RenormalizedG-convolution ofN-point functions in quantum field theory: Convergence in the Euclidean case I

The notion of Feynman amplitude associated with a graphG in perturbative quantum field theory admits a generalized version in which each vertexv ofG is associated with ageneral (non-perturbative)n _v-point functionH ⁿ _v,n _v denoting the number of lines which are incident tov inG. In the case where no ultraviolet divergence occurs, this has been performed directly in complex momentum space through Bros-Lassalle'sG-convolution procedure.In the present work we propose a generalization ofG-convolution which includes the case when the functionsH ⁿ _v arenot integrable at infinity but belong to a suitable class of slowly increasing functions. A finite part of theG-convolution integral is then defined through an algorithm which closely follows Zimmermann's renormalization scheme. In this work, we only treat the case of Euclideanr-momentum configurations.The first part which is presented here contains together with a general introduction, the necessary mathematical material of this work, i.e., Sect. 1 and appendices A and B.The second part, which will be published in a further issue, will contain the Sects. 2, 3 and 4 which are devoted to the statement and to the proof of the main result, i.e., the convergence of the renormalizedG-convolution product.The table of references will be given in both parts.     

Structural distortions in families of perovskite-like crystals

The crystallographic and group theoretical analysis of the structural phase transitions in perovskite and perovskite-like crystals is reviewed. We include ABX₃ perovskites and their relative crystals of ReO₃ type (G₀ = O¹ _h), elpasolites, cryolites and their relatives (G₀ = O⁵ _h), layered crystals of T1AlF₄ series (G₀ = D¹ _4h), Aurivillius and Ruddlesden-Popper series (Go = D¹⁷ _4h). The structures in their initial phase G₀ often contain n layers (n = 1,2,3) of vertex linked octahedra. The distorted phases produced by one kind of tilt and by superposition of tilts in the slabs are enumerated. Most of the tilts correspond to symmetry changes, which can be associated to definite librational lattice modes irreducible representations of the G₀ group. The softening of modes associated to the PT has been found experimentally in many perovskites, elpasolites and layered crystals with n = 1. In contrast, no such soft modes have been found yet for even-layered (n = 2) crystals. Examples of successive phase transitions due to the superposition of tilts in these types of crystals have been collected.     

The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single-particle levels of a potential well (mean field) and interacting through a pairing force in the framework of the Richardson equations. The associated solutions are classified in terms of a number v_l, which reduces to the seniority v in the limit of a large pairing strength G and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the G limit. We express analytically, through the moments of the single-particle levels distribution, the collective mode energy and the two critical values G_cr⁺ and G_cr^- of the coupling which can exist on a single-particle level with no pair degeneracy. Notably G_cr⁺ and G_cr^-, when the number of single particle levels goes to infinity, merge into the critical coupling of a one-pair system G_cr (when it exists), which is not envisioned by the Richardson theory. In correspondence of G_cr, the system undergoes a transition from a mean-field- to a pairing-dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes versus G finding out that the former, for G > G_cr^-, come close to the BCS predictions, whereas the latter display a divergence at G_cr, signaling the onset of a long-range off-diagonal order in the system.     

Symmetry-adapted linear combinations for the eigenvalues and eigenvectors of reciprocal graphs

ABSTRACT

Three classes of reciprocal graphs, viz. monocycle (G^C_n), linear chain (G^L_n) and star (G^K_n) with reciprocal pairs of eigenvalues (λ, 1/λ), are well known. Reciprocal graphs of monocycle (G^C_n) and linear chain (G^L_n) are obtained by putting a pendant vertex to each vertex of simple monocycle (C_n) and simple linear chain (L_n), respectively. A star graph of such kind is obtained by attaching a pendant vertex to the central vertex and to each of the (n ? 1) peripheral vertices of the star graph (K_{1, (n?1)}). An n-fold rotational axis of symmetry for G^C_n and (n ? 1)-fold rotational axis of symmetry for G^K_n have been exploited for obtaining their respective condensed graphs. The condensed graph for G^L_n has been generated from that of G^C_n incorporating proper boundary conditions. Condensed graphs are lower dimensional graphs and are capable of keeping all eigeninformation in condensed form. Thus the eigensolutions (i.e. the eigenvalues and the eigenvectors) in analytical forms for such graphs are obtained by solving 2 × 2 or 4 × 4 determinants that in turn result in the charge densities and bond orders of the corresponding molecules in analytical forms. Some mathematical properties of the eigenvalues of such graphs have also been explored.     

