An O(N logN) alternating-direction finite difference method for two-dimensional fractional diffusion equations

Fractional diffusion equations model phenomena exhibiting anomalous diffusion that cannot be modeled accurately by the second-order diffusion equations. Because of the nonlocal property of fractional differential operators, the numerical methods for fractional diffusion equations often generate dense or even full coefficient matrices. Consequently, the numerical solution of these methods often require computational work of O(N³) per time step and memory of O(N²) for where N is the number of grid points.     

Factorizable Z(N) models

The factorizable S-matrix with Z(N) symmetry is constructed. It is speculated that the field theory belonging to this S-matrix matrix is related to the scaling limit of Z(N) generalizations of the Ising model.     

Non-planar diagrams in the large N limit of U(N) and SU(N) lattice gauge theories

It is shown that the limit as N → ∞ with g²N fixed of the strong coupling expansion for the vacuum expectation values of a U(N) or SU(N) lattice gauge theory is not given by a sum of planar diagrams. This contradicts a result claimed by De Wit and 't Hooft.     

Single-particle approximation to the canonical density operator of a system of N interacting fermions

A necessary condition for the minimum of free energy Tr(ρH^N) + β^-1 Tr(ρlnρ) is investigated for a system of N interacting fermions on the set of all density matrices of the form ρ=Z^-1 exp(-βNΓ^N₁h¹), where Γ^N₁ is Kummer's (1,N)-expansion map, and h¹ is a finite- dimensional one-particle operator. It is shown that for values of β in an open circle $\text{C}\text{(0,β}{}_0\text{)}$ in the complex plane there exists a unique bounded analytic in β one-particle operator X¹(β) such that Z^-1exp(-βNΓ^N₁X¹(β)) satisfies this condition.     

Transition from strong to weak coupling in SU(N) lattice gauge theories

A possible explanation is proposed for the crossover from strong to weak coupling region in SU(N) lattice gauge theories. We predict the pointswhere the crossover takes place for all SU(N)M: For example, g² ≈ 2.0 for SU(2), g² ≈ 1.0 for SU(3) and lim_N→∞Ng²(SU(N) ≈ 2.0.     

The Cauchy problem for the O(N), CP(N − 1), and GC(N,p) models

We study the Cauchy problem for the O(N), $\text{C}$P(N ? 1) and G$\text{C}$(N, p) models in n + 1 dimensional space-time. We prove the existence and uniqueness of solutions for small time intervals and for any n. In space-time dimension two, the previous solutions can be extended to all times by the method of a priori estimates. In space-time dimensions three and four, our estimates yield only partial results on the global existence problem. In all cases the solutions are required only to belong to local spaces, which means that they satisfy local regularity conditions but have no restrictions on their behaviour at infinity in space.     

Global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on bipartite lattices

In this paper the global symmetry of the Hubbard model on a bipartite lattice is found to be larger than SO(4). The model is one of the most studied many-particle quantum problems, yet except in one dimension it has no exact solution, so that there remain many open questions about its properties. Symmetry plays an important role in physics and often can be used to extract useful information on unsolved non-perturbative quantum problems. Specifically, here it is found that for on-site interaction U ≠ 0 the local SU(2) × SU(2) × U(1) gauge symmetry of the Hubbard model on a bipartite lattice with N_a^D sites and vanishing transfer integral t = 0 can be lifted to a global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t > 0. (Examples of a bipartite lattice are the D-dimensional cubic lattices of lattice constant a and edge length L = N_aa for which D = 1, 2, 3,... in the number N_a^D of sites.) The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated-electron number of singly occupied sites operator. Although addition of chemical-potential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its 4^N_aD energy eigenstates refer to representations of the new found global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry. Consistently, we find that for the Hubbard model on a bipartite lattice the number of independent representations of the group SO(3) × SO(3) × U(1) equals the Hilbert-space dimension 4^N_aD. It is confirmed elsewhere that the new found symmetry has important physical consequences.     

