Effets des fluctuations longitudinales de l’aimantation sur la résistivité des métaux ferromagnétiques à basse température

Using a simple model which represents a ferromagnetic metal in part as an ensemble of localized magnetic moments ?γ S _n coupled by exchange interactions, and in part as a sea of conduction electrons with spinss _i , coupled to theS _n by a scalar interaction\( - \mathop \sum \limits_{n,i} J(r_i - R_n )s_i \cdot S_n\), we show that the longitudinal fluctuations of theS _n have a negligible effect on the resistivity as compared to the transverse fluctuations.     

ЗАМЕЧАНИЕ К ЭЛЕКТРОД ИНАМИКЕ БОППА И ПОДОЛЬСКОГО

Представление элект ромагнитного поля в в акууме как специφиче ского би-поля, создаваемого вектор амиE, B иH,D, приводит пр и предположении нело кального соотношения между со ставляющими би-поля к электродинамике тип аL(□) □A _μ=—j _μ, гдеL(□) является рац иональной φункцией о т p[. Исследуется рассея ние электронов в поле Боп па-Подольского и срав нивается с результат ами экспериментов Гоφφштадтера. Далее у казывается на тесную связь электродинами ки с производными высших порядков с рез ультатами и методами современной квантов ой электродинамики (пол яризация элоктрон-по зитронового вакуума, регуляризация Паули-Вилларса).     

Behavior of dirty superconductors in high magnetic fields

This paper discusses some properties of homogeneous, dirty superconductors, where the motion of electrons in the normal state can be described as a diffusion process. It is shown that at the nucleation field (H _e2 orH _e3) corresponding to the onset of superconductivity, the order parameterΔ(r) satisfies a linearised equation which has the Landau-Ginsburg form atall temperatures. This considerably extends the validity of the existing calculations ofH _e2 andH _e3; it is possible to show in particular that the ratioH _e3/H _e2 and the form of the angular dependence ofH _e3 are independent of temperature. It is also possible to compute explicitely the local density of statesN(r,ω), at any pointr and energyω, for fields slightly belowH _e2 (orH _e3), when the order parameter is stronglyr-dependent. Due to some remarkable sum rule propertiesN (r,ω) depends only on the local value of the order parameterΔ(r). These results may be of use in the interpretation of tunneling experiments on the mixed state and on surface superconductivity.     

Excitations électroniques dans un supraconducteur pur de deuxième espèce en champ élevé: Effet tunnel et relaxation nucléaire

This paper discusses some properties of fermion-type excitations in a clean type II superconductor, near the upper critical field. This situation is “ergodic” in the sense introduced byde Gennes andTinkham [1]. This ergodic behavior (in the absence of collisions) is due to the variations of thephase of the order parameter along a one-electron trajectory in a vortex lattice. The energy spectrum shows no gap, but is more singular than for “dirty” superconductors [2]. The singularity stems from the electrons with paths nearly parallel to the fieldH. We discuss in particular: 1. tunnel experiments: here it is found that the singularity in the density of states is made weaker by the existence of diffuse scattering at the junction surface; the experiment has been carried out on lead forH～H _c3 and gives qualitative agreement with the theoretical predictions; 2. nuclear relaxation rates, which are shown to depend sensitively on the bulk density of states; 3. effects related to the existence of an anisotropic Fermi surface: the latter may be interesting since the low energy excitations have their velocity parallel toH.     

Unelastische Streuung in der dynamischen Theorie der Elektronenbeugung

A general solution to the fundamental equations of inelastic scattering of fast electrons in crystals is obtained by using a Green function constructed of Bloch waves. Inelastic interband transitions are shown to vanish if they are of a direct type, but not when implying simultaneous Bragg reflexion. These selection rules hold for any type of electron-crystal interaction. The resulting imaginary absorption potentials for the different intraband and interband transitions can be calculated separately. They are reduced to a simple form in the two-beam case. The expression measuring the anomalous absorption contains the Yoshioka potential C ₀ ⁱ g and an additional term which gives a small contribution in the case of crystal electron excitation and no contribution in the case of phonon excitation. Numerical calculations for the scattering of 100 keV electrons in Al, Cu, Ge, Si and MgO are made and compared with experimental data. An analytic expression forYoshioka's C ₀ ⁱ g due to plasmon excitation is derived which vanishes in the random phase approximation.     