Degradation of the transconductance of gate-modulated generation current in nMOSFET

The degradation of transconductance (G) of gate-modulated generation current I_GD in LDD nMOSFET is investigated. The G curve shifts rightward under the single electron-injection-stress (EIS). The trapped electrons located in the gate oxide over the LDD region (Q_L) makes the effective drain voltage minish. Accordingly, the G peak in depletion (G_MD) and that in weak inversion (G_MW) decrease. It is found that Δ G_MD and Δ G_MW each have a linear relationship with the n-th power of stress time (tⁿ) in dual-log coordinate: Δ G_MD ∝ tⁿ, Δ G_MD ∝ tⁿ (n=0.25). During the alternate stress, the injected holes neutralize Q_L induced by the previous EIS. This neutralization makes the effective V_D restore to the initial value and then the I_GD peak recovers completely. Yet the threshold voltage recovery is incomplete due to the trapped electron located over the channel (Q_C). As a result, G_MW only recovers to the circa 50% of the initial value after the hole-injection-stress (HIS). Instead, G_MD is almost recovered. The relevant mechanisms are given in detail.     

High-resolution infrared spectrum of acetylene in the region of the bending fundamental v 5

The infrared spectrum of C₂H₂ in the region of the bending fundamental v ₅ has been studied at a resolution of about 0·015 cm^-1. The molecular constants G ₀(v ₅=1) = 730·3341 (1) cm^-1 and B ₀ = 1·176641 (2) cm^-1 have been derived. In addition to the fundamental, all the hot bands starting from the levels v ₄ and v ₅ have been investigated. The vibrational, vibration-rotation coupling and centrifugal constants for the excited vibrational states v ₅ = 2 and v ₄ = v ₅ = 1 have been derived using the vibration-rotation energy matrix.     

Uniqueness of the standard model neutral current predictions

In view of an excellent agreement between the recently determinedv _μ-hadron couplings and predictions of the standard model, the basic question discussed is how far its neutral current predictions can be mimiced in going either from the isodoublet to an isotriplet (or an even higher isospin) left-handed representation or from SU _L (2) × U(1) toG × U(1), whereG is a simple group of rank two. This question is addressed with reference to a sufficiently broad class of schemes. Their most distinctive properties are: in the higher isospin scheme, neutrino couplings are precisely in the form obtainable with standard l.h. representation; the higher g.g. scheme isL+R type in which, to each light fermion of evenRU parity, a superheavy fermion of the same charge and oddRU parity is associated, parity conservation forbidding their mixing. Reasons for excluding theL-type andG ₂ higher g.g. schemes are given. Their neutral current predictions are compared with those of the standard model. A higher isospin representation can mimic the predictions of the standard model in inclusive and semi-inclusivev _μ-hadron reactions but is conclusively discriminated from the isodoublet representation by elasticv _μ ⁽⁻ p scattering. TheG × U(1) scheme can mimic standard model neutrino sector but is conclusively discriminated from minimal scheme by parity violating effects.     

Relationship between torsional frequency and potential barrier height forAB n type molecular system

A relationship between the torsional frequency (v ₁₀) and the potential barrier (V _n) has been determined forAB _n type molecular system havingn-fold symmetry axis. It is found thatv ₁₀ varies prominently asV _n ^1/2 ,V _n andV _n ² in certain ranges. TheV _n value computed fromv ₁₀ andI* _r has been compared with that obtained from other experimental data for someAB _n units in different molecular-crystalline systems. Although there is in general a good agreement, in some cases the values differ significantly, perhaps due to the erroneous assignment of torsional mode and/or the large errors in theV _n value obtained from other experimental data.     

