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.     

Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System

A mathematical method is presented for solving the Schr?dinger equation for a system of identical body forces. The N-body forces are more easily introduced and treated within the hyperspherical harmonics. The problem of the N-body potential has been used at the level of both classical and quantum mechanics. The hypercentral interacting potential is assumed to depend on the hyperradius x = (ξ₁² + ξ₂² + ⋯ + ξ_N−1²)^1/2 only, where ξ₁,ξ₂,…,ξ_N−1 are Jacobi relative coordinates which are functions of N-particle relative positions r₁₂,r₂₃,…,r_N1. The problem of the harmonic oscillator and the Coulomb-type potential has been widely studied in different contexts. Using the N-body potential V(x) = ax² + bx − (c/x) as an example, and assuming an ansatz for the eigenfunction, an exact analytical solution of the Schr?dinger equation for an N-body system in three dimensions is obtained. This method is also applicable to some other types of potentials for N-identical interacting particles.     

Thermo-optic coefficients of monoclinic KLu(WO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The three thermo-optic coefficients of the biaxial laser host KLu(WO₄)₂ are measured at 633 nm by a deflection method. Their values at 300 K amount to ∂ n _g /∂ T=−7.4×10⁻⁶ K⁻¹; ∂ n _m /∂ T=−1.6×10⁻⁶ K⁻¹ and ∂ n _p /∂ T=−10.8×10⁻⁶ K⁻¹. Nearly athermal propagation directions are found for polarizations along the N _m and N _p dielectric axes.     

Fine structure of splitting of the separatrix of a nonlinear resonance

This report is a continuation of an analysis, initiated elsewhere V.V. Vecheslavov and B. V. Chirikov, Zh. éksp. Teor. Fiz. 114, 1516 (1998) [JETP 86, 823 (1998)], of the effect of splitting of the separatrix of a nonlinear resonance for the model of standard mapping, based on results of direct measurements of the splitting angle α(K), where K is the system parameter. Measurements were made in the previously used wide range 0.1≳α≳10⁻²⁰⁸ (1⩾K⩾0.0004), but with significantly higher relative (better than 10⁵⁰) and average (∼10⁻⁵⁵) accuracy. This procedure made it possible to substantially refine the effects observed in Ref. 1 and construct qualitatively new empirical dependences providing reliable extrapolation of the data obtained for the angle and the invariant in the intermediate asymptotic limit K≲10⁻² beyond the limits of the investigated region. The results obtained by us can be useful for further development of the theory of separatrix splitting and formation of the stochastic layer of a nonlinear resonance. Zh. éksp. Teor. Fiz. 116, 336–346 (July 1999)     

Absolute cross sections of electron attachment to molecular clusters. Part II: Formation of (H2O) N? , (N2O) N? , and (N2) N?

Absolute cross sections σ⁻(E, N) of electron attachment to clusters (H₂O) _N , (N₂O) _N , and (N₂) _N for varying electron energy E and cluster size N are measured by using crossed electron and cluster beams in a vacuum. Continua of σ⁻(E) are found that correlate well with the functions of electron impact excitation of molecules’ internal degrees of freedom. The electron is attached through its solvation in a cluster. In the formation of (H₂O) _N ⁻ , (N₂O) _N ⁻ , and (N₂) _N ⁻ , the curves σ⁻(N) have a well-defined threshold because of a rise in the electron thermalization and solvation probability with N. For (H₂O)₉₀₀, (N₂O)₃₅₀, and (N₂)₂₆₀ clusters at E = 0.2 eV, the energy losses by the slow electron in the cluster are estimated as 3.0 × 10⁷, 2.7 × 10⁷, and 6.0 × 10⁵ eV/m, respectively. It is found that the growth of σ⁻ with N is the fastest for (H₂O) _N and (N₂) _N clusters at E → 0 as a result of polarization capture of the s-electron. Specifically, at E = 0.1 eV and N = 260, σ⁻ = 3.0 × 10⁻¹³ cm² for H₂O clusters, 8.0 × 10⁻¹⁴ cm² for N₂O clusters, and 1.4 × 10⁻¹⁵ cm² for N₂ clusters; at E = 11 eV, σ⁻ = 9.0 × 10⁻¹⁶ cm² for (H₂O)₂₀₀ clusters, 2.4 × 10⁻¹⁴ cm² for (N₂O)₃₅₀ clusters, and 5.0 × 10⁻¹⁷ cm² for (N₂)₂₆₀ clusters; finally, at E = 30 eV, σ⁻ = 3.6 × 10⁻¹⁷ cm² for (N₂O)₁₀ clusters and 3.0 × 10⁻¹⁷ cm² for (N₂)₁₂₅ clusters. Original Russian Text ? A.A. Vostrikov, D.Yu. Dubov, 2006, published in Zhurnal Tekhnicheskoĭ Fiziki, 2006, Vol. 76, No. 12, pp. 1–15.     

