共查询到20条相似文献,搜索用时 31 毫秒
1.
We extend to the sl(N)sl(N) case the results that we previously obtained on the construction of Wq,p{\cal W}_{q,p} algebras from the elliptic algebra Aq,p([^(sl)](2)c){\cal A}_{q,p}(\widehat{sl}(2)_{c}). The elliptic algebra \elp\elp at the critical level c= m N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N(Nу)/2 integers, defining q-deformations of the WN{\cal W}_{N} algebra, are constructed. The operators t(z) also close an exchange algebra when (-p\sfrac12)NM = q-c-N(-p^\sfrac{1}{2})^{NM} = q^{-c-N} for M ? \ZZM\in\ZZ. It becomes Abelian when in addition p= qNh, where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed WN{\cal W}_{N} algebras depending on the parity of h, characterizing the exchange structures at p p qNh as new Wq,p(sl(N)){\cal W}_{q,p}(sl(N)) algebras. 相似文献
2.
Nakao Hayashi Pavel I. Naumkin Jean-Claude Saut 《Communications in Mathematical Physics》1999,201(3):577-590
We study the large time asymptotic behavior of solutions to the generalized Kadomtsev-Petviashvili (KP) equations $ \left\{\alignedat2 &u_t + u_{xxx} + \sigma\partial_x^{-1}u_{yy}= - (u^{\rho})_x, &;&;\qquad (t,x,y) \in {\bold R}\times {\bold R}^2,\\ \vspace{.5\jot} &u(0,x,y) = u_0 (x,y),&;&; \qquad (x,y) \in{\bold R}^2, \endalignedat \right. \TAG KP $ \left\{\alignedat2 &u_t + u_{xxx} + \sigma\partial_x^{-1}u_{yy}= - (u^{\rho})_x, &;&;\qquad (t,x,y) \in {\bold R}\times {\bold R}^2,\\ \vspace{.5\jot} &u(0,x,y) = u_0 (x,y),&;&; \qquad (x,y) \in{\bold R}^2, \endalignedat \right. \TAG KP where = 1 or = m 1. When = 2 and = m 1, (KP) is known as the KPI equation, while = 2, = + 1 corresponds to the KPII equation. The KP equation models the propagation along the x-axis of nonlinear dispersive long waves on the surface of a fluid, when the variation along the y-axis proceeds slowly [10]. The case = 3, = m 1 has been found in the modeling of sound waves in antiferromagnetics [15]. We prove that if S 3 is an integer and the initial data are sufficiently small, then the solution u of (KP) satisfies the following estimates: ||u(t)||¥ £ C (1 + |t|)-1 (log(2+|t|))k, ||ux(t)||¥ £ C (1 + |t|)-1 \|u(t)\|_\infty \le C (1 + |t|)^{-1} (\log (2+|t|))^{\kappa}, \|u_x(t)\|_\infty \le C (1 + |t|)^{-1} for all t ] R, where s = 1 if = 3 and s = 0 if S 4. We also find the large time asymptotics for the solution. 相似文献
3.
In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic
shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the
product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Müller (Philos
Mag A 66(5):697–715, 1992), is defined by the following functional:
(E)(u) = 2pb||u(0,·)||2[(H)\dot]1/2([0,h]) + ò0L dx ò0h dy ( |ux|2 + \frace2|uyy| ),\mathcal (E)(u) = 2\pi\beta||u(0,\cdot)||^2_{\dot H^{1/2}([0,h])} + \int_{0}^{L} dx \int_0^h dy\, \big( |u_x|^2 + \frac{\varepsilon}2|u_{yy}| \big), 相似文献
4.
Thomas Bartsch Angela Pistoia Tobias Weth 《Communications in Mathematical Physics》2010,297(3):653-686
We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain ${\Omega\subset\mathbb{R}^2}
5.
In appropriate units, the Brown-Ravenhall Hamiltonian for a system of 1 electron relativistic molecules with K fixed nuclei having charge and position Zk, Rk, k=1,2, ?,Kk=1,2, \ldots,K, is of the form \bB1,K = L+ ( D0 + aVc) L+ \bB_{1,K}= \Lambda_+ \bigl( D_0 + \alpha V_c\bigr) \Lambda_+ , where v+ is the projection onto the positive spectral subspace of the free Dirac operator D0 and Vc = - ?k=1K \fracaZk\lmod \bx-Rk \rmod + ?k < l, k,l=1K \fracaZk Zl\lmod Rk-Rl \rmod V_c= - \sum_{k=1}^K \frac{\alpha Z_k}{\lmod \bx-R_k \rmod} + \sum_{k
6.
M. Junge C. Palazuelos D. Pérez-García I. Villanueva M. M. Wolf 《Communications in Mathematical Physics》2010,300(3):715-739
In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order ${{\rm \Omega} \left(\frac{\sqrt{n}}{\log^2n} \right)}
7.
