The Geometry of¶(Super) Conformal Quantum Mechanics

N-particle quantum mechanics described by a sigma model with an N-dimensional target space with torsion is considered. It is shown that an SL(2,ℝ) conformal symmetry exists if and only if the geometry admits a homothetic Killing vector D ^a δ _a whose associated one-form D _a dX ^a is closed. Further, the SL(2,ℝ) can always be extended to Osp(1|2) superconformal symmetry, with a suitable choice of torsion, by the addition of N real fermions. Extension to SU(1,1|1) requires a complex structure I and a holomorphic U(1) isometry D ^a I _a ^b δ _b . Conditions for extension to the superconformal group D(2,1;α), which involve a triplet of complex structures and SU(2)×SU(2) isometries, are derived. Examples are given. Received: 3 September 1999 / Accepted: 30 January 2000     

Application of Boltzmann Equation on Spin Diffusion of Ferromagnetic Superfluid <Superscript>3</Superscript>He: Near Critical Temperature

Different scattering processes of quasiparticles containing a binary process, a coalescence process and a decay process in transition probabilities are taken into account. In the meantime, interaction between Bogoliubov quasiparticles as well as that between normal and superfluid components (spin up-spin down quasiparticles) of ferromagnetic superfluid ³He-A ₁ are considered. Pfitzner procedure is used in the calculation of triplet and singlet quasiparticle scattering amplitude existing in transition probabilities of the collision integral of standard Boltzmann equation at melting pressure. Pfitzner procedure is extended beyond s-p approximation by adding higher angular momentum components. Then, using the results of Boltzmann equation and considering smallness of the gap close to T _c↑, the change of the spin diffusion coefficients tensor of the A ₁-phase of superfluid ³He close to critical temperature and melting pressure is calculated. Temperature dependence of the spin diffusion coefficient change, i.e., δD _xyxy /D⌈=(3/2)(δD _xzxz /D)⌉, is −0.71(1−(T/T _c↑))^1/2. It is also shown that interaction between normal and Bogoliubov quasiparticles (normal-superfluid components interaction) is very important to transport properties such as spin diffusion close to critical temperature. Furthermore, using s-p approximation, the prefactor of δD _xyxy /D is plotted in terms of pressure; hence, the pressure dependence of δD _xyxy /D is also determined.     

Variation of interface trap level charge density within the bandgap of 4H-SiC with varying oxide thickness

Interfacial characteristics of metal oxide-silicon carbide (MOSiC) structure with different thickness of SiO₂, thermally grown in steam ambient on Si-face of 4H-SiC (0 0 0 1) substrate were investigated. Variations in interface trapped level density (D _it) was systematically studied employing high-low (H-L) frequency C–V method. It was found that the distribution of D _it within the bandgap of 4H-SiC varied with oxide thickness. The calculated D _it value near the midgap of 4H-SiC remained almost stable for all oxide thicknesses in the range of 10⁹–10¹⁰ cm⁻² eV⁻¹. The D _it near the conduction band edge had been found to be of the order of 10¹¹ cm⁻² eV⁻¹ for thicker oxides and for thinner oxides D _it was found to be the range of 10¹⁰ cm⁻² eV⁻¹. The process had direct relevance in the fabrication of MOS-based device structures.     

The Beam Propagation Factor of Nonparaxial Truncated Flattened Gaussian Beams

By using the second-order moment of the power density, the beam width, far-field divergence angle and M² factor of nonparaxial truncated flattened Gaussian (FG) beams are derived analytically. It is shown that the M² factor of nonparaxial truncated FG beams depends not only on the truncation parameter δ and beam order N, but also on the initial waist-width to wavelength ratio w₀/λ. The far-field divergence angle approaches an asymptotic value of θ_max=63.435° when the truncation parameter δ → 0. For the special cases of N = 0 and δ → ∞ our results reduce to those of nonparaxial truncated Gaussian beams and nonparaxial untruncated FG beams, respectively.     