Continuous and Discrete Painlevé Equations Arising from the Gap Probability Distribution of the Finite n Gaussian Unitary Ensembles

In this paper we study the gap probability problem in the Gaussian unitary ensembles of \(n\) by \(n\) matrices : The probability that the interval \(J := (-a,a)\) is free of eigenvalues. In the works of Tracy and Widom, Adler and Van Moerbeke, and Forrester and Witte on this subject, it has been shown that two Painlevé type differential equations arise in this context. The first is the Jimbo–Miwa–Okomoto \(\sigma \) -form and the second is a particular Painlevé IV. Using the ladder operator technique of orthogonal polynomials we derive three quantities associated with the gap probability, denoted as \(\sigma _n(a)\) , \(R_n(a)\) and \(r_n(a)\) . We show that each one satisfies a second order Painlevé type differential equation as well as a discrete Painlevé type equation. In particular, in addition to providing an elementary derivation of the aforementioned \(\sigma \) -form and Painlevé IV we are able to show that the quantity \(r_n(a)\) satisfies a particular case of Chazy’s second degree second order differential equation. For the discrete equations we show that the quantity \(r_n(a)\) satisfies a particular form of the modified discrete Painlevé II equation obtained by Grammaticos and Ramani in the context of Backlund transformations. We also derive second order second degree difference equations for the quantities \(R_n(a)\) and \(\sigma _n(a)\) .     

Eine Integralgleichungsmethode zur Behandlung der Streuung an gebundenen Teilchen

First it is pointed out that various methods known for the treatment of multi-particle scattering problems such as the methods ofLax, Watson, andFaddeev are based on the same type ofT-operator equations with eliminated interactions. They only differ by the identification of the interactions. — Then an integral equation treatment for the scattering of a particle by a system ofn bound particles is developed. If the scattering occurs via local two-body forces, the interaction matrix element splits into that of the two-particle case and a momentum-dependent factor. This fact is used to simplify the scattering equations which then get a mathematical structure similar to that of theT-operator equations discussed at the beginning (however, involving sums of bound states rather than sums of interactions) and which, therefore, can be handled in a similar way. When the interactions are eliminated by means of the two-particle scattering amplitudes, the off-shell energy parameter of these amplitudes may be chosen to be dependent on quantum numbers of the bound system. Such a choice shows indeed to be favorable if one likes to keep only the lowest order approximation of the integral equations. The resulting approximate formula leads, after some further approximations, for resonant scattering to a formula ofLamb, and for weakly energy-dependent amplitudes to a formula ofFermi (being related to the impulse approximation). — The resonant scattering formula is applied to a quantum-mechanical derivation of a method for the determination of nuclear lifetimes which had been proposed on semiclassical arguments byCiocchetti et al. — Finally the method developed for the scattering of a particle by a system of bound particles is extended to collisions between composite particles.     

Dimension of quantum channel of radiation in pure Lovelock black holes

The effects of a running gravitational coupling and the entropic force on future singularities are considered. Although it is expected that the quantum corrections remove the future singularities or change the singularity type, treating the running gravitational coupling as a function of energy density is found to cause no change in the type of singularity but causes a delay in the time that a singularity occurs. The entropic force is found to replaces the singularity type $II\, \hbox {by} \overline{III} (a=\hbox {const.}, H=\hbox {const.}, \dot{H} \rightarrow \infty , p \rightarrow \infty , \rho \rightarrow \infty )$ which differs from previously known type $III$ and to remove the $w$ -singularity. We also consider an effective cosmological model and show that the types $I$ and $II$ are replaced by the singularity type $III$ .     

Gleichgewichtsbedingungen in der Gittertheorie

The equilibrium conditions of an infinite crystal lattice result in symmetry relations of lattice sums. This was first shown byKun Huang who obtained these relations by comparing the linear theory of elasticity with the corresponding limit of lattice theory, a procedure which has been criticized by some authors. It is shown here how one can obtainKun Huang's results by using only trivial invariance properties of the potential energy. The same method is applied to get equilibrium relations for higher order (anharmonic) terms of lattice theory which are symmetry relations of tensors used in non linear elastic theory.     

