Instantons of two-dimensional fermionic effective actions by inverse scattering transformation

Effective actions, containing the logarithm of a functional Dirac determinant, appear in 1/N expansions of fermionic theories (N being the number of flavours). We introduce a method to find symmetric solutions of the corresponding non-linear and non-local saddle-point equations. This method consists in using the scattering data of the rotationally symmetric Dirac equation in two dimensions with the angular mometum as a spectral parameter. We apply the method to fermionic theories with scalar and pseudoscalar quartic couplings. The effective action that generates the 1/N expansion admits a closed form in terms of the scattering data only in the particular case when the model is integrable (Gross-Neveu and Chiral Gross-Neveu model). No instanton solutions are present in these two particular cases. This fact, together with the exact results for theS-matrix and form factors, suggests that the 1/N expansion could be convergent. In the general case, the quantum model has an additional dimensionless parameterg _R·g _R± gives the Chiral Gross-Neveu model. Wheng _R>0, tachyons appear. Forg _R0^–, andg _R–, generically complex-action instantons exists, indicating a possibly Borel-summable 1/N expansion.Laboratoire associé au CNRS LA280     

Deep bandtail states picosecond intensity-dependent carrier dynamics of GaN epilayer under high excitation

Picosecond carrier dynamics of deep bandtail states (3.1 eV) in an unintentionally n-doped GaN epilayer at room temperature under high excitation densities (i.e., N ₀ = 1.0× 10¹⁹– 1.1× 10²⁰ cm^–3) have been investigated with nondegenerate femtosecond pump–probe (267/400 nm) reflectance ( R/R ₀). All R/R ₀ traces possess a 2 ps buildup time that represents an overall time for the initial non-thermal carrier population to relax towards the continuum extremes and then into the probed tail states. We observe a saturation of R/R ₀ initial (first 10 ps) recovery rate _i at a density of 5– 6×10¹⁹ cm^–3 close to the Mott transition threshold obtained from time-integrated PL measurements. Such a saturation phenomenon has been identified as the trap-bottleneck due to the bandtail states and deep traps. As N ₀ is further increased, _i accelerates due to the onset of Auger recombination as the trap-bottleneck becomes effective. The best fit by the Auger model for N ₀ in the range of the mid-10¹⁹–10²⁰ cm^–3 yields an Auger coefficient of C _a 5.0× 10^–30 cm⁶ s^–1.     

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.     

Identification of the Dilute Regime in Particle Sedimentation

We investigate the dynamics of rigid, spherical particles of radius R sinking in a viscous fluid. Both the inertia of the particles and the fluid are neglected. We are interested in a large number N of particles with average distance dR. We investigate in which regime (in terms of N and R/d) the particles do not significantly interact and approximately sink like single particles. We rigorously establish the lower bound for the critical number N_crit of particles. This lower bound agrees with the heuristically expected N_crit in terms of its scaling in R/d. The main difficulty lies in showing that the particles cannot get significantly closer over a relevant time scale. We use the method of reflection for the Stokes operator to bound the strength of the particle interaction.     

Gas‐phase acidity of bis[(perfluoroalkyl)sulfonyl]imides. Effects of the perfluoroalkyl group on the acidity

The gas‐phase acidity (GA) values were determined for a number of perfluoroalkyl‐substituted sulfonylimides by measuring proton‐transfer equilibria using a Fourier transform ion cyclotron resonance (FT‐ICR) mass spectrometer. The GA scale below 286.5 kcal mol^?1 for (CF₃SO₂)₂NH was extended and partially revised. The GA value of (C₄F₉SO₂)₂NH which is currently the strongest acid was revised from 284.1 to 278.6 kcal mol^?1. The effect of fluorine atoms on the acidity of perfluoroalkyl‐substituted sulfonylimides was described with the following model where N_(α), N_(β), N_(γ), and N_(δ) are the numbers of fluorine atoms at α, β, γ, and δ position in R_fSO₂ (R_f = perfluoroalkyl group), respectively. This correlation indicates that the electron‐withdrawing ability of the R_fSO₂ group can be described in terms of the number of fluorine atoms in the perfluoroalkyl group corrected by taking into account their positions. Copyright © 2014 John Wiley & Sons, Ltd.     

