q-Gaussians in the porous-medium equation: stability and time evolution

The stability of q-Gaussian distributions as particular solutions of the linear diffusion equation and its generalized nonlinear form, , the porous-medium equation, is investigated through both numerical and analytical approaches. An analysis of the kurtosis of the distributions strongly suggests that an initial q-Gaussian, characterized by an index q_i, approaches asymptotically the final, analytic solution of the porous-medium equation, characterized by an index q, in such a way that the relaxation rule for the kurtosis evolves in time according to a q-exponential, with a relaxation index q_rel ≡q_rel(q). In some cases, particularly when one attempts to transform an infinite-variance distribution (q_i ≥ 5/3) into a finite-variance one (q < 5/3), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary states to the ultimate thermal equilibrium state.     

Quantum critical point in SmO1−xFxFeAs and oxygen vacancy induced by high fluorine dopant

The local lattice and electronic structure of the high‐T_c superconductor SmO_1–xF_xFeAs as a function of F‐doping have been investigated by Sm L₃‐edge X‐ray absorption near‐edge structure and multiple‐scattering calculations. Experiments performed at the L₃‐edge show that the white line (WL) is very sensitive to F‐doping. In the under‐doped region (x≤ 0.12) the WL intensity increases with doping and then it suddenly starts decreasing at x = 0.15. Meanwhile, the trend of the WL linewidth versus F‐doping levels is just contrary to that of the intensity. The phenomenon is almost coincident with the quantum critical point occurring in SmO_1–xF_xFeAs at x? 0.14. In the under‐doped region the increase of the intensity is related to the localization of Sm‐5d states, while theoretical calculations show that both the decreasing intensity and the consequent broadening of linewidth at high F‐doping are associated with the content and distribution of oxygen vacancies.     

A numerical study of sparse random matrices

A numerical study is presented for the eigensolution statistics of largeN×N real and symmetric sparse random matrices as a function of the mean numberp of nonzero elements per row. The model shows classical percolation and quantum localization transitions atp _c =1 andp _q >1, respectively. In the rigid limitp=N we demonstrate that the averaged density of states follows the Wigner semicircle law and the corresponding nearest energy-level-spacing distribution functionP(S) obeys the Wigner surmise. In the very sparse matrix limitpN, withp>p _q a singularity (E))1/¦E¦ is found as¦E¦ 0 and exponential tails develop in the high-¦E¦ regions, but theP(S) distribution remains consistent with level repulsion. The localization properties of the model are examined by studying both the eigenvector amplitude and the density fluctuations. The valuep _q 1.4 is roughly estimated, in agreement with previous studies of the Anderson transition in dilute Bethe lattices.     

q-Weyl coefficients forU q (3) andq-Racah coefficients forSU q (2)

We show that theq-Weyl coefficients of the quantum algebraSU _q (3) are equal to theq-Racah coefficients of the quantum algebraSU _q (2) (up to a simple phase factor). Using aq-analog of the resummation procedure we obtain also theq-analogues of all known general analytical expressions for the 6j-symbols (or the Racah coefficients) of the quantum algebraSU _q (2) starting from one such formula.Presented at the 4th Colloquium Quantum groups and integrable systems, Prague, 22–24 June 1995.The research described in this publication was supported in part by Grants No. MB1000 and No. NRC000 from International Science Foundation.     

Structural and electronic properties of endohedral doped SWCNTs: A DFT study

The structural and electronic properties of semiconductors (Si and Ge) and metal (Au and Tl) atoms doped armchair (n, n) and zigzag (n, 0); n=4–6, single wall carbon nanotubes (SWCNTs) have been studied using an ab-initio method. We have considered a linear chain of dopant atoms inside CNTs of different diameters but of same length. We have studied variation of B.E./atom, ionization potential, electron affinity and HOMO–LUMO gap of doped armchair and zigzag CNTs with diameter and dopant type. For armchair undoped CNTs, the B.E./atom increases with the increase in diameter of the tubes. For Si, Ge and Tl doped CNTs, B.E./atom is maximum for (6, 6) CNT whereas for Au doped CNTs, it is maximum for (5, 5) CNTs. For pure CNTs, IP decreases slightly with increasing diameter whereas EA increases with diameter. The study of HOMO–LUMO gap shows that on doping metallic character of the armchair CNTs increases whereas for zigzag CNTs semiconducting character increases. In case of zigzag tubes only Si doped (5, 0), (6, 0) and Ge doped (6, 0) CNTs are stable. The IP and EA for doped zigzag CNTs remain almost independent of tube diameter and dopant type whereas for doped armchair CNTs, maximum IP and EA are observed for (5, 5) tube for all dopants.     