Spectral rigidity and eigenfunction correlations at the Anderson transition

The statistics of energy levels for a disordered conductor are considered in the critical energy window near the mobility edge. It is shown that, if the critical wave functions are multifractal, the one-dimensional gas of levels on the energy axis is compressible, in the sense that the variance of the level number in an interval is 〈 (δN)²〉∼χ〈N〉 for 〈N〉≫1. The compressibility, χ=η/2d, is given exactly in terms of the multifractal exponent η =d−D ₂ at the mobility edge in a d-dimensional system. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 355–360 (10 September 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Breit–Wigner Approximation and the Distribution¶of Resonances

For operators with a discrete spectrum, {λ _j ²}, the counting function of λ _j 's, N (λ), trivially satisfies N ( λ+δ ) −N ( λ−δ ) =∑ _j δ_{λ j} ((λ−δ,λ+δ]). In scattering situations the natural analogue of the discrete spectrum is given by resonances, λ _j ∈ℂ₊, and of N (λ), by the scattering phase, s(λ). The relation between the two is now non-trivial and we prove that

Semiempirical study of perturbations of the Landé g factors of electronic-vibrational-rotational levels of hydrogen: II. i 3 g − and j 3Δ g − states of the H2, HD,and D2 molecules

The values of the Landé g factors of the i ³Π _g ⁻ , v, N and j ³Δ _g ⁻ , v, N states of the H₂, HD, and D₂ molecules have been found semiempirically for the following vibrational and rotational quantum numbers: v≤3; N≤7 for H₂; N≤5 for HD; and N≤11 for D₂. These values were obtained in terms of the nonadiabatic model, which takes into account the interaction between the 3dπ³Π_g and 3dδ³Δ_g states with the same values of v and N in the approximation of pure precession, with the use of semiempirical values of the expansion coefficients of the wave functions in the Born-Oppenheimer basis determined by us previously and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. The results obtained for the H₂ molecule are in good agreement with the data in the literature. For the i ³Π _g ⁻ and j ³Δ _g ⁻ states of the HD and D₂ molecules, the g factors were found for the first time. This made it possible to study for the first time the role of the isotopic effect in the perturbation of the dependences of the g factors of rovibrational levels on v and N for the triplet electronic states of the hydrogen molecule. It was found that the interference effects of interaction between the 3dπ³Π_g and 3dδ³Δ_g states lead both to significant differences—up to 8, 6, and 11 times for H₂, HD, and D₂, respectively (the i ³Π _g ⁻ state), 20 times for H₂ and HD, and two orders of magnitude for D₂ (the j ³Δ _g ⁻ state)—between the nonadiabatic values of the g factors and the corresponding adiabatic values for some isotopomers of the hydrogen molecule and to significant differences—up to 9 and 1.5 times for the j ³Δ _g ⁻ and i ³Π _g ⁻ states, respectively—in the nonadiabatic values of the g factors of rovibrational levels of different isotopomers of the hydrogen molecule. __________ Translated from Optika i Spektroskopiya, Vol. 96, No. 1, 2004, pp. 42–54. Original Russian Text Copyright ? 2004 by Astashkevich.     

On the electron mobility of δ layers in the presence of diamagnetic “ejection” of size-quantization levels

The Hall mobility of electrons is investigated as a function of the population of size-quantization subbands in the two-dimensional electron gas of a δ-doped layer in GaAs with constant total electron density N _s =3.2×10¹² cm⁻² (three initially filled subbands) at T=4.2 K. The population of the subbands is varied by diamagnetic “ejection” of size-quantization levels (i.e., pushing them over the Fermi level) by a magnetic field oriented parallel to the plane of the δ-doped layer. The measurements are made in magnetic fields making small angles (5°) with the plane of the doping. The magnetic field component normal to the plane was used to measure the Hall mobility and density. It is found that the measured Hall mobility as a function of the ejecting magnetic field has a distinct maximum. This maximum is due to an increase in the electron mobility in the first subband (the ground subband is assigned the index 0) and electron redistribution between subbands with in increasing ejecting magnetic field parallel to the plane of the δ layer. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 11, 704–708 (10 December 1997)     

Convexity of internal energy of cubic crystal deformed to orthorhombic structure

A generalized set of strain variablesq _r ^N , has been defined to develop the expression for a generalized set of second order and third-order elastic moduliC _rs ^N andC _rst ^N for a cubic crystal deformed to orthorhombic structure. The HessainC _rs ^N δq_rδq_s andC _rst ^N δq_rδq_sδq_t (r=1, 2……6; summation convention) are calculated in the new variables and compared withG-strength andS-strength, for both positive and negative loading environment. The convexity of the internal energy relative to various choice of strain measure is examined considering up to third degree terms in the internal energy expression. The computational results forbcc iron is presented according to the new moduli. The stable ranges thus obtained for iron under hydrostatic compressive and tensile stresses is found to generate the classical stable range, green-stable range and stretch-stable range as the specific cases. However,bcc iron does not seem to follow any conventional stable ranges under hydrostatic compression, where the present generalized stable range is found satisfactory.     

