Implications of time-reversal symmetry for the band structure of single-wall carbon nanotubes

When electron states in carbon nanotubes are characterized by two-dimensional wave vectors with the components K ₁ and K ₂ along the nanotube circumference and cylindrical axis, respectively, then two such vectors symmetric about a M-point in the reciprocal space of graphene are shown to be related by the time-reversal operation. To each carbon nanotube there correspond five relevant M-points with the following coordinates: K ₁⁽¹⁾ = N/2R, K ₂⁽¹⁾= 0; K ₁⁽²⁾ = M/2R, K ₂⁽²⁾= −π/T; K ₁⁽³⁾= (2N −M)/2R, K ₂⁽³⁾= π/T; K ₁⁽⁴⁾= (M + N)/2R, K ₂⁽⁴⁾= -π/T, and K ₁⁽⁵⁾= (N − M)/2R, K ₂⁽⁵⁾= π/T, where M and N are the integers relating the chiral, C _h , symmetry, R, and translational, T, vectors of the nanotube by N R = C _h + M T, T = |T|, and R is the nanotube radius. The states at the edges of the one-dimensional Brillouin zone, which are symmetric about the M-points with K ₂ = ±π/T, are shown to be degenerate due to the time-reversal symmetry.     

Superionic conductivity of the heterovalent solid solutions R 1−x M x F 3−x (R=REE, M=Ca, Ba) with tysonite-type structure

The fluorine-ion conductivity of anion-deficient solid solutions R _1−x Ca_xF_3−x and R _1−x Ba_xF_3−x having the tysonite (LaF₃) structure was investigated by the impedance spectroscopy method. R _1−x Ca_xF_3−x (R=La, Pr, Nd, Sm, Gd, Tb, Dy, Ho) and R _1−x Ba_xF_3−x (R=La, Pr, Nd) single crystals were grown from the melt by the Bridgman-Stockbarger method. The electrophysical measurements were performed in the frequency range 5−5×10⁵ and temperature range 300–700 K. The temperature dependences of the electrical conductivity for the crystals studied is determined by the migration of fluorine anions along various structural positions. It is shown that, from the standpoint of increasing the conductivity of tysonite matrices RF₃ (R=La, Pr, Nd), doping by CaF₂ and BaF₂ is less promising than SrF₂. Fiz. Tverd. Tela (St. Petersburg) 41, 638–640 (April 1999)     

Optical absorption spectrum of Cr3+ in natural ruby

Two sharp line-like bands calledN andR lines on the red side, a close doublet (B lines) on the violet side and two broad bands are observed for natural ruby. At liquid air temperature the splitting ofR line was found and also three sharp-bands calledR, R′ andB lines are identified with spin-forbidden transitions of² E,² T ₁ and² T ₂. The two broad bands calledU band andY band are assigned accordingly to the spin-allowed transitions⁴ T ₂ and⁴ T ₁ respectively. The observed bands of natural ruby have been attributed to Cr³⁺ ion in an octahedral environment with trigonal distortion. The crystal field parameters which gave a good fit to the observed band positions areB=732 cm⁻¹,C=4.25B,Dq=1830 cm⁻¹,V=−1996 cm⁻¹ andλ=34 cm⁻¹.     

Critical point phenomena in the electrical resistivity of binary liquid systems: CS2 + CH3CN and CS2 + CH3NO2

Electrical resistance measurements are reported on the binary liquid mixtures CS₂ + CH₃CN and CS₂ + CH₃NO₂ with special reference to the critical region. Impurity conduction seems to be the dominant mechanism for charge transport. For the liquid mixture filled at the critical composition, the resistance of the system aboveT _c follows the relationR=R _c−A(T−T _c) ^b withb=0·6±0·1. BelowT _c the conductivities of the two phases obey a relation σ₂−σ₁=B(T _c−T)^β with β=0·34±0·02, the exponent of the transport coefficient being the same as the exponent of the order parameter, an equilibrium property.     