Nb高掺杂量对锐钛矿TiO2导电和光学性能影响

目前, 在Nb高掺杂量摩尔数分别为0.050和0.0625的条件下, 对掺杂体系锐钛矿TiO₂电阻最低存在相反的两种实验结果都有文献报道. 为解决这个矛盾, 本文采用基于密度泛函理论的平面波超软赝势方法, 计算了纯的单胞和三种不同Nb高掺杂量对锐钛矿Ti_1-xNb_xO₂ (x=0.03125, 0.050, 0.0625)超胞的能带结构分布、态密度分布和光学性质. 结果表明, 在本文限定掺杂量的条件下, Nb掺杂量越增加, 掺杂体系的体积越增加, 总能量越升高, 稳定性越下降, 形成能越升高, 掺杂越难, 相对自由电子浓度越增加, 电子有效质量越增加, 电子迁移率越减小, 电子电导率越减小, 最小光学带隙越变宽, 吸收光谱和反射率向低能方向移动越显著, 透射率越增加. 计算结果与实验结果相吻合.     

Insulator-superconductor-metal transitions induced by spin fluctuations in the paramagnetic phase of doped insulators

AbstractThe band structure of cuprates as a doped 2D insulator is modeled assuming that the excess charge carriers are associated with the corresponding substitution atoms, and the phase diagram of the paramagnetic states as a function of the degree x of doping at zero temperature is studied. The Hamiltonian contains electronic correlations on impurity orbitals and hybridization between them and the initial band states of the insulator. It is shown that the change in the electronic structure of a doped compound includes the formation of impurity bands of distributed and localized electronic states in the initial insulator gap. It is established that in the case of one excess electron per substitution atom the spin fluctuations (1) give rise to an insulator state of the doped compound for x < x _thr, 1, (2) lead to a superconducting state for x _thr, 1 < x < x _thr, 2, and (3) decay as x > x _thr, 2 increases further, and the doped compound transforms into a paramagnetic state of a “poor” metal with a high density of localized electronic states at the Fermi level.     

Electronic structures of doped BaFe<Subscript>2</Subscript>As<Subscript>2</Subscript> materials: virtual crystal approximation versus super-cell approach

Using virtual crystal approximation and super-cell methods for doping, a detailedcomparative study of electronic structures of various doped BaFe₂As₂ materials by first principlessimulations is presented. Electronic structures remain unaltered for both the methods incase of passive site doping but in case of active site doping, the electronic structurefor virtual crystal approximation method differ from that of the super-cell methodspecially in the higher doping concentrations. For example, both of these methods giverise to a similar density of states and band structures in case of hole doping (replacingK in place of Ba) and isovalent P doping on As site. But in case of electron doped (Co inplace of Fe) systems with higher doping concentration, electronic structures calculatedusing virtual crystal approximation approach deviates from that of the super-cell method.On the other hand, in case of low isovalent Ru doping at the Fe site implemented byvirtual crystal approximation, one acquires an extra shift in the chemical potential incomparison to that for the super-cell method. This shift may be utilized to predict thecorrect electronic structure as well as the calculated Fermi surfaces within virtualcrystal approximation. But for higher Ru (that has different electronic configuration thanFe) doping concentration, simple shifting of chemical potential fails, the calculatedelectronic structure via virtual crystal approximation approach is very different fromthat by the super-cell formalism.     

On a nonstandard two-parametric quantum algebra and its connections withU p,q (gl(2)) andU p,q(gl(1/1))

A quantum algebraU _{p, q} (,H,X _±) associated with a nonstandardR-matrix with two deformation parameters (p, q) is studied and, in particular, its universal -matrix is derived using Reshetikhin's method. Explicit construction of the (p, q)-dependent nonstandardR-matrix is obtained through a coloured generalized boson realization of the universal -matrix of the standardU _{p, q}(gl(2)) corresponding to a nongeneric case. General finite dimensional coloured representation of the universal -matrix ofU _{p, q}(gl(2)) is also derived. This representation, in nongeneric cases, becomes a source for various (p, q)-dependent nonstandardR-matrices. Superization ofU _{p, q}(,H,X _±) leads to the super-Hopf algebraU _{p, q}(gl(1/1)). A contraction procedure then yields a (p, q)-deformed super-Heisenberg algebraU _{p, q}(sh(1)) and its universal -matrix.     

