Eigenvalues of graphs with twofold symmetry

There are many cases in which the spectrum of a graph contains the complete spectrum of a smaller graph. The larger (composite) graph and the smaller (component) graph are said to be subspectral. It is shown here that whenever a composite graph G has a twofold symmetry operation which defines two equivalent sets of vertices r and s, it is possible to construct two subspectral components G ₊ and G _-, whose eigenvalues, taken jointly, comprise the full spectrum of G. The following rules are given for constructing the components. (1) Draw the r set of vertices and all the edges connecting the members of the set. Then examine in G the vertices through which r and s are connected (the so-called bridging vertices). (2) If a bridging vertex r ₁ is connected to its symmetry-equivalent partner s ₁, then r ₁ is weighted +1 in G ₊ and -1 in G _-. (3) If r ₁ is connected to a vertex s ₂ which is symmetry-equivalent to a second bridging vertex r ₂ in r, then the weight of the edge between r ₁ and r ₂ in G (+1 if they are connected, zero if they are not) is increased by one unit in G ₊ and decreased by one unit in G _-. The derivation of these rules is shown, and the relationship between the spectrum of G and the spectra of G ₊ and G _- is explained in terms of the symmetry properties of the adjacency matrix of G.     

Composition and superconductivity in single layer Bi-2201 phases

Several materials with nominal 2201 composition were prepared from various systems Bi_2+xSr_2-xCuO_6+z, Bi₂Sr_2-xCuO_6+z, Bi_2-xPb_xSr₂O_6+z, Bi_2.1-xPb_xCuO_6+z,Bi₂Sr_2-yLa_yCuO_6+z, Bi_1.9Pb_0.1Sr_2-yLa_yCuO_6+z, Bi_2-xPb_xSr_1.6La_0.4CuO_6+z and Bi_2.1-xPb_xSr_1.5La_1.4CuO_6+z in different gas atmospheres. According to the structural investigations the 2201 phase shows solid solution behaviour. However, irrespectively of the method of preparation the appearance of superconductivity is confined to multiphase material. Furthermore, the superconducting volume fraction is uniformly as low as ? 3%. The observed presence of trace superconductivity is easily explainable by small admixtures of superconducting foreign phases and in disagreement with the assumption of intrinsic superconducting properties of the Bi based 2201 phase.     

Influence of anionic substitution on phase transitions in Cu6PS5I1− x Cl x mixed crystals

Cu₆PS₅I_{1? ?} ? _x Cl _x mixed crystals were grown using chemical vapour transport. Isoabsorption studies of optical absorption edge and optical polarization measurements were performed in the temperature range 77–320?K. The influence of anionic I?→?Cl substitution on the phase transitions in Cu₆PS₅I_{1? ?} ? _x Cl _x mixed crystals is studied. Compositional dependence of the phase-transition temperatures is obtained and the x,T-diagram for Cu₆PS₅I_{1? ?} ? _x Cl _x mixed crystals is constructed.     

Magnetic entropy change and large refrigerant capacity of Ce6i2Si3-type GdCoSiGe compound

Magnetic entropy change (Δ S_M) and refrigerant capacity (RC) of Ce₆Ni₂Si₃-type Gd₆Co_1.67Si_2.5Ge_0.5 compounds have been investigated. The Gd₆Co_1.67Si_2.5Ge_0.5 undergoes a reversible second-order phase transition at the Curie temperature T_C = 296 K. The high saturation magnetization leads to a large Δ S_M and the maximal value of Δ S_M is found to be 5.9 J/kg,cdot,K around T_C for a field change of 0--5 T. A broad distribution of the Δ S_M peak is observed and the full width at half maximum of the Δ S_M peak is about 101 K under a magnetic field of 5 T. The large RC is found around T_C and its value is 424 J/kg.     

Elastic constants and mechanical stability of InxAl1 − xAsySb1 − y lattice-matched to different substrates

Based on a pseudopotential approach under the virtual crystal approximation, the elastic modulus of In_xAl_1???xAs_ySb_1???y quaternaries lattice-matched to InP, GaSb and InAs substrates has been investigated. Our findings show a reasonably good accord with experiment. The dependence of the elastic features of interest on the indium concentration x shows a monotonic behaviour when In_xAl_1???xAs_ySb_1???y is lattice-matched to InP substrate. In that case, the elastic constants have larger values and the material system of interest becomes less harder and its rigidity becomes weaker. The mechanical stability criteria is verified in terms of elastic constants and shows that In_xAl_1???xAs_ySb_1???y is mechanically stable for each x and substrate being considered here. The change in indium content x and the substrate is found to have no much effect on both the Poisson ratio and machinability. The present study showed that a proper choice of the indium composition x and substrate may provide more diverse opportunities as regards the elastic modulus of In_xAl_1???xAs_ySb_1???y.     

