Solving the constrained modified KP hierarchy by gauge transformations

In this paper, we mainly investigate two kinds of gauge transformations for the constrained modified KP hierarchy in Kupershmidt-Kiso version. The corresponding gauge transformations are required to keep not only the Lax equation but also the Lax operator. For this, by selecting the special generating eigenfunction and adjoint eigenfunction, the elementary gauge transformation operators of modified KP hierarchy T_D(Φ) = (Φ^?1)^?_x¹? Φ^?1 and T_I (Ψ) = Ψ^?1? ^?1Ψ_x, become the ones in the constrained case. Finally, the corresponding successive applications of T_D and T_I on the eigenfunction Φ and the adjoint eigenfunction Ψ are discussed.     

Higher order field equations II; Limit properties of green's functions

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions G^M_R(x) and G^M_A(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for |M| → ∞ the Green's functions G^M_R(x) and G^M_A(x) approach the Green's functions Δ_R(x) and Δ_A(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of G^M_A(x) and G^M_A(x) is the same as of Δ_R(x) and Δ_A(x) - and also the same as for D_R(x) and D_A(x) for t→ ± ∞, where D_R and D_A are the Green n's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense.     

拍波激光加速器中的频率匹配

本文从广义协变的运动方程和麦克斯韦方程出发,导出了电子等离子体波各量的解析表达式。指出△ω=2ω_p的等离子体波是完全简谐的。完全共振的条件由△ω=2ω_(p0)[1+(e²(A₂⁽⁽¹⁾²⁾+(A₂^((2)2))/(2m²c⁴)+(3e²A₂⁽¹⁾A₂⁽²⁾)/(m²c⁴)]^-1/2 给出。 关键词：     

D<Subscript>sJ</Subscript>(2860) and D<Subscript>sJ</Subscript>(2715)

Recently the Babar Collaboration reported a new cs̄ state, D_sJ(2860), and the Belle Collaboration observed D_sJ(2715). We investigate the strong decays of the excited cs̄ states using the ³ P ₀ model. After comparing the theoretical decay widths and decay patterns with the available experimental data, we are inclined to conclude that: (1) D_sJ(2715) is probably the 1^-(1³ D ₁) cs̄ state, although the 1^-(2³ S ₁) assignment is not completely excluded; (2) D_sJ(2860) seems unlikely to be the 1^-(2³ S ₁) and 1^-(1³ D ₁) candidate; (3) to consider D_sJ(2860) either as a 0⁺(2³ P ₀) or as a 3^-(1³ D ₃) cs̄ state is consistent with the experimental data; (4) the experimental search of D_sJ(2860) in the channels D_sη, DK^*, D^*K and D_s ^*η will be crucial to distinguish the above two possibilities. PACS 13.25.Ft; 12.39.-x     

Long-Time Asymptotics for Strong Solutions¶of the Thin Film Equation

In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic equation u _t =−(u u _xxx ) _x , modeling the evolution of the interface of a spreading droplet. For nonnegative initial values u ₀(x)∈H ¹(ℝ), both compactly supported or of finite second moment, we prove explicit and universal algebraic decay in the L ¹-norm of the strong solution u(x,t) towards the unique (among source type solutions) strong source type solution of the equation with the same mass. The method we use is based on the study of the time decay of the entropy introduced in [13] for the porous medium equation, and uses analogies between the thin film equation and the porous medium equation. Received: 2 February 2001 / Accepted: 7 October 2001     

Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order <Emphasis Type="Italic">α</Emphasis>

In a first stage, the paper deals with the derivation and the solution of the equation of the probability density function of a stochastic system driven simultaneously by a fractional Gaussian white noise and a fractional Poissonian white noise both of the same order. The key is the Taylor’s series of fractional order f(x + h) = E _α(h^αD _x ^α)f(x) where E _α() denotes the Mittag-Leffler function, and D _x ^α is the so-called modified Riemann-Liouville fractional derivative which removes the effects of the non-zero initial value of the function under consideration. The corresponding fractional linear partial differential equation is solved by using a suitable extension of the Lagrange’s technique involving an auxiliary set of fractional differential equations. As an example, one considers a half-oscillator of fractional order driven by a fractional Poissonian noise.      