Carrier diffusion in InGaAs/GaAs quantum wells grown on vicinal GaAs(0 0 1) substrates

We have investigated the influence of vicinal GaAs substrates on the optical and electronic properties of InGaAs/GaAs quantum wells (QWs). A single In_0.10Ga_0.90As QW was grown by molecular-beam epitaxy on a vicinal GaAs(0 0 1) substrate with a miscut angle of 0° (nominal), 2°, 4° and 6° towards [1 1 0]. The carrier diffusion was obtained by a micro-photoluminescence scan technique that permits to observe the effective diffusion length characterized by the lateral spread of carriers in the QW followed by radiative recombination. The carrier diffusion length was obtained parallel (L_||) and perpendicular (L) to the atomic steps. The diffusion length decreases as the temperature increases up to 100 K. Above this temperature we found different behaviours that depend on the sample miscut angle.     

The quantum super-Yangian and Casimir operators of Uq(gl(M |N))

TheZ ₂ graded Yangian Yq(gl(M |N)) associated with the Perk-SchultzR matrix is introduced. Its structural properties, the central algebra in particular, are studied. AZ ₂-graded associative algebra epimorphism Yq(gl(M |N)) Uq (gl(M |N)) is obtained in explicit form. Images of central elements of the quantum super-Yangian under this epimorphism yield the Casimir operators of the quantum supergroup Uq(gl(M |N)) constructed in an earlier publication.     

Realisations of quantum GL p,q(2) and Jordanian GLh,h′(2)

The quantum group GL _p,q(2) is known to be related to the Jordanian GL_h,h(2) via a contraction procedure. It can also be realised using the generators of the Hopf algebra G _r,s. We contract the G _r,s quantum group to obtain its Jordanian analogue G _m,k, which provides a realisation of GL_h,h(2) in a manner similar to the q-deformed case.     

Tuning electronic properties of In<Subscript>2</Subscript>O<Subscript>3</Subscript> nanowires by doping control

We present two effective routes to tune the electronic properties of single-crystalline In₂O₃ nanowires by controlling the doping. The first method involves using different O₂ concentrations during the synthesis. Lightly (heavily) doped nanowires were produced by using high (low) O₂ concentrations, respectively, as revealed by the conductances and threshold voltages of nanowire-based field-effect transistors. Our second method exploits post-synthesis baking, as baking heavily doped nanowires in ambient air led to suppressed conduction and a positive shift of the threshold voltage, whereas baking lightly doped nanowires in vacuum displayed the opposite behavior. Our approaches offer viable ways to tune the electronic properties of many nonstoichiometric metal oxide systems such as In₂O₃, SnO₂, and ZnO nanowires for various applications. PACS 85.35.-p     

The effect of doping by IV-family elements on the electronic structure and electrical characteristics of Sb2O5

The electronic structures of doped Sb₂O₅ by IV-family elements (Si, Ge and Sn) were examined using the density function theory (DFT). Density of states (DOSs) results showed that the substituted IV-family elements act as acceptors in Sb₂O₅. Partial DOSs indicates that by substituting Ge(Ge _Sb ) or Sn(Sn _Sb ), there may be a larger contribution to the total DOSs near E _F than by substituting Si, which suggests that doping Ge or Sn in Sb₂O₅ produces better ptype doping compared to doping Si. Formation energy results show that IV-family elements are more likely to exist in the substituted position rather than in the interstitial position in Sb₂O₅, decreasing any self-compensation effect and making it easier for IV-family elements to realize ptype doping in Sb₂O₅. Ionization energy results show that Ge _Sb or SnSb, two among the three impurities considered, act as shallow acceptors in Sb₂O₅, thus producing a higher concentration of holes.      

Quasi-Stable Configurations of Torus Vortex Knots and Links

The dynamics of torus vortex configurations V_{n, p, q} in a superfluid liquid at zero temperature (n is the number of quantum vortices, p is the number of turns of each filament around the symmetry axis of the torus, and q is the number of turns of the filament around its central circle; radii R₀ and r₀ of the torus at the initial instant are much larger than vortex core width ξ) has been simulated numerically based on the regularized Biot–Savart law. The lifetime of vortex systems till the instant of their substantial deformation has been calculated with a small step in parameter B₀ = r₀/R₀ for various values of parameter Λ = ln(R₀/ξ). It turns out that for certain values of n, p, and q, there exist quasi-stability regions in the plane of parameters (B₀, Λ), in which the vortices remain almost invariable during dozens and even hundreds of characteristic lengths.