First-principle calculations of structural,electronic, optical,elastic and thermal properties of $$\hbox {MgXAs}_{2}$$ ($$\hbox {X}=\hbox {Si}, \hbox {Ge}$$X=Si,Ge) compounds

First-principle calculations on the structural, electronic, optical, elastic and thermal properties of the chalcopyrite \(\hbox {MgXAs}_{2}\) (\(\hbox {X}=\hbox {Si}, \hbox {Ge}\)) have been performed within the density functional theory (DFT) using the full-potential linearized augmented plane wave (FP-LAPW) method. The obtained equilibrium structural parameters are in good agreement with the available experimental data and theoretical results. The calculated band structures reveal a direct energy band gap for the interested compounds. The predicted band gaps using the modified Becke–Johnson (mBJ) exchange approximation are in fairly good agreement with the experimental data. The optical constants such as the dielectric function, refractive index, and the extinction coefficient are calculated and analysed. The independent elastic parameters namely, \(C_{11}\), \(C_{12}\), \(C_{13}\), \(C_{33}\), \(C_{44}\) and \(C_{66 }\) are evaluated. The effects of temperature and pressure on some macroscopic properties of \(\hbox {MgSiAs}_{2}\) and \(\hbox {MgGeAs}_{2}\) are predicted using the quasiharmonic Debye model in which the lattice vibrations are taken into account.     

Approximation of the naive black hole degeneracy

In 1996, Rovelli suggested a connection between black hole entropy and the area spectrum. Using this formalism and a theorem we prove in this paper, we briefly show the procedure to calculate the quantum corrections to the Bekenstein–Hawking entropy. One can do this by two steps. First, one can calculate the “naive” black hole degeneracy without the projection constraint (in case of the $U(1)$ symmetry reduced framework) or the $SU(2)$ invariant subspace constraint (in case of the fully $SU(2)$ framework). Second, then one can impose the projection constraint or the $SU(2)$ invariant subspace constraint, obtaining logarithmic corrections to the Bekenstein–Hawking entropy. In this paper, we focus on the first step and show that we obtain infinite relations between the area spectrum and the naive black hole degeneracy. Promoting the naive black hole degeneracy into its approximation, we obtain the full solution to the infinite relations.     

Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observables

It is shown that, in theories of exactly localized observables, of the type proposed byAraki andHaag, the reaction amplitude for two particles giving two particles is polynomially bounded ins for fixed momentum transfert<0. The proof does not need observables localized in space-time regions of arbitrarily small volume, but uses relativistic invariance in an essential way. It is given for the case of spinless neutral particles, but is easily extendable to all cases of charge and spin. The proof can also be generalized to the case of particles described by regularized products $$\int {\varphi (x_1 ,..., x_n ) \phi _1 } (x - x_1 ) ... \phi _n (x - x_n )dx_1 ...dx_n $$ ofWightman orJaffe fields.     

Evolution of primordial magnetic fields in mean-field approximation

We study the evolution of phase-transition-generated cosmic magnetic fields coupled to the primeval cosmic plasma in the turbulent and viscous free-streaming regimes. The evolution laws for the magnetic energy density and the correlation length, both in the helical and the non-helical cases, are found by solving the autoinduction and Navier–Stokes equations in the mean-field approximation. Analytical results are derived in Minkowski spacetime and then extended to the case of a Friedmann universe with zero spatial curvature, both in the radiation- and the matter-dominated era. The three possible viscous free-streaming phases are characterized by a drag term in the Navier–Stokes equation which depends on the free-streaming properties of neutrinos, photons, or hydrogen atoms, respectively. In the case of non-helical magnetic fields, the magnetic intensity $B$ and the magnetic correlation length $\xi _B$ evolve asymptotically with the temperature, $T$ , as $B(T) \simeq \kappa _B (N_i v_i)^{\varrho _1} (T/T_i)^{\varrho _2}$ and $\xi _B(T) \simeq \kappa _\xi (N_i v_i)^{\varrho _3} (T/T_i)^{\varrho _4}$ . Here, $T_i$ , $N_i$ , and $v_i$ are, respectively, the temperature, the number of magnetic domains per horizon length, and the bulk velocity at the onset of the particular regime. The coefficients $\kappa _B$ , $\kappa _\xi $ , $\varrho _1$ , $\varrho _2$ , $\varrho _3$ , and $\varrho _4$ , depend on the index of the assumed initial power-law magnetic spectrum, $p$ , and on the particular regime, with the order-one constants $\kappa _B$ and $\kappa _\xi $ depending also on the cutoff adopted for the initial magnetic spectrum. In the helical case, the quasi-conservation of the magnetic helicity implies, apart from logarithmic corrections and a factor proportional to the initial fractional helicity, power-like evolution laws equal to those in the non-helical case, but with $p$ equal to zero.     