Twists in Hopf algebras andRT 1 T 2=T 2 T 1 relations

LetR be a matrix unitary quasi-classical solution of the Yang-Baxter equation. Considering an associative algebra defined by the relationRT ₁ T ₂=T ₂ T ₁ we find a universal twistF such thatR is the image ofR=F ₂₁ F ⁻¹ in the vector representation. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.     

Generalized holographic and Ricci dark energy models

In this paper, we consider generalized holographic and Ricci dark energy models where the energy densities are given as ρ _R =3c ² M _pl² Rf(H ²/R) and ρ _h =3c ² M _pl² H ² g(R/H ²), respectively; here f(x), g(y) are positive defined functions of the dimensionless variables H ²/R or R/H ². It is interesting that holographic and Ricci dark energy densities are recovered or recovered interchangeably when the function f(x)=g(y)≡1 or f(x)=Id and g(y)=Id are taken, respectively (for example f(x),g(x)=1−ε(1−x), ε=0or1, respectively). Also, when f(x)≡xg(1/x) is taken, the Ricci and holographic dark energy models are equivalent to a generalized one. When the simple forms f(x)=1−ε(1−x) and g(y)=1−η(1−y) are taken as examples, by using current cosmic observational data, generalized dark energy models are considered. As expected, in these cases, the results show that they are equivalent (ε=1−η=1.312), and Ricci-like dark energy is more favored relative to the holographic one where the Hubble horizon was taken as an IR cut-off. And the suggested combination of holographic and Ricci dark energy components would be 1.312R−0.312H ², which is 2.312H²+1.312[(H)\dot]2.312H^{2}+1.312\dot{H} in terms of H ² and [(H)\dot]\dot{H} .     

Super-Diffusivity in a Shear Flow Model¶from Perpetual Homogenization

This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dy _t =dω _t −∇Γ(y _t ) dt, y ₀=0 and d=2. Γ is a 2 &\times; 2 skew-symmetric matrix associated to a shear flow characterized by an infinite number of spatial scales Γ₁₂=−Γ₂₁=h(x ₁), with h(x ₁)=∑ _{n =0} ^∞γ _n h ⁿ (x ₁/R _n ), where h ⁿ are smooth functions of period 1, h ⁿ (0)=0, γ _n and R _n grow exponentially fast with n. We can show that y ^t has an anomalous fast behavior (?[|y ^t |²]∼t ^1+ν with ν > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization. Received: 1 June 2001 / Accepted: 11 January 2002     

Concerning the two magnetic correlation lengths above T c in an Invar iron-nickel alloy

The magnetic phase transition in the Invar alloy Fe₇₀Ni₃₀ is investigated by means of small-angle neutron scattering over a wide range of momentum transfer. This method was used to measure two magnetic correlation lengths R _c 1 and R _c 2 which coexist in the alloy above the phase transition temperature T _c . The critical correlations with correlation length R _c 1 are described well by an Ornstein-Zernicke expression, and the critical correlations with the second correlation length, an order of magnitude larger than R _c 2, are described well by a squared Ornstein-Zernicke expression. The temperature dependences obtained for the correlation lengths R _c 1 and R _c 2 satisfy the power law R _c ∼((T−T _c )/T _c ) ^−υ with critical exponents υ₁=0.65±0.05 and υ₂=1.3±0.1 for the shorter and longer scales, respectively. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 1, 53–57 (10 July 1997)     

Growth morphology of nanoscale sputter-deposited Au films on amorphous soft polymeric substrates