Effect of carbon ion bombardment and surface oxidation on the twinning rate of single-crystal bismuth

A study is made of the change in the dependences of the normal velocity of twinning boundaries on the magnitude of shear stresses in the twinning plane v _n =v _n (τ) in bismuth crystals owing to ion-cluster doping and oxidation of the irradiated surface. Irradiation was by 25 keV carbonions at a dose of 10¹⁷ ion/cm². Twinning of the crystals took place under pulsed loading conditions with pulse durations of 10⁻⁵−10⁻⁴ s and stress amplitudes of (0.2–2.0)×10³ g/mm³. Carbon ion bombardment of single-crystal bismuth causes a shift in the v _n =v _n (τ) curve toward lower stresses. An oxide film slows down the motion of twinning dislocations. Zh. Tekh. Fiz. 69, 130–131 (May 1999)     

Structural and electronic properties of silver-doped gold clusters Au n Ag v (2 ≤ n ≤ 10; v = 0, ±1): comparison with pure gold clusters

The structural and electronic properties of silver-doped gold clusters Au _n Ag ^v (2?≤?n?≤?10; v?=?0,?±1) have been systematically investigated using density functional theory. The results show that the ground state optimal structures of the cationic and neutral clusters are found to be planar up to n?=?3 and 9, respectively. However, for the anionic clusters, no three-dimensional lowest-energy structures are obtained according to DFT calculations. The calculated binding energy and dissociation energy as a function of cluster size exhibit odd–even alternations. The natural population analysis indicates that in Au _n Ag ^v clusters charges transfer from the Ag atom to the Au frames. The trends for the vertical detachment energies, adiabatic electron affinities, adiabatic ionization potentials, and chemical hardness of Au _n Ag ^v clusters, as the cluster size increases, are studied in detail and compared with the available experimental data.     

The static potential in quantum chromodynamics

The effective interaction between a static quark-antiquark pair is computed within the framework of 〈G_μv^aG_a^μv〉 ≠ 0. Due to the static approximation the interaction takes the form of a potential, which is in striking agreement with phenomenological potentials.     

中低速C3+与He，Ne，Ar原子相互作用过程中单电子转移绝对截面的测量

实验测量了1.7v₀—4.2v₀(v₀为玻尔速度,v₀=2.19×10⁸cm/s)的C³⁺与He,Ne,Ar原子碰撞过程中单电子转移绝对截面.将实验结果与多体经典轨道蒙特卡罗模拟计算结果做了比较,发现测量结果与多体经典轨道蒙特卡罗模拟计算结果在趋势上相符.当入射离子速度在1.7v₀—2 关键词： 离子-原子碰撞 单电子转移 绝对截面     

A regular potential which is nowhere in L 1

A nonnegative potential V: ℝ^v→ℝ is constructed for which V ∉ L _q (G) for any nonempty open G⊂→^v, q>0, and for which nevertheless W _inf2 ^sup1 ∩ Q(V) is dense in W _inf2 ^sup1 , i.e., is a form core for −1/2Δ in L ₂.     

Extraction of G<Subscript>M</Subscript><Superscript>n</Superscript> from inclusive electron scattering on D, <Superscript>4</Superscript>He

We use the relation between Structure Functions (SFs) of nuclei A and nucleons N in order to fomulate a criterion which isolates the QE part out of the total inclusive cross-section. From data points around the QEP we extract the reduced neutron magnetic form factor 〈α _n = G _M ⁿ/μ _n G _d〉. The latter shows an unexpected decrease up to Q ² = 10GeV^2, the largest measured.     

The configuration of the benzylradical

4. Conclusions

Provided reliable values for the inertia factors, A_j , are available, the Newton-Raphson approach to the analysis of (v(T)_n.q.r.)_P provides a direct convergent method of deriving the Einstein temperatures and, in theory, the α _j and n_j terms associated with the volume dependence of the ?_j modes.

A preliminary study of v(T)_P for [P³⁵Cl₄]⁺[FeCl₄]^- provides evidence of a torsional mode, at 40·4 cm^-1, which modulates the electric field gradient.     

G v,CKM unitarity,neutron decay; WR?