Illumination dependence of I-V and C-V characterization of Au/InSb/InP(1 0 0) Schottky structure

The effects of surface preparation and illumination on electric parameters of Au/InSb/InP(100) Schottky diode were investigated, in the later diode InSb forms a fine restructuration layer allowing to block In atoms migration to surface. In order to study the electric characteristics under illumination, we make use of an He-Ne laser of 1 mW power and 632.8 nm wavelength. The current-voltage I(V_G), the capacitance-voltage C(V_G) measurements were plotted and analysed. The saturation current I_s, the serial resistance R_s and the mean ideality factor n are, respectively, equal to 2.03 × 10⁻⁵ A, 85 Ω, 1.7 under dark and to 3.97 × 10⁻⁵ A, 67 Ω, 1.59 under illumination. The analysis of I(V_G) and C(V_G) characteristics allows us to determine the mean interfacial state density N_ss and the transmission coefficient θ_n equal, respectively, to 4.33 × 10¹² eV⁻¹ cm⁻², 4.08 × 10⁻³ under dark and 3.79 × 10¹² eV⁻¹ cm⁻² and 5.65 × 10⁻³ under illumination. The deep discrete donor levels presence in the semiconductor bulk under dark and under illumination are responsible for the non-linearity of the C⁻²(V_G) characteristic.     

Mass scale of grand unification in N = 8 extended supergravity

The mass scale for the running coupling of the conjectured SU(5) grand unified theory embedded in N = 8 extended supergravity is shown to (almost) coincide with the Planck mass. Furthermore, the masses of the superheavy particles in the theory are expected to be order O(m_X) rather than O(m_Planck).     

Integral equations for the scattering of N identical particles

Integral equations are obtained for the scattering of N identical particles using a form of the N-particle scattering equations derived previously. The equations couple together only transition operators between physical two cluster channels, the breakup amplitudes being expressed in terms of quadratures over two-cluster amplitudes. The kernel of the equations becomes connected after a single iteration. The number of coupled equations for identical particles is $\text{1}\text{2}\text{N}\text{or}\text{1}\text{2}\text{(N?1)}$ when N is even or odd respectively.     

Lower bounds to the I = 0, I = 2 ππ s-wave scattering lenghts

Roy's exact partial wave equations allow us to find bounds for any linear combination of the isospin I = 0 and s-wave scattering lengths, with positive coefficients. The bound is a function of the quantity a_D = a₂⁽⁰⁾ + a₂⁽²⁾, where a₂^(I) are the D-wave sacttering lengths. Thus, we can draw on the (a₀⁽⁰⁾, a₀⁽²⁾) plane an allowed domain whose boundary is fairly close to the phenomenological region. For a value of a_D = 1.7×10^?3, we find the following particular bounds: a₀⁽⁰⁾??0.49, a₀⁽²⁾??0.29.     

Two dimensional gases of weight charges and SU(N) fermino theories

We analyze two dimensional gases composed of particles interacting via a Coulomb or Yakawa potential through their “non-Abelian” charges. These charges are taken to be elementary weight or root vectors of SU(N). The grand partition function of these gases is shown to be equivalent to the generating functional of sine-Gordon models with weight vectors and hence to that of SU(N) fermion models. The fermion field creates or annihilates topological solitons which have elementary weight vectors as topological quantum numbers. Then, we discuss the confinement of fermions in the SU(N) Higgs models, where instantons (Z_N vortices) constitute a Yukawa gas of weight charges. We prove that fermions are confirmed by the effects of instantons in the SU(N) Higgs models in contrast with the Abelian Higgs model.     

The bΣ(b0) → XΣ(X10,X21) and aΔ(a2) → X21 transitions of AsBr

Emission spectra of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺,X₂1) and a¹Δ(a2) → X₂1 transitions of AsBr have been measured in the near-infrared spectral region with a Fourier-transform spectrometer. The arsenic bromide radicals were generated in fast-flow systems by reaction of arsenic vapor (As_x) with bromine and were excited by microwave-discharged oxygen. The most prominent features in the spectrum are the Δv = +1,0,−1, and −2 band sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺) transition in the range 11 700-12 700 cm⁻¹. With lower intensities, the Δv = 0 and −1 sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₂1) sub-system show up in the same range. Further to the red, between 6000 and 6700 cm⁻¹, the Δv = 0, +1, and −1 sequences of the hitherto unknown a¹Δ(a2) → X₂1 transition are observed. Analyses of medium- and high-resolution spectra have yielded improved molecular constants for the X₁0⁺, X₂1, and b0⁺ states and first values of the electronic energy and the vibrational constants of the a2 state.     