Absorption and emission spectroscopic characterisation of F<Subscript>3</Subscript><Superscript>-</Superscript> colour centers in a LiF crystal

For a LiF crystal containing F₃ (R₁, R₂), F₂, F₃ ⁺, F₄ (N₁, N₂), F₃ ^-, and F₂ ^- colour centers the absorption and emission spectroscopic behaviour of the F₃ ^- centers is studied. The absorption cross-section spectrum and the number density of F₃ ^- centers are extracted from saturable absorption and transmission measurements. Additionally fluorescence quantum distribution measurements and fluorescence lifetime measurements are carried out to determine the stimulated emission cross-section spectrum and the fluorescence quantum yield of the F₃ ^- centers. Fluorescence excitation spectroscopy reveals the presence of an absorption band with its absorption peak around 700 nm (called R ₁ band) in addition to the ground-state to first excited-state F₃ ^- center absorption band centered at 800 nm (called R ₂). PACS 61.72.Ji; 78.40.Ha; 78.55.Fv     

CyclicL-operator related with a 3-stateR-matrix

We consider the problem of constructing a cyclicL-operator associated with a 3-stateR-matrix related to theU _q (sl(3)) algebra atq ^N =1. This problem is reduced to the construction of a cyclic (i.e. with no highest weight vector) representation of some twelve generating element algebra, which generalizes theU _q (sl(3)) algebra. We found such representation acting inC ^N C ^N C ^N . The necessary conditions of the existence of the intertwining operator for two representations are also discussed.     

Free-field realization of theWKP(N) algebra

TheW _KP ^(N) algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW _KP ^(N) can also be decomposed toN independent copies ofW _KP ⁽¹⁾ algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW _KP ⁽¹⁾ . In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW _KP ^(N) in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R) _k algebras with levelk = 1. By reductions, we give similar results forW ^(N) andW ₃ ⁽²⁾ algebra.     

第Ⅱ种强度不等的非对称两态叠加多模叠加态光场的任意奇数阶等阶N次方Y压缩

本文利用多模压缩态理论,研究了第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)>_q的任意奇数阶等阶N次方Y压缩特性.结果发现:在压缩阶数N=2p+1的条件下,无论p=2m还是p=2m+1(m=0,1,2,3,…,…),只要构成态|Ψ_Ⅱ^(ab)>_q的两个不同的量子态|{-Z_j^(a)*}>_q与|{-iZ_j^(b)*}>_q的各对应模的强度(即平均光子数)和初始相位都不相等,亦即Rj(a)≠Rj(b)和φj(a)≠φj(b)(j=1,2,3,…,q),并且 R_j^(a)(2p+1)= R_j^(b)(2p+1),则当各对应模的初始相位φ_j^(a)与φ_j^(b)、各对应模的初始相位差(φ_j^(a)-φ_j^(b)),态间的初始相位差(θ_nq^(aR)-θ_nq^(bI))以及光子干涉项的幅度 =R_j^(a)R_j^(b)等分别满足一定的量子化条件时,态|Ψ_Ⅱ^(ab)>_q的第一及第二这两个正交分量总可分别呈现出周期性变化的、任意奇数阶等阶N次方Y压缩效应.这一结果,与现有报道的结果截然不同.     

Angular dependence of the superexchange interaction Fe3+-O2−-Cr3+

The super-exchange interaction parametersI(Fe, Cr) of Fe³⁺ and Cr³⁺ in iron doped rate-earth orthochromitesRCr_0.99Fe_0.01 O₃ (R=La, La_0.5Nd_0.5, Nd, Sm, Gd, Dy, Y, Er, Yb or Lu) have been obtained from⁵⁷Fe magnetic hyperfine structure measurementsvia the Mössbauer effect.The dependence of the experimental valuesI(Fe, Cr) on the Fe–O–Cr average superexchange angle (depending upon the relative size of the rare-earth (RE) ionR ³⁺) is well described by the equationI(d⁵, d ^N ) = _N + _N cos + _N cos² .Within the accessible range of super-exchange angles 142°156°, the Fe³⁺–O^2––Cr³⁺ interaction is negative (antiferromagnetic). However, a theoretical analysis predicts a sign reversal forI(Fe, Cr.) at about 162° and thus ferromagnetic character of the interaction between 162° and 180°.The spin-only super-exchange interaction integrals fore _g andt _2g electrons, separately, are also calculated. Their angular dependence is accounted for by the behaviour of the antiferromagnetic kinetic and ferromagnetic potential exchange which are of different character when passing from 180° to 90° super-exchange geometry. The magnitude and the sign of the spin-only super-exchange integral for an arbitrary 3d cation, pair is predicted.     