A new approach to calculate the gluon polarization

We derive the Leading-Order (LO) master equation to extract the polarized gluon distribution G(x,Q ²)=xδg(x,Q ²) from polarized proton structure function, g^p₁(x,Q²)g^{p}_{1}(x,Q^{2}). By using a Laplace-transform technique, we solve the master equation and derive the polarized gluon distribution inside the proton. The test of accuracy which is based in our calculations on two different methods, confirms that we achieve to the correct solution for the polarized gluon distribution. To determine the polarized gluon distribution xδg(x,Q ²) more accurately, we only need to have more experimental data on the polarized structure functions, g₁^p(x,Q²)g_{1}^{p}(x,Q^{2}). Our result for polarized gluon distribution is in good agreement with some phenomenological models.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

Non-abelian T-duality,Ramond fields and coset geometries

We extend the recently constructed double field theory formulation of the low-energy theory of the closed bosonic string to the heterotic string. The action can be written in terms of a generalized metric that is a covariant tensor under O(D, D + n), where n denotes the number of gauge vectors, and n additional coordinates are introduced together with a covariant constraint that locally removes these new coordinates. For the abelian subsector, the action takes the same structural form as for the bosonic string, but based on the enlarged generalized metric, thereby featuring a global O(D, D + n) symmetry. After turning on non-abelian gauge couplings, this global symmetry is broken, but the action can still be written in a fully O(D, D + n) covariant fashion, in analogy to similar constructions in gauged supergravities.

     

Zerfallende Zustände als physikalisch nichtisolierbare Teilsysteme

Presently the investigations of decaying quantum mechanical systems lack a well-founded concept, which is reflected by several formal difficulties of the corresponding mathematical treatment. In order to clarify in some respect the situation, we investigate, within the framework of nonrelativistic quantum mechanics, the resonant scattering of an initially well localized partial wave packet ϕ_l(r, t). If the potential decreases sufficiently fast for r → ∞, ϕ_l(r, t) can be expressed at sufficiently long time after the scattering has taken place, as ϕ_l(r, t) = I(r, t) + ∑ N_iϕl(K_i, r) exp {–iK_i² t/2M} × Θ(k_i – γ_i – Mr/t), ϕ_l(K_i, r) being the resonant solution with complex “momentum” K_i = k_i – iγ_i. From this heuristic relation one can deduce not only the probability for the creation of unstable particles but also obtain some hints to a connection between decaying states and physically nonisolable partial systems. On the other hand, this connection can perhaps display the inadequacy of attempts which suggest to solve the problem of decaying states within the usual Hilbert space methods.     

Double field formulation of Yang-Mills theory

Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge symmetries. In double field formulation, in a manifestly covariant manner our action couples a single O(D,D) vector potential to the closed string double field theory. In terms of undoubled component fields, it couples a usual Yang-Mills gauge field to an additional one-form field and also to the closed string background fields which consist of a dilaton, graviton and a two-form gauge field. Our resulting action resembles a twisted Yang-Mills action.     

Form factors of exponential operators and exact wave function renormalization constant in the Bullough-Dodd model

We compute the form factors of exponential operators e^kgϕ(x) in the two-dimensional integrable Bullough-Dodd model (a₂⁽²⁾ affine Toda field theory). These form factors are selected among the solutions of general non-derivative scalar operators by their asymptotic cluster property. Through analytical continuation to complex values of the coupling constant these solutions permit to compute the form factors of scaling relevant primary fields in the lightest-breather sector of integrable /gf_1,2 and /gf_1,5 deformations of conformal minimal models. We also obtain the exact wave-function renormalization constant Z(g) of the model and the properly normalized form factors of the operators ϕ(x) and : ϕ²(x) :.     

