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151.
We present a complete characterization of Gabor frame operators on finite dimensional Hilbert space $L^2(\Gamma)$, where $\Gamma = \mathbb{Z}_{m_1} \times \mathbb{Z}_{m_2} \times \dots \times \mathbb{Z}_{m_p}$ and $m_1,m_2,\dots,m_p$ are positive integers. The notion of generalized $B$-modulation and generalized $B$-translation is introduced and some significant properties of the generalized pseudo $B$-Gabor like frames are discussed. 相似文献
152.
Using the coherent state representation we derive some new operator
identities and study some mathematical relations in combinatorics. The
technique of integral within an ordered product (IWOP) of operators plays an
essential role in realizing our goal. 相似文献
153.
FAN Hong-Yi 《理论物理通讯》2006,45(2):245-248
The Moyal bracket is an exemplification of Weyl's correspondence to
formulate quantum mechancis in terms of Wigner function. Here we present a
formalism of Weyl-ordered operator Moyal bracket by virtue of the method of
integral within a Weyl ordered product of operators and the Weyl
ordering operator formula. 相似文献
154.
Higher-Dimensional KdV Equations and Their Soliton Solutions 总被引:2,自引:0,他引:2
A (2+1)-dimensional KdV equation is obtained by use of Hirota
method, which possesses N-soliton solution, specially its exact
two-soliton solution is presented. By employing a proper algebraic
transformation and the Riccati equation, a type of bell-shape
soliton solutions are produced via regarding the variable in the
Riccati equation as the independent variable. Finally, we extend
the above (2+1)-dimensional KdV equation into (3+1)-dimensional
equation, the two-soliton solutions are given. 相似文献
155.
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach, and further investigate some mathematical aspects of Anderson localization that are rarely discussed before. First, we observe that under the Neumann boundary condition, the low energy quantum states are localized on the boundary of the domain with high probability. We provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional case. Second, we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary conditions. Finally, we examine a bifurcation phenomenon of the localization subregion as the strength of disorder varies. The critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed. 相似文献
156.
157.
《Journal of Nonlinear Mathematical Physics》2013,20(1):161-178
In this paper, we give a unified construction of the recursion operators from the Lax representation for three integrable hierarchies: Kadomtsev–Petviashvili (KP), modified Kadomtsev–Petviashvili (mKP) and Harry Dym under n-reduction. This shows a new inherent relationship between them. To illustrate our construction, the recursion operator are calculated explicitly for 2-reduction and 3-reduction. 相似文献
158.
159.
In this paper we introduce a new notion of complexified nonlocal-in-time-space material derivative operator and we discuss its implications in fluid mechanics. After deriving the complexified fluid equations, we investigate the problem of laminar flow of a particle fluid in a microtube. We demonstrate the occurrence of pulsatile flows through microtubes in agreement with recent findings. 相似文献
160.