     

掺稀土元素(Y，La)的γ-Si3N4的电子结构和光学性质

采用基于密度泛函的平面赝势方法(PWP)和广义梯度近似(GGA)，计算了未掺杂和掺杂稀土(Y，La)的γ-Si₃N₄中N-Y(La)键的布居值和它们的键长、掺杂后能带结构和态密度.发现掺杂后的带隙要减小，并且可能形成新的半导体，这将为找到新的半导体提供一个方向.还进一步研究了掺杂稀土(Y，La)后的光学性质，掺杂后有更高的静态介电常数，可以作为新的介电材料和好的折射材料，这对于一定的光学元件有潜在的应用前景.     

Quantum group (CO)actions onG-spaces and quantum modules

A generalized transformation theory is introduced by using quantum (non-commutative) spaces transformed by quantum Lie groups (Hopf algebras). In our method dual pairs of -quantum groups/algebras (co)act on quantum spaces equipped with the structure of a -comodule algebra. We use the quantized groupSU _q (2) as a show case, and we determine its action on modules such as theq-oscillator and the quantum sphere. We also apply our method for the quantized Euclidean groupF _q (E(2)) acting on a quantum homogeneous space. For the sphere case the construction leads to an analytic pseudodifferential vector field realization of the deformed algebra su _q (2) on the quantum projective plane for north and south pole.Presented by A.A. at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–20 June 1996 and by D.E. at the 4th International Congress of Geometry, Thessaloniki.     

Ca3－x AgxCo4O9(x=0—0.05)氧化物的电输运性能

Ca位掺杂可以优化Ca₃Co₄O₉复合氧化物的电输运性能. 采用柠檬酸溶胶凝胶结合放电等离子烧结制备了Ca位微量掺杂Ag的Ca_3-xAg_xCo₄O₉(x=0—005)氧化物块体试样,通过X射线衍射、扫描电子显微镜、电参数测试仪分析了所得试样. 试验结果表明: 产物呈单一物相,Ca位微量掺杂Ag降低了Ca_{关键词： 3}Co₄O₉')" href="#">Ca₃Co₄O₉ 掺杂 电输运     

Excitations in Heisenberg spin glasses

Within the RPA approach forT=0, the excitations of the Heisenberg spin glass system Eu _x Sr_1–x S are studied by numerical methods, using a continued fraction algorithm. Both the density of statesg(E) and also the spectral functionS(q,E) are calculated for systems with (16)³ sites, withx=0.4, 0.5, and 0.6 (spin glass phase), and also forx0.7 (ferromagnetic phase). Forq-vectors within the (1,1,1) plane,S(q,E) shows magnon peaks even in the spin glass phase, over the whole range ofq. However, these peaks are quite broad, and there is considerable intensity at small energies even for largeq, leading to a finite intercept ofg(E) forE0. Over a large temperature range, the specific heat is approximately linear inT forx0.7.     

第Ⅰ种非对称两态叠加多模叠加态光场等阶N次方H压缩——1.腔模总数与压缩阶数两者之积取偶的情形

本文利用多模压缩态理论研究了第Ⅰ种非对称两态叠加多模叠加态光场|Ψ_Ⅰ^(ab)>_q的广义非线性等阶N次方H压缩特性.结果发现:在腔模总数q与压缩阶数N这两者之积qN为偶数亦即qN=2p的条件下,无论p=2m(m=1,2,3,…,…)还是p=2m+1(m=0,1,2,…,…),当两非对称态中各模的初始相位和 =φ_j^(a)、 =φ_j^(b)、态间的初始相位差(θ_pq^bI-θ_nq^aR),以及各单模相干态光场的光子干涉项之和 =[R_j^(a)R_j^(b)]cos(φ_j^(a)-φ_j^(b))]等满足一定条件时,态|Ψ_Ⅰ^(ab)>_q可分别呈现出周期性变化的奇数模-偶数阶、偶数模-奇数阶和偶数模-偶数阶的等阶N次方H压缩效应.