Relativistic field-theoretical equations for the three-body multichannel πN and γN scattering reactions and propagator of the Δ-resonance

A new form of the relativistic three-body equations for the coupled πN and γN scattering reactions with three particle final states ππN and γπN is suggested. These equations are derived in the framework of the time-ordered three dimensional field theory. The solutions of the considered equations satisfy the unitarity condition and are exactly gauge invariant. The form of these three-body equations is does not depend on the choice of the model of Lagrangian and is also the same for the formulations with and without quark degrees of freedom.

The effective potentials of the suggested equations are defined by the vertex functions with two on-mass shell particles. It is emphasized that these input vertex functions can be constructed from experimental data. Special attention is given to the construction of the propagator of the Δ-resonance in the framework of the separable πN potential model. The strong dependence of the multichannel πN and γN cross sections on the form of the Δ-resonance propagator[2] is discussed.

The used formulation of the relativistic three-dimensional and three-body equations allows us to overcome a number of approximations which are usually used by practical calculations of the πN and γN scattering reactions.     

表面不平整对半无限超晶格表面电磁耦子的影响

本文讨论表面不平整对半无限超晶格表面电磁耦子(polariton)的影响。文中推导了平整表面半无限超晶格情形,Maxwell方程的格林函数。由此导出表面电磁耦子的色散关系。主要结论是:在表面不平整情形,将出现新的模式——表面型TE模表面电磁耦子,可资实验检验。 关键词：     

Quenched master field equations for unitary matrix models

We derive the quenched master field equations for constrained systems such as the O(N) non-linear sigma model, U(N)×U(N) chiral models, and U(N) lattice gauge theory. The master equations are algebraic, and involve quenching in both the space and “fifth” (Langevin) time directions. The quenched master field for the O(N) nonlinear sigma model is found exactly. The 0-dimensional unitary matrix model is solved perturbatively, and we recover the Gross-Witten result. The master equation for the U(N)×U(N) chiral model is set up for non-perturbative approximation methods, and some qualitative results are obtained.     

Local modes in structures with multicomponent plasma

The dispersion relations of a surface plasmon are determined for the case where two- and three-dimensional plasmas coexist, which is typical of topological insulators. Local plasma modes originating from two- and one-dimensional defects in multilayer superlattices and quantum-wire superlattices are investigated.     

Algorithms for flattened Gaussian beams passing through apertured and unapertured paraxial ABCD optical systems

The propagation property of flattened Gaussian beams (FGBs) is studied based on the Collins formula, and analytical propagation equations for FGBs with and without an aperture are derived. It is shown that the closed-form expressions for the FGB of order N passing through paraxial ABCD optical systems without an aperture can be written as the combinations of Confluent Hyper-geometric Functions, and that the analytical equations for the FGB of order N passing through apertured paraxial ABCD optical systems may involve Error Functions. The proposed algorithms for the considered beams can save computing time, provide intuitive physical insights, and help to design optical systems. Our results are confirmed and illustrated with numerical examples.     

Spontaneous localization of bulk fields: the six-dimensional case

We study N=2 supersymmetric gauge theories with d=6 bulk and d=4 brane fields charged under a U(1) gauge symmetry. Radiatively induced Fayet–Iliopoulos terms lead to an instability of the bulk fields. We compute the profile of the bulk zero modes and observe the phenomenon of spontaneous localization towards the position of the branes. While this mechanism is quite similar to the d=5 case, the mass spectrum of the excited Kaluza–Klein modes shows a crucial difference.     

Infinite-dimensional gauge groups and special nonlinear gravitons

A gauge theory in flat space—time, in which the gauge algebra is the (infinite-dimensional) algebra of vector fields on a surface, determines a curved space—time metric. This note deals with some completely integrable examples, concentrating on the N → ∞ limit of the Euler—Arnol'd equations [geodesics on SO(N)]. In this case, the metric turns out to be flat, which points the way to a coordinate transformation that solves the original equations.     

