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In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result. 相似文献
5.
Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when
viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms
whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential
equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration
process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using
the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order
algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions”
defined by nonvanishing Lie brackets. 相似文献
6.
Algebra matrix and similarity classification of operators 总被引:1,自引:0,他引:1
ZHANG Zilong & LI Yucheng Department of Mathematics Hebei Normal University Shijiazhuang China 《中国科学A辑(英文版)》2006,49(3):398-409
In this paper, by the Gelfand representation theory and the Silov idempotents theorem, we first obtain a central decomposition theorem related to a unital semi-simple n-homogeneous Banach algebra, and then give a similarity classification of two strongly irreducible Cowen-Douglas operators using this theorem. 相似文献
7.
We give a coring version for the duality theorem for actions and coactions of a finitely generated projective Hopf algebra.
We also provide a coring analogue for a theorem of H.-J. Schneider, which generalizes and unifies the duality theorem for
finite Hopf algebras and its refinements.
This paper was written while the first author visited the Mathematics Departments of Syracuse University and California State
University Dominguez Hills. He would like to thank both departments for their hospitality. 相似文献
8.
Exact closed-form solutions are exhibited for the Hopf equation for stationary incompressible 3D Navier-Stokes flow, for the cases of homogeneous forced flow (including a solution with depleted nonlinearity) and inhomogeneous flow with arbitrary boundary conditions. This provides an exact method for computing two- and higher-point moments, given the mean flow. 相似文献
9.
Alexander Krasnosel'skii Dmitrii Rachinskii 《NoDEA : Nonlinear Differential Equations and Applications》2002,9(1):93-115
We consider autonomous systems with a nonlinear part depending on a parameter and study Hopf bifurcations at infinity. The
nonlinear part consists of the nonlinear functional term and the Prandtl--Ishlinskii hysteresis term. The linear part of the
system has a special form such that the close-loop system can be considered as a hysteresis perturbation of a quasilinear
Hamiltonian system. The Hamiltonian system has a continuum of arbitrarily large cycles for each value of the parameter. We
present sufficient conditions for the existence of bifurcation points for the non-Hamiltonian system with hysteresis. These
bifurcation points are determined by simple characteristics of the hysteresis nonlinearity. 相似文献
10.
Several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors [Proc. Natl. Acad. Sci. 96 (1999) 14687; Commun. Pure Appl. Math. 54 (2001) 891] are developed here. In this procedure, reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables. While the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small, it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big. Typically, the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1/2. The examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated Burgers–Hopf equations as a nonlinear heat bath. Systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two-time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables. In an important illustrative example presented here, the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises. Even for large value of the correlation time ratio of the order of 1/2, the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non-Gaussian statistics of the original nonlinear systems with 102 modes extremely well. Furthermore, it is shown here that the standard regression fitting of the second-order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example. 相似文献