On Ruelle’s Construction of the Thermodynamic Limit for the Classical Microcanonical Entropy

In 1969 Ruelle published his construction of the thermodynamic limit, in the sense of Fisher, for the quasi-microcanonical entropy density of classical Hamiltonian N-body systems with stable and tempered pair interactions. Here, “quasi-microcanonical” refers to the fact that he discussed the entropy defined with a regularized microcanonical measure as ln (N!⁻¹ ∫ χ _{{ℰ−▵ℰ<H<ℰ}}d^6N X) rather than defined with the proper microcanonical measure as ln (N!⁻¹ ∫ δ(ℰ−H) d^6N X). Replacing δ(ℰ−H) by χ _{{ℰ−▵ℰ<H<ℰ}} seems to have become the standard procedure for rigorous treatments of the microcanonical ensemble hence. In this note we make a very elementary technical observation to the effect that Ruelle’s proof (still based on regularization) does establish the thermodynamic limit also for the entropy density defined with the proper microcanonical measure. We also show that with only minor changes in the proof the regularization of δ(ℰ−H) is actually not needed at all.     

Photoproduction of baryons decaying into Nπ and Nη

A combined analysis of photoproduction data on γp↦ πN, ηN was performed including the data on KΛ and KΣ. The data are interpreted in an isobar model with s-channel baryon resonances and π, ρ (ω), K, and K ^* exchange in the t-channel. Three baryon resonances have a substantial coupling to ηN, the well-known N(1535)S ₁₁, N(1720)P ₁₃, and N(2070)D ₁₅. The inclusion of data with open strangeness reveals evidence for further new resonances, N(1840)P ₁₁, N(1875)D ₁₃ and, with weaker evidence, for N(2170)D ₁₃.     

Theoretical optimization of metalp–n silicon Schottky barrier solar cell

The theoretical optimization of the design parametersN _A ,N _D andW _P has been done for efficient operation of Au-p-n Si solar cell including thermionic field emission, dependence of lifetime and mobility on impurity concentrations, dependence of absorption coefficient on wavelength, variation of barrier height and hence the optimum thickness ofp region with illumination. The optimized design parametersN _D =5×10²⁰ m⁻³,N _A =3×10²⁴ m⁻³ andW _P =11.8 nm yield efficiencyη=17.1% (AM0) andη=19.6% (AM1). These are reduced to 14.9% and 17.1% respectively if the metal layer series resistance and transmittance with ZnS antireflection coating are included. A practical value ofW _P =97.0 nm gives an efficiency of 12.2% (AM1).     

Bosonic string theories with new boundary conditions

We show that the classical Nambu-Goto string inD dimensions admits Poincaré invariance ind dimensions (d⩽D) if (i)d − 2 of the transverse co-ordinatesx ⁱ are periodic and the rest quasi-periodic involving a real orthogonal matrix with (D − d) (D − d − 1)/2 free parameters, or if (ii)d − 2 ofx ⁱ obey Neumann and the rest obey a boundary condition involvingN free parameters, whereN=(D − d)²/2 ifD − d is even, andN=[(D − d)² − 1]/2 ifD − d is odd.     

Theory of Ordered Spaces¶II. The Local Differential Structure

In this paper we investigate the conditions under which the ordered spaces defined in [1] are locally diffeomorphic to ℝ ^N . In Sect.~1 we give an introduction and an overview of the results. In Sect. 2 we show that the axioms of [1] do not suffice to make light rays locally homeomorphic to ℝ. We introduce this structure via the new connectedness axiom 2.13, and work out some of its immediate consequences. In Sect. 3 we give the (somewhat involved) construction of timelike curves in a D-set, which are basic to everything that follows. They are used in Sect. 4 to prove (i) a nested interval theorem for ordered spaces; (ii) the contractibility of order intervals in D-sets; and (iii) that order intervals in D-sets are star-shaped. The notion of D-countability (meaning that a D-set has a countable base in the subspace topology) is introduced in Sect. 5. The Urysohn lemma shows that a D-countable ordered space is locally metrizable. If this space is also locally compact, then it has finite topological dimension N; these results are established in Sect. 6. The local differential structure now follows from known results: the embedding of such spaces in ℝ^{2 n +1}, and the result that an open star-shaped region in ℝ ⁿ is diffeomorphic to ℝ ⁿ . In conclusion, we exhibit these inclusions in Fig. 3, and suggest the possibility that Wigner's position on the “Unreasonable effectiveness of mathematics in the natural sciences” may be open to reasonable doubt. The axioms of [1] are given in the Appendix. Received: 26 November 1997 / Accepted: 10 February 1999     