Long-wavelength nonpolar phonons in semiconductor heterostructures

Employing a phenomenological long-wavelength approach recently developed, both acoustic and optical phonons in nonpolar heterostructures are studied. Phonon modes in an arbitrary direction can be calculated without additional effort respect to high symmetry directions. A simple analytical expression for the dispersion relation in superlattices guides the physical discussion. We apply this to the calculation of phonon modes in unstrained short period isotopic Ge superlattices, in quantum wells and in strained short period Si/Ge superlattices. We find very good agreement with the results of other, more elaborated and costly calculations.Received: 21 July 2004, Published online: 5 November 2004PACS: 63.20.Dj Phonon states and bands, normal modes, and phonon dispersion - 63.22. + m Phonons or vibrational states in low-dimensional structures and nanoscale materials - 68.65.Cd Superlattices     

Acoustic phonons localized at an interface between superlattice and liquid

The vibrational modes localized at a superlattice–liquid interface are studied theoretically. We calculated the phonon transmission rate and found the peculiar peak due to the interface-localized mode. The magnitude of this peak is governed by the number of constituent bilayers (N) of superlattice. We derived the equation determining N=N_max for which the transmission rate takes the maximum value for a given combination of the superlattice and liquid. When N=N_max, the interface-localized mode has the same feature inside the superlattice as the surface-localized mode generated in the semi-infinite superlattice.     

A new method in the theory of many-body scattering

New coupled equations for the transition (T) and reactance (K) operators for N-channel, many-body, rearrangement scattering are derived. The key to the new method is the channel coupling array W, which links the various rearrangement channels together. By specializing W to the class of channel permuting arrays, it is shown that the (N−1)st iterate of the kernel of the coupled equations is connected.     

Anisotropic plasmon dispersion and damping in multilayer 8-Pmmn borophene structures

We investigate the collective plasma oscillations theoretically in multilayer 8-Pmmn borophene structures, where the tilted Dirac electrons in spatially separated layers are coupled via the Coulomb interaction. We calculate the energy dispersions and Landau dampings of the multilayer plasmon excitations as a function of the total number of layers, the interlayer separation, and the different orientations. Like multilayer graphene, the plasmon spectrum in multilayer borophene consists of one in-phase optical mode and N - 1 out-of-phase acoustical modes. We show that the plasmon modes possess kinks at the boundary of the interband single-particle continuum and the apparent anisotropic behavior. All the plasmon modes approach the same dispersion at a sufficiently large interlayer spacing in the short-wavelength limit. Especially along specific orientations, the optical mode could touch an energy maximum in the nondamping region, which shows non-monotonous behavior. Our work provides an understanding of the multilayer borophene plasmon and may pave the way for multilayer borophene-based plasmonic devices.     

Non-perturbative effects in two-dimensional lattice O(N) models

Non-abelian analogues of Kosterlitz-Thouless vortices may have important effects in two-dimensional lattice spin systems with O(N) symmetries. Renormalization group equations which include these effects are developed in two ways. The first set of equations extends the renormalization group equations of Kosterlitz to O(N) spin systems, in a form suggested by Cardy and Hamber. The second is derived from a Villain-type O(N) model using Migdal's recursion relations. Using these equations, the part played by topological excitations in the crossover from weak to strong coupling behavior is studied. Another effect which influences crossover behavior is also discussed: irrelevant operators which occur naturally in lattice theories can make important contributions to the renormalization group flow in the crossover region. When combined with conventional perturbative results, these two effects may explain the observed crossover behavior of these models.     

The bose form of two-dimensional quantum chromodynamics

By means of a special choice of gauge QCD₂ [SU(N)] with one flavor of quarks is recast into the Bose form. Weak (g m) and strong (gm) coupling regimes are studied. The former is shown to be the SU(N)-symmetric confining phase in which bound states possess stringlike configurations with strings being represented by electric vortex lines; the ordinary mesons and baryons appear as longitudinal modes of electric strings. The strong coupling regime describes the Higgs phase with the residual symmetry [U(1)]^N−1 S_N where the left and right factors are the maximal abelian subgroup of SU(N) and the permutation group of N quarks, respectively; the particle spectrum consists of S_N multiplets and the [Uw(1)]^N−1 charges are trapped.     