Strange hadron production in Σ-<Emphasis Type="Italic">A</Emphasis> interactions in the SELEX experiment

We report our observations on the resonance signals of masses of 1520, 1670, 1810 (1 820), and 2100 MeV c ⁻², produced inclusively in the reaction Σ⁻ + C(Cu) → p + K⁻ + X, and the signals of masses of 1020 and 1525 MeV c ⁻², produced inclusively in the reaction Σ⁻ + C(Cu) → K⁺ + K⁻ + X, with a 600-GeV c ⁻¹- momentum hyperon beam in the SELEX experiment at the Fermilab. The masses, widths, and branching ratios were measured. The resonance signal of mass of 1520 MeV c ⁻² correspond to the known Λ(1520) hyperon. The signals of masses of 1020 and 1525 MeV c ⁻² in the K⁺K⁻ system correspond to the φ⁰(1020)- and f ₂′(1525) mesons, respectively. The branching ratio of the resonance of mass of 1670 MeV c ⁻² relative to Λ(1520) is (24.92 ± 0.45 ± 0.48)%, while that of the resonance of mass of 1810 (or 1 820) MeV c ⁻² relative to Λ(1520) is (16.13 ± 0.38 ± 0.45)%. The branching ratio of the f ₂′(1525) resonance relative to φ⁰(1020) is (10.75 ± 0.25 ± 0.45)%. Data analysis was performed over 6 × 10⁷ trigger events registered by the SELEX setup on the FNAL Tevatron.     

The search for and study of the strange multibaryon states in systems with Λ-hyperon and Ks0 -meson in pA collision at momentum of 10 GeV/c

Exotic strange multibaryon states have been observed in the effective mass spectra of: Λπ^±, Λπ⁺π⁻, Λp, Λpp, Λπp, ΛΛ and ΛK _s ⁰, K _s ⁰ p, K _s ⁰π^± subsystems. The measured Λ/π⁺ ratio for average multiplicities from the pC reaction is equal to (5.3 ± 0.8) × 10⁻², and it is approximately two times larger than the Λ/π⁺ ratio simulated by the FRITIOF model and than that of experimental pp reactions at the same energy. The observed wellknown resonances Σ*⁺ (1385) and K*^± (892) from PDG are good tests of this method. The mean value of the mass for the Σ*⁻(1385) resonance is shifted to 1370 MeV/c ² and the width is two times larger than the same value from PDG. Such kind of behavior for the width and invariant mass of Σ*⁻ (1385) resonance is interpreted as an extensive contribution from stopped Ξ⁻ → Λπ⁻ and medium effect. There is enhancement of the production contribution for all observed hyperons. A few events were registered by hypothesis of light H ⁰ and heavy H ^{0, +} dihyperons. Dihyperons were observed by weak decay channels: (Σ⁻ p), (Λpπ⁻), (Λpπ⁰), and (K ⁻ pp). The text was submitted by the author in English.     

On the Fundamental Solution of a Linearized Homogeneous Coagulation Equation

We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel K(x, y) = (xy)^λ/2, around the steady state f(x) = x ^?(3+λ)/2 with ${\lambda \in (1, 2)}We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel K(x, y) = (xy)^λ/2, around the steady state f(x) = x ^−(3+λ)/2 with l ? (1, 2){\lambda \in (1, 2)} . Detailed estimates on its asymptotics are obtained. Some consequences are deduced for the flux properties of the particles distributions described by such models.     

Non-equilibrium Stationary States in the Symmetric Simple Exclusion with Births and Deaths

We consider the symmetric simple exclusion process in the interval Λ _N :=[−N,N]∩ℤ with births and deaths taking place respectively on suitable boundary intervals I ₊ and I ₋, as introduced in De Masi et al. (J. Stat. Phys. 144:1151–1170, 2011). We study the stationary measure and its macroscopic density profile in the limit N→∞.     