Discrete symmetries in SO(N) grand unified groups and the survival hypothesis

The possibility of introducing the discrete symmetry D is studied, which along with SU^c(3) × SU_L(2) × U(1)-symmetry, remains after the breaking of SO(N) grand unified symmetry by the Higgs fields vevs ～ 10¹⁵ GeV. The D quantum number distinguishes the fermions coupled with W-bosons via left and right currents. As a result, the presence of low-mass fermions in the theory is provided.     

Chiral symmetry,the 1/N expansion and the SU(N) thirring model

In the two-dimensional SU(N) Thirring model, the 1/N expansion seems to predict spontaneous breaking of the continuous chiral symmetry. This is impossible in two-dimensions. Reasoning along the lines of Berezinski, Kosterlitz and Thouless for the two-dimensional XY model, we argue that, in fact, rather than showing long-range order, $\text{〈}\text{ψ}\text{ψ(x)}\text{ψ}\text{ψ(0)〉}$ vanishes in this model as |x|^?1/N at large |x|. The 1/N expansion is, in fact, a rather good guide to the properties of this model.     

Systematic study of the product((E(2_2~+)/E(2_1~+)) * B(E2)↑) through the asymmetric rotor model

A systematic study of the product((E(2_2~+)/E(2_1~+))*B(E2)↑) is carried out in the major shell space Z=50-82,N=82-126 within the framework of the asymmetric rotor model where the asymmetry parameter γ0reflects change in the nuclear structure.A systematic study of the product((E(2+)/E(2+))*B(E2)↑) with neutron number N is also discussed.The product((E(2_2~+)/E(2_1~+))*B(E2)↑) provides a direct correlation with the asymmetry parameter γ0.The effect of subshells is visible in Ba-Gd nuclei with N 82,but not in Hf-Pt nuclei with N 104.We study,for the first time,the dependency of the product((E(2_2~+)/E(2_1~+))*B(E2)↑) on the asymmetry parameterγ0.     

N2- and O2-broadening of CO2 for the (301)III ← (000) band at 6231 cm

The N₂- and O₂-broadening effect have been investigated for 10 absorption lines of the CO₂ (30⁰1)_III ← (00⁰0) band centered at 6231 cm⁻¹, in the range from P(28) to R(28) by a near-infrared diode-laser spectrometer. We have analyzed the observed line profiles with the Galatry function, and determined the N₂- and O₂-broadening coefficients precisely. The air-broadening coefficients for these lines have been derived. The present results are compared with those of the previous studies for this band and with some of the other bands.     

A multilevel Cartesian non-uniform grid time domain algorithm

A multilevel Cartesian non-uniform grid time domain algorithm (CNGTDA) is introduced to rapidly compute transient wave fields radiated by time dependent three-dimensional source constellations. CNGTDA leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay- and amplitude-compensated field samples. This property is used in conjunction with a multilevel scheme, in which the computational domain is hierarchically decomposed into subdomains with sparse non-uniform grids used to obtain the fields. For both surface and volumetric source distributions, the computational cost of CNGTDA to compute the transient field at N_s observation locations from N_s collocated sources for N_t discrete time instances scales as O(N_tN_slogN_s) and O(N_tN_slog²N_s) in the low- and high-frequency regimes, respectively. Coupled with marching-on-in-time (MOT) time domain integral equations, CNGTDA can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems.     

A nontrivial vacuum state in D = 10, N = 1 supergravity

We find a ground state of D = 10, N = 1 supergravity of the form (AdS(3) × R¹) × S³ × T³ which preserves all supersymmetries and should provide a gauged D = 4, N = 4 supergravity coupled to supermatter after dimensional reduction.     

N Law for bosons in 2D

A rigorous upper bound is derived for the exact ground-state energy of N negative charged bosons and N motionless, i.e. fixed, positive charges with Coulomb interactions in 2D for arbitrary N ? 4 giving rise to an N²-upper bound. The consistency of such an N² behaviour is also investigated by examining a lower bound to the ground-state energy.