Unexpected Features of the Intramolecular Spin Exchange in Imidazoline Nitroxide Biradicals Dissolved in Ionic Liquids

Three imidazoline-type nitroxide biradicals of the similar composition R ₅ ^NO –CH=N–N=CH–R ₅ ^N , B1, R ₅ ^NO –CH=N–N=C(CH₃)–R ₅ ^N , B2, and R ₅ ^N –C(CH₃)=N–N=C(CH₃)–R ₅ ^N , B3, with R ₅ ^N and R ₅ ^NO denoting, respectively, the nitroxide rings 1-oxyl-2,2,5,5-tetramethyl-3-imidazoline and 1-oxyl-2,2,5,5-tetramethyl-3-N–oxide imidazoline, have been studied by X-band electron paramagnetic resonance (EPR) spectroscopy. Variations of the intramolecular electron spin exchange in these biradicals dissolved in ethanol and the room temperature ionic liquid bmimBF₄ were characterized as a function of temperature by means of the analysis of the EPR lines shape. Thermodynamic parameters of the conformational rearrangements in ethanol were calculated. Analyzing the EPR spectra of these biradicals in bmimBF₄, it was revealed that the two-conformational model does not describe their conformational transitions. Moreover, the observed EPR spectra are not central symmetric especially at low temperatures that cannot be described and explained in the framework of the current theory of the intramolecular spin exchange. Probable reasons of this “strange” behavior are discussed.     

On the number of invariant measures for higher-dimensional chaotic transformations

LetS be a bounded region inR ^N and letP={S _l } _i=1 ^m be a partition ofS into a finite number of closed subsets having piecewiseC ² boundaries of finite (N–1)-dimensional measure. Let :SS be piecewiseC ² onP and expanding in the sense that there exists 0<<1 such that for anyi=1,2,...,m, DT _i ^–1<, whereDT _i ^–1 is the derivative matrix ofT _i ^–1 and · is the Euclidean matrix norm. We prove that for some classes of such mappings, for example, Jabtonski transformations or convexity-preserving transformations, the number of crossing points constitutes a bound for the number of ergodic absolutely continuous -invariant measures. We give examples showing that in general the simple bound of one-dimensional dynamics cannot be generalized to higher dimensions. In fact, we show that it is possible to construct piecewise expandingC ² transformations on a fixed partition with a finite number of elements but which have an arbitrarily large number of ergodic, absolutely continuous invariant measures.     

Conservation of Energy,Entropy Identity,and Local Stability for the Spatially Homogeneous Boltzmann Equation

For nonsoft potential collision kernels with angular cutoff, we prove that under the initial condition f ₀(v)(1+|v|²+|logf ₀(v)|)L ¹(R ³), the classical formal entropy identity holds for all nonnegative solutions of the spatially homogeneous Boltzmann equation in the class L ([0, ); L ¹ ₂(R ³))C ¹([0, ); L ¹(R ³)) [where L ¹ _s (R ³)={ff(v)(1+|v|²) ^s/2L ¹(R ³)}], and in this class, the nonincrease of energy always implies the conservation of energy and therefore the solutions obtained all conserve energy. Moreover, for hard potentials and the hard-sphere model, a local stability result for conservative solutions (i.e., satisfying the conservation of mass, momentum, and energy) is obtained. As an application of the local stability, a sufficient and necessary condition on the initial data f ₀ such that the conservative solutions f belong to L ¹ _loc([0, ); L ¹ ₂₊ (R ³)) is also given.     

Photoproduction of Boson Pairs in a Radiation-Dominated Universe. II

The average number of pairs of scalar massive particles produced by a decaying photon in a radiation-dominated universe is calculated. The dependence of the expression obtained on the energy of the initial photon is investigated. Numerical estimates are found for the formative time t ₀ of the processes of decay of photons in an early universe and for the total number N ^(±) _{out pair} of photoproduced scalar pairs. The estimates are: t ₀ 3 min and N ^(±) _{out pair} 10³¹·N ^(±) ₀(0), where N ^(±) ₀(0) is the total number of pairs produced from the vacuum of a free quantized field.     

Unified and generalized Fresnel numbers

The concept of Fresnel number is discussed and expressions are derived for misaligned optical systems. For the case of perfectly aligned optical elements, the usual number,N, based on a Fresnel zone concept is found to be given byN = (a ²/)(D ₁/B ₁ +A ₂/B ₂), whereB ₁,D ₁ andB ₂,A ₂ are the transfer matrix elements of the optical systems before and after a circular aperture of radiusa respectively. A modified definition of the Fresnel number is proposed for Gaussian beam propagation. This parameterN _G, is related to the complex beam parameter and may be represented by the angle = tan^–1 N _G, found in the familiar Collins chart and its dual representation. A general relation for the transformation of this Fresnel number is found. The expressions for Gaussian beam transformation are thus simplified, since the waist-waist transform is given byN _G1 =N _G2 = 0. Finally, these two kinds of Fresnel numbers are written as tensors when applied to cases involving elliptical apertures, astigmatic beams and nonsymmetrical systems.     