Rank-Driven Markov Processes

We study a class of Markovian systems of N elements taking values in [0,1] that evolve in discrete time t via randomized replacement rules based on the ranks of the elements. These rank-driven processes are inspired by variants of the Bak–Sneppen model of evolution, in which the system represents an evolutionary ‘fitness landscape’ and which is famous as a simple model displaying self-organized criticality. Our main results are concerned with long-time large-N asymptotics for the general model in which, at each time step, K randomly chosen elements are discarded and replaced by independent U[0,1] variables, where the ranks of the elements to be replaced are chosen, independently at each time step, according to a distribution κ _N on {1,2,…,N} ^K . Our main results are that, under appropriate conditions on κ _N , the system exhibits threshold behavior at s ^∗∈[0,1], where s ^∗ is a function of κ _N , and the marginal distribution of a randomly selected element converges to U[s ^∗,1] as t→∞ and N→∞. Of this class of models, results in the literature have previously been given for special cases only, namely the ‘mean-field’ or ‘random neighbor’ Bak–Sneppen model. Our proofs avoid the heuristic arguments of some of the previous work and use Foster–Lyapunov ideas. Our results extend existing results and establish their natural, more general context. We derive some more specialized results for the particular case where K=2. One of our technical tools is a result on convergence of stationary distributions for families of uniformly ergodic Markov chains on increasing state-spaces, which may be of independent interest.     

Reflection asymmetry in the structure and spectroscopy of224Ac

Minor changes in the assignments of gamma rays following the alpha decay of²²⁸Pa in two previous studies make possible a reinterpretation of²²⁴Ac into two alternative level schemes. The resulting level structures arise from the reflection asymmetric configurations π3/2^±(0.0 −0.3)−ν3/2^±(−0.1 0.6), π5/2^±(0.0 −0.2)±ν3/2^±(−0.1 0.6) and π5/2^±(0.0 −0.2)±ν1/2^±(0.2 −0.1 3) which give rise to eitherK=0^± or 1^±,K=4^±,K=2^± andK=3^± parity doublet bands. The bands with appreciable band structure, namelyK=0^± or 1^± andK=3^±, have average parity doublet splittings of 11.0 and 5.8 keV respectively. These are extremely small values and suggest that²²⁴Ac is the most octupole deformed nucleus studied thus far. A method of calculating the parity doublet splitting in odd-odd nuclei is suggested and tested for²²⁴Ac. It seems to work remarkably well. The systematics of the hindrance factors for the bands with extended band structures confirm their interpretations as band structures. Finally, the two alternative level schemes are analyzed in the framework of the axially-symmetric rigid rotor model including the Coriolis interaction.     

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.     

KNΛ and KNΣ coupling constants from the Chiral Bag Model

The KNΛ and KNΣ coupling constants have been calculated in the framework of the Chiral Bag Model(CBM). We find −3.88 ≤g _KNΛ≤−3.67 and 1.15 ≤g _KNΣ≤ 1.24 by taking into account pseudoscalar mesons (π, K) and vector mesons (ρ, ω, K ^*) field effects. Particularly, it is shown that vector mesons make significant contributions to the coupling constants g _KNΛ and g _KNΣ. Our values are existing within the experimental limits compared to the phenomenological values extracted from the kaon photoproduction and kaon-nucleon scattering experiments. Also, form factors are suggested for the πNN, πNΔ, KNΛ and KNΣ couplings. Received: 17 August 1998 / Revised version: 22 December 1998     

A Study of the Interaction Between Malachite Green and Lysozyme by Steady-State Fluorescence

The interaction of a N-methylated diaminotriphenylmethane dye, malachite green, with lysozyme was investigated by fluorescence spectroscopic techniques under physiological conditions. The binding parameters have been evaluated by fluorescence quenching methods. The results revealed that malachite green caused the fluorescence quenching of lysozyme through a static quenching procedure. The thermodynamic parameters like ΔH and ΔS were calculated to be −15.33 kJ mol⁻¹ and 19.47 J mol⁻¹ K⁻¹ according to van’t Hoff equation, respectively, which proves main interaction between malachite green and lysozyme is hydrophobic forces and hydrogen bond contact. The distance r between donor (lysozyme) and acceptor (malachite green) was obtained to be 3.82 nm according to Fӧrster’s theory. The results of synchronous fluorescence, UV/vis and three-dimensional fluorescence spectra showed that binding of malachite green with lysozyme can induce conformational changes in lysozyme. In addition, the effects of common ions on the constants of lysozyme-malachite green complex were also discussed.     