Superallowed Fermi beta-decay is analyzed in the light of new experimental data, new methodology and new treatment of the radiative and charge-dependent corrections. The following values are recommended:G _v /(c) ³=(1.13769±0.00091)×10^–5 GeV^–2;G _v ^* /(c) ³ =(1.15128±0.00084) × 10^–5GeV^–2 whereG _v is purged of radiative corrections suitably for combining withG to gain: ¦V _ud ¦=0.97539±0.00080 which leads to:¦V _ud ¦ ² +¦V _us ¦ ² +¦V _ub ¦²=1.0000+0.0017 and whereG _V ^* is the operational constant, incorporating the inner radiative correction, suitable for use in ordinary nuclear physics. It is noted that present results on the beta-decay of the neutron, when confronted by the above values, are inconclusive as to possible conflict with the minimal standard model and that judgement as to, for example, the intervention of a right-handed sector, should be suspended. The valueG _A ^* =1.2657±0.0030 is also recommended.     

Invasion Percolation and the Incipient Infinite Cluster in 2D

 We establish two links between two-dimensional invasion percolation and Kesten's incipient infinite cluster (IIC). We first prove that the k ^th moment of the number of invaded sites within the box [−n, n]×[−n, n] is of order (n ²π _n ) ^k , for k≥1, where π _n is the probability that the origin in critical percolation is connected to the boundary of a box of radius n. This improves a result of Y. Zhang. We show that the size of the invaded region, when scaled by n ²π _n , is tight. Secondly, we prove that the invasion cluster looks asymptotically like the IIC, when viewed from an invaded site v, in the limit |v|→∞. We also establish this when an invaded site v is chosen at random from a box of radius n, and n→∞. Received: 3 December 2000 / Accepted: 3 December 2002 Published online: 18 February 2003 RID="⋆" ID="⋆" Present address: CWI, PNA 3, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. E-mail:jarai@cwi.nl Communicated by M. Aizenman     

Das Neutralgasprofil und die Elektronentemperatur in der Freifallsäule bei hohem Ionisationsgrad

The neutral gas flux from the wall into the column - connected with the ion flux to the wall - and the anisotropy of the velocity distribution of the neutral gas are included into the theory of the steady-state positive column. d/l_n and v_n0/v₀ occur as characteristic parameters. d denotes the radius of the column, l_n the mean free path of the neutral atoms for ionization, v_n0 the mean velocity of the neutral atoms re-emitted from the wall, v₀ = (2kT_e/M)^1/2, M the ion mass, T_e the electron temperature. On the axis the neutral gas density N_n is decreasing, if d/l_n is rising. At the wall N_n is increasing for v_n0 ? v₀, but it is almost constant or decreasing for v_n0 ? v₀ at the same time. In the plasma the total number of the atoms and the ions is taken as constant. In the case of small v_n0 the degree of ionization is high only for d ? l_n. However, it is already high for d ≈ l_n in the case of high v_n0. Therefore, the radial profiles of the neutral gas densities of different gases in a column can differ from each other. Almost full ionization can be reached near the axis. These results hold, too, if the initial velocity of the ions and a magnetic field are taken into account. d/l_n, the degree of ionization, and the electron temperature are given as functions of the electric power input and of the total number of the neutrals and the ions. The velocities of the re-emitted atoms depend on the accomodation coefficient of the ions recombining at the wall. With rising d/l_n an increasing number of the neutral atoms is re-emitted with superthermal velocities and the total number of the neutrals and the ions can be decreased. The anisotropy of the velocity distribution of the neutral atoms and the ions must be taken into account for the interpretations of spectroscopical measurements.     

中速C3+与Ne原子靶相互作用过程中单电子转移绝对截面的测量

实验测量了2.2v₀—4.2v₀(v₀为玻尔速度,v₀=2.19×10⁸cm/s)的C³⁺与Ne原子碰撞过程中单电子转移绝对截面.将实验结果与多体经典轨道蒙特卡罗模拟计算结果进行了比较.用电离能的变化、屏蔽效应、动态关联对实验和理论计算结果间的数值差异做了分析.总体上,实验结果与多体经典轨道蒙特卡罗方法计算结果在趋势上相 关键词： 离子-原子碰撞 单电子转移 绝对截面