The growth of a room-temperature sputter-deposited thin Au film on two soft polymeric substrates, polystyrene (PS) and poly(methyl methacrylate) (PMMA), from nucleation to formation of a continuous film is investigated by means of atomic force microscopy. In particular, we studied the surface morphology evolution of the film as a function of the deposition time observing an initial Au three-dimensional island-type growth. Then the Au film morphology evolves, with increasing deposition time, from hemispherical islands to partially coalesced worm-like island structures, to percolation, and finally to a continuous and rough film. The overall Au morphology evolution is discussed in the framework of the interrupted coalescence model, allowing us to evaluate the island critical radius for the partial coalescence R _c=8.7±0.9 nm for Au on PS and R _c=7.6±0.8 nm for Au on PMMA. Furthermore, the application of the kinetic freezing model allows us to evaluate the room-temperature surface diffusion coefficient D _s≈1.8×10⁻¹⁸ m²/s for Au on PS and D _s≈1.1×10⁻¹⁸ m²/s for Au on PMMA. The application of the Vincent model allows us, also, to evaluate the critical coverage (at which the percolation occurs) P _c=61% for Au on PS and P _c=56% for Au on PMMA. Finally, the dynamic scaling theory of a growing interface was applied to characterize the kinetic roughening of the Au film on both PMMA and PS. Such analyses allow us to evaluate the dynamic scaling, growth, and roughness exponents z=3.8±0.4, β=0.28±0.03, α=1.06±0.05 for the growth of Au on PS and z=4.3±0.3, β=0.23±0.03, α=1.03±0.05 for the growth of Au on PMMA, in agreement with a non-equilibrium but conservative and linear growth process in which the surface diffusion phenomenon plays a key role.     

A study of 223Ra populated by α-decay

The low spin states of ²²³Ra have been populated via α-decay from ²²⁷Th which was itself produced following β⁻ decay of an ²²⁷Ac source. α–γ and α−e _K,L,M angular correlation measurements have been analysed using the correct ground state spins of ²²⁷Th(=1/2⁺) and ²²³Ra(=3/2⁺) for the first time. The analysis has allowed unique J^π values to be assigned to almost all levels below 400 keV excitation in ²²³Ra. Values of (g _K−g _R)/Q ₀ have been deduced for several members of the K= 3/2^± bands (for the first time in an odd N nucleus in this mass region) allowing estimates of g _K and g _R to be extracted. The values of g _K and g _R are not significantly different for the positive and negative parity band members and tend to support other strong evidence that stable octupole deformation exists in ²²³Ra at low excitation energies. Received: 17 November 1997 / Revised version: 8 January 1998     

On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System

In a previous work [1] matter models such that the energy density ρ ≥ 0, and the radial- and tangential pressures p ≥ 0 and q, satisfy p + q ≤ Ωρ, Ω ≥ 1, were considered in the context of Buchdahl’s inequality. It was proved that static shell solutions of the spherically symmetric Einstein equations obey a Buchdahl type inequality whenever the support of the shell, [R ₀, R ₁], R ₀ > 0, satisfies R ₁/R ₀ < 1/4. Moreover, given a sequence of solutions such that R ₁/R ₀ → 1, then the limit supremum of 2M/R ₁ was shown to be bounded by ((2Ω + 1)² − 1)/(2Ω + 1)². In this paper we show that the hypothesis that R ₁/R ₀ → 1, can be realized for Vlasov matter, by constructing a sequence of static shells of the spherically symmetric Einstein-Vlasov system with this property. We also prove that for this sequence not only the limit supremum of 2M/R ₁ is bounded, but that the limit is ((2Ω + 1)² − 1)/(2Ω + 1)² = 8/9, since Ω = 1 for Vlasov matter. Thus, static shells of Vlasov matter can have 2M/R ₁ arbitrary close to 8/9, which is interesting in view of [3], where numerical evidence is presented that 8/9 is an upper bound of 2M/R ₁ of any static solution of the spherically symmetric Einstein-Vlasov system.     