Consider the diffusive Hamilton-Jacobi equation u t = Δu + |?u| p , p > 2, on a bounded domain Ω with zero-Dirichlet boundary conditions, which arises in the KPZ model of growing interfaces. It is known that u remains bounded and that ?u may blow up only on the boundary ?Ω. In this paper, under suitable assumptions on ${\Omega\subset \mathbb{R}^2}
8.
We obtain convergent multi-scale expansions for the one-and two-point correlation functions of the low temperature lattice classical N - vector spin model in d S 3 dimensions, N S 2. The Gibbs factor is taken as exp[-b(1/2 ||?f||2 +l/8 || |f|2 - 1 ||2 + v/2||f- h||2)], \exp [-\beta (1/2 ||\partial \phi||^2 +\lambda/8 ||\, |\phi|^2 - 1 ||^2 + v/2||\phi - h||^2)], where f(x), h ? RN\phi(x), h \in R^N, x ? Zdx \in Z^d, |h|=1, b < ¥|h|=1, \beta < \infty, l 3 ¥\lambda \geq \infty are large and 0 < v h 1. In the thermodynamic and v ˉ 0v \downarrow 0 limits, with h = e1, and j L ½ , the expansion gives áf1(x)? = 1+0(1/b1/2)\langle \phi_1(x)\rangle = 1+0(1/\beta^{1/2}) (spontaneous magnetization), áf1(x)fi(y)? = 0\langle \phi_1(x)\phi_i(y)\rangle=0, áfi (x)fi (y)? = c0 D-1(x,y)+R(x,y)\langle \phi_i (x)\phi_i (y)\rangle = c_0 \Delta^{-1}(x,y)+R(x,y) (Goldstone Bosons), i = 2, 3, ?, Ni= 2, 3,\,\ldots, N, and áf1(x)f1(y)?T=R¢(x,y)\langle \phi_1(x)\phi_1(y)\rangle^T=R'(x,y), where |R(x,y)||R(x,y)|, |R¢(x,y)| < 0(1)(1+|x-y|)d-2+r|R'(x,y)|< 0(1)(1+|x-y|)^{d-2+\rho} for some > 0, and c0 is aprecisely determined constant. 相似文献
9.
We make the cosmological constant, Λ, into a field and restrict the variations of the action with respect to it by causality.
This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and
is the requirement that the cosmological wave function possess a classical limit. When applied to the Friedmann metric it
requires that the cosmological constant measured today, t
U
, be L ~ tU-2 ~ 10-122{\Lambda \sim t_{U}^{-2} \sim 10^{-122}} , as observed. This is the classical value of Λ that dominates the wave function of the universe. Our new field equation
determines Λ in terms of other astronomically measurable quantities. Specifically, it predicts that the spatial curvature
parameter of the universe is Wk0 o -k/a02H2=-0.0055{\Omega _{\mathrm{k0}} \equiv -k/a_{0}^{2}H^{2}=-0.0055} , which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological
history. 相似文献
10.
11.
Zhi-Gang Wang Zhi-Cheng Liu Xiao-Hong Zhang 《The European Physical Journal C - Particles and Fields》2009,64(3):373-386
In this article, we assume that there exist scalar D*[`(D)]*{D}^{\ast}{\bar {D}}^{\ast}, Ds*[`(D)]s*{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B*[`(B)]*{B}^{\ast}{\bar {B}}^{\ast} and Bs*[`(B)]s*{B}_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states, and study their masses using the QCD sum rules. The numerical results indicate that the masses are about
(250–500) MeV above the corresponding D
*–[`(D)]*{\bar{D}}^{\ast}, D
s
*–[`(D)]s*{\bar {D}}_{s}^{\ast}, B
*–[`(B)]*{\bar{B}}^{\ast} and B
s
*–[`(B)]s*{\bar {B}}_{s}^{\ast} thresholds, the Y(4140) is unlikely a scalar Ds*[`(D)]s*{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast} molecular state. The scalar D*[`(D)]*D^{\ast}{\bar{D}}^{\ast}, Ds*[`(D)]s*D_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B*[`(B)]*B^{\ast}{\bar{B}}^{\ast} and Bs*[`(B)]s*B_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states maybe not exist, while the scalar D¢*[`(D)]¢*{D'}^{\ast}{\bar{D}}^{\prime\ast}, Ds¢*[`(D)]s¢*{D}_{s}^{\prime\ast}{\bar{D}}_{s}^{\prime\ast}, B¢*[`(B)]¢*{B}^{\prime\ast}{\bar{B}}^{\prime\ast} and Bs¢*[`(B)]s¢*{B}_{s}^{\prime\ast}{\bar{B}}_{s}^{\prime\ast} molecular states maybe exist. 相似文献
12.