Concentrated Kondo systems

This review considers the experimental and theoretical studies of concentrated Kondo systems (CKS), Kondo lattices, substitutional solid solutions and their transition from Kondo impurity to Kondo lattice, and ‘intermediate valence compounds’ which are, in fact, high T _K CKS (T _K is the Kondo temperature). The anomalous low temperature properties of CKS are related to the formation of the narrow (～k _B T _K) high-amplitude Abrikosov-Suhl resonance E _R in the vicinity of the Fermi level E _F. This resonance is situated exactly at E _F in low T _K CKS with T _K < Δ_CF and near E _F in high T _K CKS with T _K > Δ_CF (Δ_CF is the crystal field splitting). In low T _K ‘j=1/2’ CKS the condition E _R=E _F leads to an increase of the density of states at E _F, which is large enough to induce heavy fermion superconductivity in CeCu₂Si₂, UBe₁₃. We demonstrate that the transition from low T _K (E _R=E _F) to high T _K CKS (E _R≠E _F) might be what was formerly considered as a ‘Kondo-lattice-intermediate valence state’ transition. It appears that in many cases the essentially non-integer valence state of the rare-earth elements in metallic compounds is thermodynamically unstable with respect to a transition to an almost integer valence state, because it realizes the maximum gain in free energy from the Kondo condensation.     

Meyer–Neldel DC conduction in chalcogenide glasses

Meyer–Neldel (MN) formula for DC conductivity (σ _DC) of chalcogenide glasses is obtained using extended pair model and random free energy barriers. The integral equations for DC hopping conductivity and external conductance are solved by iterative procedure. It is found that MN energy (ΔE _MN) originates from temperature-induced configurational and electronic disorders. Single polaron-correlated barrier hopping model is used to calculate σ _DC and the experimental data of Se, As₂S₃, As₂Se₃ and As₂Te₃ are explained. The variation of attempt frequency ν ₀ and ΔE _MN with parameter (r/a), where r is the intersite separation and a is the radius of localized states, is also studied. It is found that ν ₀ and ΔE _MN decrease with increase of (r/a), and ΔE _MN may not be present for low density of defects.     

Clarifying the nature of the Johari-Goldstein β-relaxation and emphasising its fundamental importance

ABSTRACT

Since 1998 the primitive relaxation time τ ₀(T,P) of the Coupling Model (CM) and the Johari-Goldstein (JG) β-relaxation time τ_JG (T,P) are shown approximately equal in many glass-formers. The CM relation between τ ₀(T,P) and τ_α (T,P) at any T and P is exact. Additionally from the CM relation τ_α (T,P)/τ ₀(T,P) is exactly invariant to variations of T and P while τ_α (T,P) is kept constant, and τ ₀ is exactly a function of ρ ^γ/T like τ_α . However, since τ_JG (T,P) ≈ τ ₀(T,P), the exact invariance of τ_α (T,P)/τ ₀(T,P) leads to approximate invariance of τ_α (T,P)/τ_JG (T,P), and τ_JG is approximately a function of ρ ^γ/T. Notwithstanding, the CM prediction of the approximate relations between τ_β and τ_α were mistaken as exact relations by some researchers. In this paper, we remove this misunderstanding by demonstrating via simulations and experiments that the JG β-relaxation is comprised of processes with different length-scales and degrees of cooperativity, and the process is heterogeneous. The distribution of processes makes τ_JG (T,P) equivocal, because it is just a single relaxation time used to represent the different processes within the distribution, which may change on varying T and P, at constant τ_α (T,P). The problem is compounded if the β-relaxation is not resolved, and fitting procedure used to extract τ_JG (T,P) and τ_α (T,P). Despite the relations of τ_JG (T,P) to τ_α (T,P) are approximate, we show these properties of τ_JG (T,P) are truly remarkable, fundamental, general, and important.     

Materials parameters and ion-induced track formation

ABSTRACT

The role of various materials parameters in track formation is discussed. Experimental information is utilized showing a direct quantitative relationship in different solids between the melting points T_m and the ion-induced track radii R_e without involving other materials parameters. It is shown for Θ?=?T_m???T_ir (T_ir – irradiation temperature) that Θ～exp{?R_e²/w²} for S_e/N?=?constant, where S_e and N are the electronic stopping power and the number density of atoms and w?=?4.5?nm. The validity of this universal-type relation is demonstrated for 14 different insulators including LiNbO₃ and BaFe₁₂O₁₉. It is shown that the thermal diffusivity D, the heat of fusion L the band gap energy E_g and the absorption radius α_e of the electron distribution must not affect the track sizes as this would not be coherent with this identical behavior. Original reports on LiNbO₃ and BaFe₁₂O₁₉ with opposite conclusions are critically analyzed. It is shown that an arbitrary value of the ion energy was used in the analysis that modified substantially the results leading to an undue justification of the contribution of L and E_g in apparent agreement with the experimental data.     