Electron screening in backward elastic scattering

Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θ_lab=165° and E _lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σ_R(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σ_R(E,θ)=(1+U_e/E)⁻¹, where U _e is an atomic screening potential energy. The deduced average value, U _e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998     

Overall values of conventional discrepancy indices for crystals with heavy atoms. Part II. Results for monoclinic and orthorhombic crystals when the heavy-atom part alone constitutes the model

Theoretical expressions of 〈y _N〉, 〈|y _N − σ₁ y _P ^c |〉 and 〈|y _N ² −σ ₁ ² (y _P ^c )²|〉 (wherey _N andy _P ^c are the normalized structure amplitudes of the structure and the model respectively) are derived in terms of the heavy atom contributionσ ₁ ² for monoclinic and orthorhombic crystals containing a few (i.e., 1 or 2) heavy atoms of the same kind per asymmetric unit by taking the heavy atom part alone as the model. Results are obtained for both the related and unrelated cases. The local values of 〈y _N〉 and 〈|y _N ⁿ − σ ₁ ⁿ (y _P ^c ) ⁿ |〉, (n=1, 2) calculated from these expressions can be used to calculate the overall values of the conventionalR-indicesR(F) andR(I) for the related and unrelated cases. These overall values could be used to check the correctness of heavy atoms located in the structure. Contribution No. 550     

Temperature dependence of surface impedance of Tl2Ba2CaCu2O8−δ and YBa2Cu3O6.95 single crystals measured in the microwave band

The real part R _s and the imaginary part X _s of the surface impedance Z _s=R _s+ iX _s of Tl₂Ba₂CaCu₂O_8−δ and YBa₂Cu₃O_6.95 single crystals have been measured with high precision at frequency ω/2π=9.4 GHz in the temperature range 0<T<140 K. In the Tl₂Ba₂CaCu₂O_8−δ crystal a linear temperature dependence R _s(T) has been found for T⩽50 K, and the magnetic field penetration depth λ(4.2 K)=X _s(4.2 K)/ω μ ₀≈3760 Å has been measured. Along with well known features of the function Z _s(T) in high-quality YBa₂Cu₃O_6.95 single crystals, such as the linearity of λ(T) and R _s(T) for T<T _c/3 and a maximum of R _s(T) at T∼T _c/2, the linearity range of λ(T) extends to T≃50 K, and this curve has a plateau in the range 60<T<85 K. The curve of R _s(T) in both the superconducting and normal states of YBa₂Cu₃O_6.95 is well described by a two-fluid model with the electron-phonon mechanism of quasiparticle relaxation. A formula describing the curve of λ ²(0)/λ ²(T) throughout the studied temperature range is also given. Zh. éksp. Teor. Fiz. 112, 2210–2222 (December 1997)     

Cross section and resonance strength measurements of 19F(p, αγ)16O at Ep= 200–800 keV

An excitation function of the ¹⁹F(p, αγ)¹⁶O reaction has been measured over the proton beam energy range E_p= 200–800 keV using a 4 π NaI summing spectrometer. A new resonance was found at E_R= 237 keV and its properties Γ_R, σ_R and ωγ have been extracted. The strengths of all resonances at E_p= 200–800 keV have been also extracted. The importance of the 1⁺ resonance at E_R= 11 keV is discussed and its width has been estimated taking into account interference effects with the strong 1⁺ resonance at E_R= 340 keV. The reaction rates have been calculated over a wide range of temperatures and compared with the rates of the (p, α₀) and (p, α_π) branches of the ¹⁹F(p, α)¹⁶O reaction. Received: 21 June 1999 / Revised version: 30 September 1999     

Assessment of Blood Hemodynamics by USPIO-Induced R 1 Changes in MRI of Murine Colon Carcinoma

The objective of this study is to assess whether ultrasmall superparamagnetic iron oxide (USPIO)-induced changes of the water proton longitudinal relaxation rate (R ₁) provide a means to assess blood hemodynamics of tumors. Two types of murine colon tumors (C26a and C38) were investigated prior to and following administration of USPIO blood-pool contrast agent with fast R ₁ measurements. In a subpopulation of mice, R ₁ was measured following administration of hydralazine, a well-known blood hemodynamic modifier. USPIO-induced R ₁ increase in C38 tumors (ΔR ₁ = 0.072 ± 0.0081 s⁻¹) was significantly larger than in C26a tumors (ΔR ₁ = 0.032 ± 0.0018 s⁻¹, N = 9, t test, P < 0.001). This was in agreement with the immunohistochemical data that showed higher values of relative vascular area (RVA) in C38 tumors than in C26a tumors (RVA = 0.059 ± 0.015 vs. 0.020 ± 0.011; P < 0.05). Following administration of hydralazine, a decrease in R ₁ value was observed. This was consistent with the vasoconstriction induced by the steal effect mechanism. In conclusion, R ₁ changes induced by USPIO are sensitive to tumor vascular morphology and to blood hemodynamics. Thus, R ₁ measurements following USPIO administration can give novel insight into the effects of blood hemodynamic modifiers, non-invasively and with a high temporal resolution.     