The newly observed open-charm states in quark model

Comparing the measured properties of the newly observed open-charm states D(2550), D(2600), D(2750), D(2760), D _s1(2710), D _sJ (2860), and D _sJ (3040) with our predicted spectroscopy and strong decays in a constituent quark model, we find that (1) the D(2 ¹ S ₀) assignment to D(2550) remains open for its too broad width determined by experiment; (2) the D(2600) and D _s1(2710) can be identified as the 2 ³ S ₁–1 ³ D ₁ mixtures; (3) if the D(2760) and D(2750) are indeed the same resonance, they would be the D(1 ³ D ₃); otherwise, they could be assigned as the D(1 ³ D ₃) and D^￠₂(1D)D^{\prime}_{2}(1D), respectively; (4) the D _sJ (2860) could be either the D _s1(2710)’s partner or the D _s (1 ³ D ₃); and (5) both the D _s1(2P) and D^￠_s1(2P)D^{\prime}_{s1}(2P) interpretations for the D _sJ (3040) seem likely. The E1 and M1 radiative decays of these sates are also studied. Further experimental efforts are needed to test the present quarkonium assignments for these new open-charm states.     

Unitary equivalence between a spin 1/2 charged particle in a two-dimensional magnetic field and a spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electric field

We prove the unitary equivalence between the Dirac HamiltonianH _D for a relativistic spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electrostatic fieldE = (E ₁,E ₂) and the direct sum of the Dirac-Weyl operatorsD(±A) for a spin 1/2 charged particle in two-dimensional magnetic fields ±dA with the vector potentialA =E ₂ dx ¹ -E ₁ dx ², (x ¹,x ²) ². As applications, we investigate the ground state and the spectra ofH _D.     

Table-like magnetocaloric effect involving the enhancement of refrigerant capacity in (AMn0.9Ti0.1O3)1−x/(AMn0.85Ti0.15O3)x composite

In this paper, a table-like magnetocaloric effect (MCE) is obtained in the (AMn_0.9Ti_0.1O₃)_1?x/(AMn_0.85Ti_0.15O₃)_x composite system. A flattening behaviour of the entropy change is investigated from the isothermal magnetic entropy change versus temperature curves ?S(T) of AMn_0.9Ti_0.1O₃ and AMn_0.85Ti_0.15O₃ (A = La_0.57Nd_0.1Pb_0.33) manganite materials. Both compounds exhibit nearly some large MCE, 5.2–4.85 J kg^?1 K^?1, under an applied field of 0–5 T, around their respective Curie temperature (T_C) ranged from 279 to 299 K. The temperature dependence of the isothermal magnetic entropy change ΔS(T) is calculated for (AMn_0.9Ti_0.1O₃)_1?x/(AMn_0.85Ti_0.15O₃)_x composite with 0 ≤ x ≤ 1. The optimum ΔS(T) of the composite with x = 0.495 approaches a nearly constant value of ～3.63 J kg^?1 K^?1 in a field change of 0–5 T in a wide temperature span over 15 K, resulting in large refrigerant capacity value of ～172.3 J kg^?1. The (AMn_0.9Ti_0.1O₃)_0.505/(AMn_0.85Ti_0.15O₃)_0.495 composite system indicates that this approach can be used to design magnetic refrigerant materials with enhanced magnetocaloric response in a magnetic refrigerator performing an Ericsson cycle near room temperature.     

Renormalizations and Operator Expansion in σ-Model

The operator expansion (OPE) is studied for the Green function n(0) n(x)) at x² → 0 (n(x) is the dynamical field of σ-model) in the framework of the two-dimensional σ-model with the O(N) symmetry group at large N. As a preliminary step we formulate the ronormalization scheme which permits introduction of an arbitrary intermediate scale μ² in the framework of 1/N expansion and discuss factorization (separation) of small (p < μ ) and large (p > μ ) momentum region. It is shown that definition of composite local operators and coefficient functions figuring in OPE is unambiguous only in the leading order in 1/N expansion when dominant are the solutions with exrtemum of action. Corrections of order f(μ²)/N (here /(μ²) is the effective interaction constant at the point μ²) in composite operators and coefficient functions essentially depend on factorization method of high and low momentum regions. It is shown also that contributions to the power corrections of order m²x²/(μ²)/N in the Green function (here m is the dynamical mass-scale factor in σ-model) arise simultaneously from two sources: from the mean vacuum value of the composite operator n ∂²n and from the hard particle contributions in the coefficient function of unite operator. Due to the analogy between σ-model and QCD the obtained result indicates theoretical limitations to the sum rule method in QCD.     

