotropy of Isovector Nuclear Dencity Component Oscillations in Deformed Nuclei

The experimental measurement data on the fine structure of beta-decay strength function S_β(E) in spherical, transitional, and deformed nuclei are analyzed. Modern high-resolution nuclear spectroscopy methods made it possible to identify the splitting of peaks in S_β(E) for deformed nuclei. By analogy with splitting of the peak of E1 giant dipole resonance (GDR) in deformed nuclei, the peaks in S_β(E) are split into two components from the axial nuclear deformation. In this report, the fine structure of S_β(E) is discussed. Splitting of the peaks connected with the oscillations of neutrons against protons (E1GDR), of proton holes against neutrons (peaks in S_β(E) of β⁺/EC-decay), and of protons against neutron holes (peaks in S_β(E) of β^–-decay) is discussed.     

Surface superconductivity and<Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">c3</Emphasis></Subscript> in UPt<Subscript>3</Subscript>

Ginzburg-Landau (GL) theory is used to study surface superconductivity for UPt₃ for various order parameter symmetries (OPS), andH _c3 is found for all principal directions of the surface normal\(\hat n\) and the field [1]. Assuming specular reflection, and allowing for reorientation of the antiferromagnetic symmetry breaking field in the models withE _1g ,E _2g ,E _1u , orE _2u symmetry, the experiments of Keller et al. [2] with\(\hat n = \hat a\) can be qualitatively explained for all OPS except possiblyA _1u ⊕B _1u . The implied GL parameters then predict qualitatively different and OPS dependent behavior for\(\hat n = \hat a^* \) and\(\hat n = \hat c\). Study ofH _c3 for these surfaces would give strong clues about the OPS of UPt₃.