Spectroscopy of quasiparticle excitations of superconducting bismuth cuprate at high pressures

We study the energy spectrum of Bi2223 (Bi_1.6Pb_0.4Sr_1.8Ca_2.2Cu₃O_x) at high hydrostatic pressures by Andreev-and tunneling-spectroscopy methods. We determine the gap anisotropy in the basal ab plane and find the following values for the parameters Δ(ϕ): Δ_max=42 mV, and Δ_min=19.5 mV (T _c =110 K and dT _c /dP=0.16 K/kbar). We detect an increase in the ratio R=2Δ_max/kT _c with pressure P; for Bi2223 cuprate, dR/dP≈0.017 kbar⁻¹. In the phonon-frequency region we detect a “softening,” due to pressure, of the high-frequency part of the phonon spectrum corresponding to “breathing” modes of oxygen, as well as other optical modes of Cu-O. The characteristic frequencies of the spectrum for ℏΩ>60 mV are found to decrease, with increasing pressure, at a rate d ln(ℏΩ)/dP≈−6.5±0.5×10⁻³ kbar⁻¹. This result explains the observed increase in the ratio 2Δ/kT _c (P) in the model of strong electron-phonon interaction. Zh. éksp. Teor. Fiz. 113, 1397–1410 (April 1998)     

Indirect determination of the ratio R=σL/σT at small x from HERA data

The value of the deep inelastic scattering cross-section ratio R=σ _L /σ _T is found in the range 10⁻⁴⩽x⩽10⁻² from F ₂ and dF ₂/d ln Q ² HERA data using very simple relations based on perturbative QCD. Zh. éksp. Teor. Fiz. 112, 32–36 (July 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Investigation of a magnetic phase transition in fcc iron-nickel alloys

A magnetic phase transition in carbon-doped (0.1 and 0.7 at. %) Fe₇₀Ni₃₀ Invar alloys was investigated by the method of depolarization of a transmitted neutron beam and by small-angle scattering of polarized neutrons. It is shown that for both alloys, two characteristic length scales of magnetic correlations coexist above T _c. Small-angle scattering by critical correlations with radius R _c is described well by the Ornstein-Zernike (OZ) expression. The longer-scale (second) correlations, whose size can be estimated from depolarization data, are not described by the OZ expression, and hypothetically can be modeled by a squared OZ expression, which in coordinate space corresponds to the relation 〈M(r)M(0)〉∝exp(−r/R _d), where R _d is the correlation length of the second scale. The temperature dependence of the correlation radius R _c was obtained: R _c ∝ ((T−T _c)/Tc)^−ν , where ν≈2/3 is the critical exponent for ferromagnets, over a wide temperature range up to T _c ^exp , at which the correlation radius becomes constant and equals its maximum value R _c(T _c)=R _c ^max . The maximum correlation radius established (R _c ^max =140 Å and 230 Å for the first and second alloys, respectively) characterizes the length-scale of the fluctuation for which the appearance of critical correlations first results in the formation of a ferromagnetic phase, and the phenomenon itself exhibits a “disruption” of the second-order phase transition at T=T _c ^exp , as a result of which a first-order transition arises. Temperature hysteresis was also detected in the measured polarization of the transmitted beam and intensity of small-angle neutron scattering in the alloy above T _c, confirming the character of this magnetic transition as a first-order transition close to a second-order transition. Zh. éksp. Teor. Fiz. 112, 2134–2155 (December 1997)