Measurement of the diffractive cross section in deep inelastic scattering using ZEUS 1994 data 总被引:1,自引:0,他引:1
The DIS diffractive cross section, dsdiffg* p ? XN/dMXd\sigma^{di\!f\!f}_{\gamma^* p \to XN}/dM_X, has been measured in the mass range MX < 15M_X < 15 GeV for g*p\gamma^*p c.m. energies 60 < W < 20060 < W < 200 GeV and photon virtualities Q2 = 7Q^2 = 7 to 140 GeV2^2. For fixed Q2Q^2 and MXM_X, the diffractive cross section rises rapidly with WW, dsdiffg*p ? XN(MX,W,Q2)/dMX μ Wadiffd\sigma^{di\!f\!f}_{\gamma^*p \to XN}(M_X,W,Q^2)/dM_X \propto W^{a^{diff}} with adiff = 0.507 ±0.034 (stat)+0.155-0.046(syst)a^{diff} = 0.507 \pm 0.034 (stat)^{+0.155}_{-0.046}(syst) corresponding to a t-averaged pomeron trajectory of [`( a\mathbb P )] = 1.127 ±0.009 (stat)+0.039-0.012 (syst)\overline{ \alpha_{_{{\mathbb P}}} } = 1.127 \pm 0.009 (stat)^{+0.039}_{-0.012} (syst) which is larger than [`( a\mathbb P )]\overline{ \alpha_{_{{\mathbb P}}} } observed in hadron-hadron scattering. The W dependence of the diffractive cross section is found to be the same as that of the total cross section for scattering of virtual photons on protons. The data are consistent with the assumption that the diffractive structure function FD(3)2F^{D(3)}_2 factorizes according to x\mathbb P FD(3)2 (x\mathbb P,b,Q2) = (x0/ x\mathbb P)n FD(2)2(b,Q2)x_{_{{\mathbb P}}} F^{D(3)}_2 (x_{_{{\mathbb P}}},\beta,Q^2) = (x_0/ x_{_{{\mathbb P}}})^n F^{D(2)}_2(\beta,Q^2). They are also consistent with QCD based models which incorporate factorization breaking. The rise of x\mathbb P FD(3)2x_{_{{\mathbb P}}} F^{D(3)}_2 with decreasing x\mathbb Px_{_{{\mathbb P}}} and the weak dependence of FD(2)2F^{D(2)}_2 on Q2Q^2 suggest a substantial contribution from partonic interactions. 相似文献
13.
Using chiral perturbation theory we calculate for pion Compton scattering the isospin-breaking effects induced by the difference
between the charged and neutral pion mass. At one-loop order this correction is directly proportional to mp±2-mp02\ensuremath{m_{\pi^\pm}^2-m_{\pi^0}^2} and free of (electromagnetic) counterterm contributions. The differential cross-section for charged pion Compton scattering
p-g? p-g\ensuremath{\pi^-\gamma \rightarrow \pi^-\gamma} gets affected (in backward directions) at the level of a few permille. At the same time the isospin-breaking correction leads
to a small shift of the pion polarizabilities by d(ap- bp) @ 1.3 ·10-5\ensuremath{\delta(\alpha_\pi- \beta_\pi) \simeq 1.3 \cdot 10^{-5}} fm^3. In case of the low-energy gg? p0p0\ensuremath{\gamma\gamma \rightarrow \pi^0\pi^0} reaction isospin breaking manifests itself through a cusp effect at the p+p-\ensuremath{\pi^+\pi^-} threshold. We give an improved estimate for it based on the empirical p \pi
p \pi -scattering length difference a0-a2\ensuremath{a_0-a_2} . 相似文献
14.
In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial
data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and
B-\frac12,\frac124{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS
ν
) has a unique global solution with initial data u0 = (u0h, u03){u_0 = (u_0^h, u_0^3)} which satisfies
||u0h||B exp(\fracCn4 ||u03||B4) £ c0n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or
||u0h||B-\frac12,\frac124 exp(\fracCn4 ||u03||B-\frac12,\frac1244) £ c0n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c
0 sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner
type spaces, [(Lpt)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L2t, f)\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L
1 function f(t). 相似文献
15.
In this paper, we prove a maximum principle for a frequency localized transport-diffusion equation. As an application, we
prove the local well-posedness of the supercritical quasi-geostrophic equation in the critical Besov spaces
\mathringB1-a¥,q{\mathring{B}^{1-\alpha}_{\infty,q}}, and global well-posedness of the critical quasi-geostrophic equation in
\mathringB0¥,q{\mathring{B}^{0}_{\infty,q}} for all 1 ≤ q < ∞. Here
\mathringBs¥,q {\mathring{B}^{s}_{\infty,q} } is the closure of the Schwartz functions in the norm of Bs¥,q{B^{s}_{\infty,q}}. 相似文献
16.
This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order
operators on the half-line is developed, and the trace inequality
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