One Dimensional Behavior of Singular N Dimensional Solutions of Semilinear Heat Equations

We consider u(x,t) a solution of u _t =Δu+|u| ^{p − 1} u that blows up at time T, where u:ℝ ^N ×[0, T)→ℝ, p>1, (N−2)p<N+2 and either u(0)≥ 0 or (3N−4)p<3N+8. We are concerned with the behavior of the solution near a non isolated blow-up point, as T−t→ 0. Under a non-degeneracy condition and assuming that the blow-up set is locally continuous and N−1 dimensional, we escape logarithmic scales of the variable T−t and give a sharper expansion of the solution with the much smaller error term (T−t)^{1, 1/2−η} for any η>0. In particular, if in addition p>3, then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow-up set. Finally, we prove that the mere hypothesis that the blow-up set is continuous implies that it is C ^{1, 1/2−η} for any η>0. Received: 20 June 2001 / Accepted: 6 October 2001     

Reflectance fluctuations in an absorbing random waveguide

We study the statistics of the reflectance (the ratio of reflected and incident intensities) of an N-mode disordered waveguide with weak absorption g per mean free path. Two distinct regimes are identified. The regime γ N ²≫1 shows universal fluctuations. With increasing length L of the waveguide, the variance of the reflectance changes from the value 2/15N ², characteristic for universal conductance fluctuations in disordered wires, to another value 1/8N ², characteristic for chaotic cavities. The weak-localization correction to the average reflectance performs a similar crossover from the value 1/3N to 1/4N. In the regime γ N ²≫1, the large-L distribution of the reflectance R becomes very wide and asymmetric, P(R)∝(1−R)⁻² for R≪1−γN. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 289–293 (25 August 1996) Published in English in the original Russian journal. Edited by J. R. Anderson.     

Symmetric Simple Exclusion Process:¶Regularity of the Self-Diffusion Coefficient

We prove that the self-diffusion coefficient of a tagged particle in the symmetric exclusion process in Z ^d , which is in equilibrium at density α, is of class C ^∞ as a function of α in the closed interval [0,1]. The proof provides also a recursive method to compute the Taylor expansion at the boundaries. Received: 6 December 2000 / Accepted: 6 April 2001     

Observation of the radiative kaon decay K − → µ−π0γν

Using data collected with the ISTRA+ spectrometer during the 2001 run of the U-70 proton synchrotron in Protvino, the first observation of the radiative kaon decay K ⁻ → μ⁻π⁰γν is reported. The ratio Br(K _μ3γ, 5 < E*_γ < 30 MeV)/Br(K _μ3) is found to be [0.270 ± 0.029(stat.) ± 0.026(syst.)]% and the ratio Br(K _μ3γ, 30 < E*_γ < 60 MeV)/Br(K _μ3) = [0.0448 ± 0.0068(stat.) ± 0.0099(syst.)]%. These ratios are consistent with the theoretical predictions 0.21 and 0.047%, respectively. The measured angular distribution asymmetry for the region 5 < E*_γ < 30 MeV, A(cos ϑ*_μγ) = 0.093 ± 0.141, is two standard deviations away from the theoretical prediction of 0.354. The measured asymmetry in the T-odd variable ξ = p_γ · (p_μ × p_π)/m _K ³ is −0.03 ± 0.13. The text was submitted by the authors in English.     

Filler-matrix thermal boundary resistance of diamond-copper composite with high thermal conductivity

A composite material with a high thermal conductivity is obtained by capillary infiltration of copper into a bed of diamond particles of 400 μm size, the particles having been pre-coated with tungsten. The measured thermal conductivity of the composite decreases from 910 to 480 W m⁻¹ K⁻¹ when the coating thickness is increased from 110 to 470 nm. Calculations of the filler/matrix thermal boundary resistance R and the thermal conductivity of the coating layer λ _i using differential effective medium, Lichtenecker’s and Hashin’s models give similar numerical values of R and λ _i ≈ 1.5 W m⁻¹ K⁻¹. The minimal thickness of the coating h ∼ 100 nm necessary for ensuring production of a composite while maximizing its thermal conductivity, is of the same order as the free path of the heat carriers in diamond (phonons) and in copper (electrons). The heat conductance of the diamond/tungsten carbide coating/copper interface when h is of this thickness is estimated as (0.8–1) × 10⁸ W m⁻² K⁻¹ and is at the upper level of values characteristic for perfect dielectric/metal boundaries.