共查询到6条相似文献,搜索用时 15 毫秒
1.
Joakim Arnlind Martin Bordemann Laurent Hofer Jens Hoppe Hidehiko Shimada 《Communications in Mathematical Physics》2009,288(2):403-429
We introduce C-Algebras of compact Riemann surfaces as non-commutative analogues of the Poisson algebra of smooth functions on . Representations of these algebras give rise to sequences of matrix-algebras for which matrix-commutators converge to Poisson-brackets
as N → ∞. For a particular class of surfaces, interpolating between spheres and tori, we completely characterize (even for the
intermediate singular surface) all finite dimensional representations of the corresponding C-algebras. 相似文献
2.
We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the
projective superalgebra
\mathfrakpgl(p+1|q){\mathfrak{pgl}(p+1|q)} is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the
quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of
\mathfrakpgl(n|n)\not @ \mathfraksl(n|n){\mathfrak{pgl}(n|n)\not\cong \mathfrak{sl}(n|n)}), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms
of a generalized divergence operator acting on supersymmetric tensor fields. 相似文献
3.
4.
Marius Beceanu 《Communications in Mathematical Physics》2008,280(1):145-205
Consider the focussing cubic nonlinear Schrödinger equation in \({\mathbb{R}}^3\) :It admits special solutions of the form e itα ?, where \(\phi \in {\mathcal{S}}({\mathbb{R}}^3)\) is a positive (? > 0) solution ofThe space of all such solutions, together with those obtained from them by rescaling and applying phase and Galilean coordinate changes, called standing waves, is the 8-dimensional manifold that consists of functions of the form \(e^{i(v \cdot + \Gamma)} \phi(\cdot - y, \alpha)\) . We prove that any solution starting sufficiently close to a standing wave in the \(\Sigma = W^{1, 2}({\mathbb{R}}^3) \cap |x|^{-1}L^2({\mathbb{R}}^3)\) norm and situated on a certain codimension-one local Lipschitz manifold exists globally in time and converges to a point on the manifold of standing waves. Furthermore, we show that \({\mathcal{N}}\) is invariant under the Hamiltonian flow, locally in time, and is a centre-stable manifold in the sense of Bates, Jones [BatJon]. The proof is based on the modulation method introduced by Soffer and Weinstein for the L 2-subcritical case and adapted by Schlag to the L 2-supercritical case. An important part of the proof is the Keel-Tao endpoint Strichartz estimate in \({\mathbb{R}}^3\) for the nonselfadjoint Schrödinger operator obtained by linearizing (0.1) around a standing wave solution. All results in this paper depend on the standard spectral assumption that the Hamiltonianhas no embedded eigenvalues in the interior of its essential spectrum \((-\infty, -\alpha) \cup (\alpha, \infty)\) .
相似文献
$i\psi_t+\Delta\psi = -|\psi|^2 \psi. \quad (0.1) $
$-\Delta \phi + \alpha\phi = \phi^3. \quad (0.2)$
$\mathcal H = \left ( \begin{array}{cc}\Delta + 2\phi(\cdot, \alpha)^2 - \alpha &;\quad \phi(\cdot, \alpha)^2 \\ -\phi(\cdot, \alpha)^2 &;\quad -\Delta - 2 \phi(\cdot, \alpha)^2 + \alpha \end{array}\right ) \quad (0.3)$
5.
Boyan Sirakov 《Communications in Mathematical Physics》2007,271(1):199-221
In this paper we consider systems of coupled Schrödinger equations which appear in nonlinear optics. The problem has been considered mostly in the one-dimensional case. Here we make a rigorous study of the existence of least energy standing waves (solitons) in higher dimensions. We give: conditions on the parameters of the system under which it possesses a solution with least energy among all multi-component solutions; conditions under which the system does not have positive solutions and the associated energy functional cannot be minimized on the natural set where the solutions lie. 相似文献
6.
The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra
(m/n ) were described by Serganova, leading to her solution of the character problem for
(m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed. 相似文献