A theory of generally invariant lagrangians for the metric fields. I

The second-order generally invariant Lagrangians for the metric fields are studied within the framework of the Ehresmann theory of jets. Such a Lagrangian is a function on an appropriate fiber bundle whose structure group is the groupL _n ³ of invertible 3-jets with source and target at the origin 0 of the real,n-dimensional Euclidean spaceR ⁿ, and whose type fiber is the manifold T_n ²(R^n* R ^n*) of 2-jets with source at 0 R ⁿ and target in the symmetric tensor productR ^n* R^n*. Explicit formulas for the action ofL _n ³ onT _n ²(R^n* R ^n*) are considered, and a complete system of differential identities for the generally invariant Lagrangians is obtained.     

Ultrasound promoted the synthesis of N-propargylic β-enaminones

The synthesis of 14 novel N-propargylic β-enaminones from the reaction of β-alkoxy vinyltrihalomethyl[carboxyethyl] ketones [R³C(O)CHC(R¹)OMe, where R³ = CF₃, CCl₃, CO₂Et and R¹ = Me, Et, Pr, Bu, i-Pent, CH₂CH₂CO₂Me] with propargyl amines [R²NHCH₂CCH, where R² = Pr, PhCH₂] is reported. Yields, solvents and reaction times needed for reaction completion, by microwave irradiation (MW), conventional thermal heating (TH) and under ultrasound irradiation (US) are compared. The best results were obtained under US irradiation in good to excellent yields (70-93%).     

Detection of heavy Majorana neutrinos and right-handed bosons

The SU _c (3) ⊗ SU _L (2) ⊗ SU _R (2) ⊗ U(1) left-right (LR) symmetric model explains the origin of the parity violation in weak interactions and predicts the existence of additional gauge bosons W _R and Z′. In addition, heavy right-handed Majorana neutrino states N arise naturally within the LR symmetric model. The states N could be partners of light neutrino states, related to their nonzero masses through the seesaw mechanism. This makes the searches for W _R , Z′, and N interesting and important. In the framework of the minimal LR model, we study the possibility to observe signals from N and W _R production in pp collisions after three years of running at low LHC luminosity. We show that their decay signals can be identified with a small background, especially in the case of same-sign leptons in the final state. For the integral LHC luminosity of L _t = 30 fb⁻¹, the 5σ discovery of W _R boson and heavy Majorana neutrinos N _e with masses up to 4 TeV and up to 2.4 TeV, respectively, is found to be possible. The text was submitted by the authors in English.     

Observable N \overline N oscillation, high-scale see-saw and origin of matteroscillation, high-scale see-saw and origin of matter

See-saw mechanism has been a dominant paradigm in the discussion of neutrino masses. We discuss how this idea can be tested via a baryon number violating process such as N- oscillation. Since the expected see-saw scale is high and the N- amplitude goes like M _R ⁻⁵ , one might think that this process is not observable in realistic see-saw models for neutrino masses. In this talk I show that in supersymmetric models, the above conclusion is circumvented leading to an enhanced and observable rate for N oscillation. I also discuss a new mechanism for baryogenesis in generic models for neutron-anti-neutron oscillation.     

Finite- N effects for ideal polymer chains near a flat impenetrable wall

This paper addresses the statistical mechanics of ideal polymer chains next to a hard wall. The principal quantity of interest, from which all monomer densities can be calculated, is the partition function, G _N(z) , for a chain of N discrete monomers with one end fixed a distance z from the wall. It is well accepted that in the limit of infinite N , G _N(z) satisfies the diffusion equation with the Dirichlet boundary condition, G _N(0) = 0 , unless the wall possesses a sufficient attraction, in which case the Robin boundary condition, G _N(0) = - G _N ^′(0) , applies with a positive coefficient, . Here we investigate the leading N ^-1/2 correction, G _N(z) . Prior to the adsorption threshold, G _N(z) is found to involve two distinct parts: a Gaussian correction (for z aN ^1/2 with a model-dependent amplitude, A , and a proximal-layer correction (for z a described by a model-dependent function, B(z) .