On the Theory of Gravitational Field in Finsler Spaces

Some structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as g_λχ(x, y) = γ_λχ(x) + h_λχ(x, y) is proposed, where γ_λχ denotes the Riemann metric of Einstein's gravitational field, while hλχ the Finsler metric induced by the Riemann metric h_ij(y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as ?ⁱ = K(x, y) y^j in the internal field, is grasped by the Finslerian parallelism δyⁱ (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δy^χ = e(x) δyⁱ. The whole metrical Finsler connection D for g_λχ(i.e., Dg_λχ = 0) is determined by taking account of the intrinsic behaviour δy^χ.     

Internal waves in a compressible two-layer model atmosphere: Hamiltonian description

We consider slow, compared to the speed of sound, motions of an ideal compressible fluid (gas) in a gravitational field in the presence of two isentropic layers with a small specific-entropy difference between them. Assuming the flow to be potential in each of the layers (v _{1, 2} = ▿ϕ_{1, 2}) and neglecting the acoustic degrees of freedom (div($ \bar \rho $ \bar \rho (z)▿ϕ_{1, 2}) ≈ 0, where $ \bar \rho $ \bar \rho (z) is the average equilibrium density), we derive the equations of motion for the boundary in terms of the shape of the surface z = η(x, y, t) itself and the difference between the boundary values of the two velocity field potentials: ψ(x, y, t) = ψ₁ − ψ₂. We prove the Hamilto nian structure of the derived equations specified by a Lagrangian of the form ℒ = ∫$ \bar \rho $ \bar \rho (η)η _t ψdxdy − ℋ{η, ψ}. The system under consideration is the simplest theoretical model for studying internal waves in a sharply stratified atmosphere in which the decrease in equilibrium gas density due to gas compressibility with increasing height is essentially taken into account. For plane flows, we make a generalization to the case where each of the layers has its own constant potential vorticity. We investigate a system with a model dependence $ \bar \rho $ \bar \rho (z) ∝ e ^−2αz with which the Hamiltonian ℋ{η, ψ} can be represented explicitly. We consider a long-wavelength dynamic regime with dispersion corrections and derive an approximate nonlinear equation of the form u _t + auu _x − b[−$ \hat \partial _x^2 $ \hat \partial _x^2 + α²]^1/2 u _x = 0 (Smith’s equation) for the slow evolution of a traveling wave.     

Light Quark Hadron Mass Scale

With a symmetry procedure based on Noether's theorem, the field equation of motion is obtained from the Dirac Hamiltonian H(D_μ) of a massless quark interacting with a gluon. The equation of motion is the Yang-Mills equation with external current which is spin-dependent and follows from the group algebra. In addition to the pure gauge solution we find a gauge covariant solution which follows from current conservation and sets the mass scale m₀/M = g². This gluon field is due to the density of dipole moments squared and represents four harmonic oscillators with quadratic constraints; the gluon can be written as a string potential or as a 1/x potential with a sharp cutoff. The chiral symmetry group G^spin × G^D gives the light quark hadron degenerate multiplet mass spectrum in terms of m₀[SU(2) × SU(2)] with the spinorial decomposition and the multipole breaks into dipoles. Scaling from atomic lengths it is found that g = em₀/nM for light quarks is the quark charge e/3 renormalized by m₀/M and g is magnetic. Thus quarks occur at the ends of spinning magnetic strings with dipole lengths ∼m₀⁻¹. The mass scale is that of a degenerate magnetic multipole with charge n = 3, 4… .