Instantons and the chiral phase transition

We examine the role of instantons in the zero-temperature chiral phase transition in an SU(N) gauge theory. For a range of N_f (the number of fermion flavors) depending on N, the theory exhibits an infrared fixed point at coupling _*. As N_f decreases, _* increases, and it eventually exceeds a critical value sufficient to trigger chiral symmetry breaking. For the case N = 2, we estimate the critical values of N_f and _* due to instantons by numerically solving a gap equation with an instanton-generated kernel. We find instanton effects of strength comparable to that of gluon exchange.     

Self-dual supergravity from N = 2 strings

A new heterotic N = 2 string with manifest target space supersymmetry is constructed by combining a conventional N = 2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma mode] is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in t', all in superspace. The resulting field equations describe N = 1 self-dual supergravity.     

PPV中极化子动力学方程的龙格-库塔求解

构造求解-阶微分方程组初值问题的八阶龙格-库塔递推公式,结合描述有机分子运动的-维紧束缚模型,研究PPV原子链中极化子的形成及运动.对碳原子数N=160的PPV原子链,由可控步长八阶龙格-库塔公式求解2N(2N+1)=102720个方程组成的方程组,用Fortran语言编程计算,得到稳定的极化子结构和运动图像;在场强E=1×105V·cm^-1的电场作用下,极化子沿分子链的运动速率约为0.2635Å·fs^-1.计算结果表明,八阶龙格-库塔方程可以有效地用于有机分子链中载流子运动的模拟.     

Determining finite volume elements for the 2D Navier-Stokes equations

We consider the 2D Navier-Stokes equations on a square with periodic boundary conditions. Dividing the square into N equal subsquares, we show that if the asymptotic behavior of the average of solutions on these subsquares (finite volume elements) is known, then the large time behavior of the solution itself is completely determined, provided N is large enough. We also establish a rigorous upper bound for N needed to determine the solutions to the Navier-Stokes equation in terms of the physical parameters of the problem.     

Plasmon modes of a superlattice — Classical vs quantum limits

The collective plasmon excitations of a superlattice are investigated in both the classical and quantum limits. Using a model that is applicable to superlattices whose constituent layers are either semiconductor- semiconductor, semiconductor-metal, or metal-metal, we show that the surface plasmon interface modes of each layer (slab) couple via the long range Coulomb interaction into two bands of plasmons with dispersion along the superlattice axis. Results for plasmon dispersion are presented for the classical limit (de Broglie wavelength less than the layer width) where the response is treated via a solution of Maxwell's equations using the bulk 3-D dielectric constant to describe each intervening layer. These results are compared to the plasmon dispersion in the quantum regime where the wave-vector frequency dependent dielectric constant of the superlattice is calculated taking into account quantization effects (subband structure). The relationship between the modes in both limits is derived.     

Renormalization of N = 2, 4 Yang-Mills theories with soft breaking of an extended supersymmetry by N = 1 mass term

N = 2, 4 Yang-Mills theories with soft breaking of an extended supersymmetry by mass terms are considered. It is proved that for N = 4 there are no ultraviolet divergences in the mass renormalization constants to all orders of perturbation theory. For N = 2 our two-loop calculations show that the charge and mass renormalization constants contain only one-loop divergences and are the same in this order. It is shown by direct calculation that mass terms can acquire finite quantum corrections starting from the two-loop approximation. The renormalization scheme dependence of N = 4 renormalization group functions is investigated. We have found that unlike renormalization schemes with minimal subtractions of divergences other renormalization schemes give a nonzero β-function. At nonzero masses the β-function in MOM schemes is not zero even at the one-loop level. In the massless case β≠0 beginning from the two-loop approximation.     

Branched polymers from a double-scaling limit of matrix models

Multicritical potentials and correlation functions are given for models of rectangular M × N matrices, in the limit that N goes to infinity. These models are soluble without using orthogonal polynomials, and describe filamentary random surfaces, or, equivalently, a phase of branched polymers. It is shown that the equations describing multicritical behaviour are obtained from the hierarchy of flows that preserve Burgers' equation. Instanton solutions are studied - they imply that only the k = 2 model is unitary, and that the coefficients (for arbitrary k) of g_st^l is the perturbative expansion of the specific heat grow as l!.