Effective Action in Multidimensional (Super)Gravities and Spontaneous Compactification (Quantum Aspects of Kaluza-Klein Theories)

The review of modern status of problem of quantum effects in Kaluza-Klein theories is given. The effective action (EA) in multidimensional (super)gravities (SG's) on the compactified background is investigated. The standard gauge dependent EA in d=5 Einstein gravity and d=5 R²-gravity on the background R₄ × S₁, where R₄ is 4-dimensional space, S₁ is one-dimensional sphere is calculated. Gauge and parametrization independent Vilcovisky-De Witt EA in d=5 Einstein gravity and d=5 R²-gravity on the background R₄×S₁ at zero and non-zero temperature is obtained. We have found that there are no physically acceptable self-consistent solutions of the form R₄×S₁ at the one-loop level in d=5 Einstein gravity. We calculated also EA for arbitrary multidimensional SG on the background R₄×T_d-n where T_d is d-dimensional torus as expansion on the curvature and its derivatives. The mechanizm of induced of four-dimensional gravity with zero Λ-term is proposed. The Vilcovisky-De Witt EA in d=5 SG's on the background R₄×S₁ at non-zero temperature is obtained. The three gauge parameter dependent off-shell EA in N=2, d=5 gauged SG on R₄⁰×S₁ where R₄⁰ is flat four-dimensional space is calculated. The expression for vacuum energy for bosonic string with torus compactification is presented. Vacuum energy for superstrings with supersymmetry broken as the result of choice of boundary conditions on background R₄×T₆ is calculated.     

The anisotropic 3D Ising model

An expression for the free energy of an (001) oriented domain wall of the anisotropic 3D Ising model is derived. The order--disorder transition takes place when the domain wall free energy vanishes. In the anisotropic limit, where two of the three exchange energies (e.g. J_x and J_y ) are small compared to the third exchange energy (J_z ), the following asymptotically exact equation for the critical temperature is derived, sinh(2J_z /k _B T _c)sinh(2(J_x ?+?J_y )/k _B T _c))?=?1. This expression is in perfect agreement with a mathematically rigorous result (k _B T _c/J_z ?=?2[ln(J_z /(J_x ?+?J_y ))?ln(ln(J_z /(J_x ?+?J_y ))?+?O(1)]^?1) derived earlier by Weng, Griffiths and Fisher (Phys. Rev. 162, 475 (1967)) using an approach that relies on a refinement of the Peierls argument. The constant that was left undetermined in the Weng et al. result is estimated to vary from ～0.84 at ((H_x ?+?H_y )/H_z )?=?10^?2 to ～0.76 at ((H_x ?+?H_y )/H_z )?=?10^?20.     

The Thermodynamic Evolution of the Cosmological Event Horizon

By manipulating the integral expression for the proper radius R _e of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe we obtain an analytical expression for the change δR _e in response to a uniform fluctuation δρ in the average cosmic background density ρ. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately stationary, and evolves subsequently such that δρ/ρ is constant. The respective variations 2πR _e δR _e and δE _e in the horizon entropy S _e and enclosed energy E _e should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature T _e of the CEH at an arbitrary time in a flat FRW universe is E _e /S _e , which recovers asymptotically the usual static de Sitter temperature. Furthermore it is proven that during radiation-dominance and in late times the CEH conforms to the fully dynamical First Law T _e dS _e =PdV _e −dE _e , where V _e is the enclosed volume and P is the average cosmic pressure.     

Evaluation of photoelastic constants from first-order Raman intensities of MgF2

A formalism to connect first-order Raman intensities of MgF₂ and its photoelastic constants is developed by developing a method of writing internal coordinates in terms of displacement gradientsu _ij which are not symmetric. It is found that for crystals containing only one line inA ₁ species, the ratiosP ₁₃/P ₃₃ and (P ₁₁ +P ₁₂)/P ₃₁ can be directly evaluated from the intensities, without having to derive the intensity formulae; while (P ₁₁ +P ₁₂)/P ₁₃ is independent of the intensities as well as the refractive index of the crystal. It is a function of only the dimensional parameters. In this crystal, since the speciesB _1g andB _2g also contain only one line each, the ratio (P ₁₁ −P ₁₂)/P ₆₆ can also be directly obtained from the intensities.     