Bootstrap Percolation in Power-Law Random Graphs

A bootstrap percolation process on a graph $G$ is an “infection” process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours becomes infected and remains so forever. The parameter $r\ge 2$ is fixed. Such processes have been used as models for the spread of ideas or trends within a network of individuals. We analyse this process in the case where the underlying graph is an inhomogeneous random graph, which exhibits a power-law degree distribution, and initially there are $a(n)$ randomly infected nodes. The main focus of this paper is the number of vertices that will have been infected by the end of the process. The main result of this work is that if the degree sequence of the random graph follows a power law with exponent $\beta $ , where $2 < \beta < 3$ , then a sublinear number of initially infected vertices is enough to spread the infection over a linear fraction of the nodes of the random graph, with high probability. More specifically, we determine explicitly a critical function $a_c(n)$ such that $a_c(n) = o(n)$ with the following property. Assuming that $n$ is the number of vertices of the underlying random graph, if $a(n) \ll a_c(n)$ , then the process does not evolve at all, with high probability as $n$ grows, whereas if $a(n)\gg a_c(n)$ , then there is a constant $\varepsilon > 0$ such that, with high probability, the final set of infected vertices has size at least $\varepsilon n$ . This behaviour is in sharp contrast with the case where the underlying graph is a $G(n, p)$ random graph with $p=d/n$ . It follows from an observation of Balogh and Bollobás that in this case if the number of initially infected vertices is sublinear, then there is lack of evolution of the process. It turns out that when the maximum degree is $o(n^{1/(\beta - 1)})$ , then $a_c(n)$ depends also on $r$ . But when the maximum degree is $\Theta (n^{1/(\beta - 1)})$ , then $a_c (n) = n^{\beta - 2 \over \beta - 1}$ .     

Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy

Pinsker’s and Fannes’ type bounds on the Tsallis relative entropy are derived. The monotonicity property of the quantum f -divergence is used fot its estimation from below. For order $\alpha \in (0,1)$ , a family of lower bounds of Pinsker type is obtained. For $\alpha >1$ and the commutative case, upper continuity bounds on the relative entropy in terms of the minimal probability in its second argument are derived. Both the lower and upper bounds presented are reformulated for the case of Rényi’s entropies. The Fano inequality is extended to Tsallis’ entropies for all $\alpha >0$ . The deduced bounds on the Tsallis conditional entropy are used to obtain inequalities of Fannes’ type.     

Zur Darstellung der Reichweite-Energie-Beziehung von Ionen

Previous published pentration depth-energy-relations are represented in a reduced manner with different parameters by the theories ofLindhard andScharff and ofHolmes. The results are discussed.     

Synthesis and anti-cancer activity of a glycosyl library of \varvec{N}-acetylglucosamine-bearing oleanolic acid

N-Acetylglucosamine-bearing triterpenoid saponins (GNTS) were reported to be a unique type of saponins with potent anti-tumor activity. In order to study the structure–activity relationship of GNTS, 24 oleanolic acid saponins with ( $1 \rightarrow 3$ )-linked, ( $1\rightarrow 4$ )-linked, ( $1\rightarrow 6$ )-linked $N$ -acetylglucosamine oligosaccharide residues were synthesized in a combinatorial and concise method. The cytotoxicity of these compounds toward the leukemia cell line HL-60 and the colorectal cancer cell line HT-29 could not be improved. Half maximal inhibition below $10\,\upmu \hbox {M}$ was achieved in one single case. The study revealed that the activity decreased following the order of $3^{\prime }>4^{\prime }>6^{\prime }$ glycosyl modifications. GNTS that incorporated (d/l)-xylose and l-arabinose at positions $3^{\prime }$ and $4^{\prime }$ were more potent than those bearing other sugars.     

Asymptotic Results for Random Walks in Continuous Time with Alternating Rates

We investigate some large deviation problems for a random walk in continuous time $\{N(t);\,t\ge 0\}$ with spatially inhomogeneous rates of alternating type. We first deal with the large deviation principle for the convergence of $N(t)/t$ to a suitable constant. Then, the case of moderate deviations is also discussed. Motivated by possible applications in chemical physics context, we finally obtain an asymptotic lower bound for level crossing probabilities both in the case of finite and infinite horizon.