The influence of a metalloid on ordered structure in titanium carbide

X-ray and neutron diffraction were used to investigate the effect of oxygen and nitrogen atoms on the formation of the intermediate δ′-cubic (sp. gr. Fd3m) and δ″-tetragonal (sp. gr. P3₁21) ordered structures in titanium carbide. In TiC_0.545O_0.08, TiC_0.545N_0.09 samples that were investigated, the metal atoms were shifted from ideal positions in the direction from vacancies to metalloid atoms. In the intermediate cubic phase (δ′), the free-parameter values of titanium atoms in the two samples are the same, but are different from their analogous value in titanium carbide. Fiz. Tverd. Tela (St. Petersburg) 39, 2207–2209 (December 1997)     

Study of the reaction γp → pπ0η

The reaction γp → pπ⁰η has been studied with the CBELSA detector at the tagged photon beam of the Bonn electron stretcher facility. The reaction shows contributions from Δ⁺(1232)η , N(1535)⁺π⁰ and pa ₀(980) as intermediate states. A partial-wave analysis suggests that the reaction proceeds via formation of six Δ -resonances, Δ(1600)P ₃₃ , Δ(1920)P ₃₃ , Δ(1700)D ₃₃ , Δ(1940)D ₃₃ , Δ(1905)F ₃₅ , Δ(2360)D ₃₃ , and two nucleon resonances N(1880)P ₁₁ and N(2200)P ₁₃ , for which pole positions and decay branching ratios are given.     

C M ? C N D -computable state

The notions of D-computable state and D-concurrence are generalized to the C ^M ⊗ C ^N system. A class of D-computable state on C ^M ⊗ C ^N is given and the calculating method of the lower bound of D-concurrence is provided. The obvious expression of the lower bound of D-concurrence for the state mixed by two D-pure states is derived. Supported by the National Natural Science Foundation of China (Grant No. 60433050) and the Key Project of the Science Foundation of Xuzhou Normal University (Grant No. 06XLA05)     

Realistic searches on stretched exponential networks

We consider navigation or search schemes on networks which have a degree distribution of the form P(k) ∝ exp(−k ^γ). In addition, the linking probability is taken to be dependent on social distances and is governed by a parameter λ. The searches are realistic in the sense that not all search chains can be completed. An estimate of μ = ρ/s _d, where ρ is the success rate and s _d the dynamic path length, shows that for a network of N nodes, μ ∝ N ^−δ in general. Dynamic small world effect, i.e., δ ≃ 0 is shown to exist in a restricted region of the λ−γ plane.      

Interactions of charmed mesons with nucleons in the ¯<Emphasis Type="Italic">p</Emphasis><Emphasis Type="Italic">d</Emphasis> reaction

We study the possibility to measure the elastic ΦN (Φ≡J/ψ,ψ(2S), ψ(3770), χ_2c) scattering cross section in the reaction ˉp+d→Φ+n _sp and the elastic D(ˉD)N scattering cross section in the reaction ˉp+d→D ⁻ D ⁰ p _sp. Our studies indicate that the elastic scattering cross sections can be determined for Φ momenta about 4–6 GeV/c and D/ˉD momenta 2–5 GeV/c by selecting events with p _t≥ 0.4 GeV/c for Φ's and p _t(p _sp) ≥ 0.5 GeV/c for D/ˉD-meson production. Received: 8 November 1999     

Quantum information entropies of ultracold atomic gases in a harmonic trap

The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems containing N atoms confined in a D( ≤ 3)-dimensional harmonic trap has a universal form as S_t^(D) = N(a D - b lnN) S_\mathrm{t}^{(D)} = N(a D - b \ln N) , where a ≃ 2.332 and b = 2 for interacting bosonic systems and a ≃ 1.982 and b = 1 for ideal fermionic systems. These results obey the entropic uncertainty relation given by Beckner, Bialynicki-Birula and Myceilski.