超薄栅超短沟LDD nMOSFET中栅电压对栅致漏极泄漏电流影响研究

本文研究了90nm CMOS工艺下栅氧化层厚度为1.4 nm沟道长度为100 nm的轻掺杂漏(LDD)nMOSFET栅电压V_G对栅致漏极泄漏 (GIDL)电流I_d的影响,发现不同V_G下ln (I_d/(V_DG-1.2))-1/(V_DG-1.2)曲线相比大尺寸厚栅器件时发生了分裂现象. 通过比较V_G变化下ln(I_d/(V_DG-1.2))的差值,得出V_G与这种分裂现象之间的作用机理,分裂现象的产生归因于V_G的改变影响了GIDL电流横向空穴隧穿部分所致. 随着|V_G|的变小,ln(I_d/(V_DG-1.2))曲线的斜率的绝对值变小.进一步发现不同V_G对应的ln (I_d/(V_DG-1.2))曲线的斜率c及截距d与V_G呈线性关系,c,d曲线的斜率分别为3.09和-0.77. c与d定量的体现了超薄栅超短沟器件中V_G对GIDL电流的影响,基于此,提出了一个引入V_G 影响的新GIDL电流关系式.     

Electron cooling in three‐dimensional Dirac fermion systems at low temperature: Effect of screening

Hot electron cooling rate P, due to acoustic phonons, is investigated in three‐dimensional Dirac fermion systems at low temperature taking account of the screening of electron–acoustic phonon interaction. P is studied as a function of electron temperature T_e and electron concentration n_e. Screening is found to suppress P very significantly for about T_e < 0.5 K and its effect reduces considerably for about T_e > 1 K in Cd₃As₂. In Bloch–Grüneisen (BG) regime, for screened (unscreened) case the T_e dependence is P ～ T_e⁹(T_e⁵) and the n_e dependence gives P ～ n_e^–5/3 (n_e^–1/3). The T_e dependence is characteristic of 3D phonons and n_e dependence is characteristics of 3D Dirac fermions. The plot of P /T_e⁴ vs. T_e shows a maximum at temperature T_em which shifts to higher values for larger n_e. Interestingly, the maximum is nearly same for different n_e and T_em/n_e^1/3 being nearly constant. More importantly, we propose, the n_e dependent measurements of P would provide a clearer signature to identify 3D Dirac semimetal phase. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

带栅极纳米线冷阴极的场增强因子研究

场增强因子是体现场发射冷阴极器件性能优劣的重要参数.利用静电场理论给出了一种带栅极(normal-gated)纳米线冷阴极的场增强因子表示式β=k₁{N²·(L-d₁)²+［1/k₁+(L-d₁)］²}^1/2，且进一步分析了几何参数对场增强因子的影响.结果表明，纳米线突出栅孔的部分(L-d₁)与栅孔半径越大，则场增强因子越大；而纳米线半径越小，则场增强因子越大；当L远大于d₁时满足β∝L/r₀.其中N=N₁(k₁r₀)/N₀(k₁r₀)，N₀(k₁r₀)和N₁(k₁r₀)分别代表零阶和一阶Neumann函数，k₁=0.8936/R，R为栅孔半径，L为纳米线长度，r₀为纳米线半径，d₁表示阴极与栅极间距.     

Magneto-intersubband zener tunneling in a wide GaAs quantum well at high filling factors

The dependence of the differential resistance r _xx on the dc current density J _dc in a wide GaAs quantum well with two occupied size quantization subbands has been investigated at the temperature T = 4.2 K in the magnetic fields B < 1 T. A peak, whose position is given by the relation 2R _c eE _H = ħω_c/2, where R _c is the cyclotron radius, E _H is the Hall electric field, and ω_c is the cyclotron frequency, has been observed in the r _xx (J _dc) curves at high filling factors. The experimental results are attributed to Zener tunneling of electrons between the Landau levels of different subbands.     

A possible assignment for the ground scalar meson nonet

Based on the main assumption that a₀(980) and D ^* _sJ(2317) belong to the 1³P₀ q¯ multiplet, in the framework of Regge phenomenology and meson-meson mixing, it is suggested that a₀(980), K ^* ₀(1052), f₀(1099) and f₀(530) constitute the ground scalar meson nonet, and that the f₀(1099) is composed mostly of s¯, while the f₀(530) is mainly a u¯ + d¯ system. It is supposed that these states would likely correspond to the observed scalar states a₀(980), κ(900), f₀(980) and f₀(600)/σ, respectively. The agreement between the present findings and those given by other different approaches is satisfactory.