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81.
We discuss deformations of the classical systems in the phase space and show that one can use non-canonical transformations to relate regular and deformed models. On the other hand some of the models can be obtained as a classical limit of the deformed quantum models, i.e. as the result of the dequantization procedure. Nonrelativistic deformations are described. 相似文献
82.
A.I. Molev 《Czechoslovak Journal of Physics》2003,53(11):1073-1078
We introduce a new algebra depending on two nonzero complex parameters z and q such that its specialization at z=q
n and q=1 coincides the Brauer algebra. We show that the action of the new algebra commutes with the representation of the twisted deformation of the enveloping algebra U(o
n) in the tensor power of the vector representation. 相似文献
83.
In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional (1D) fermion algebra, and we investigate the properties of this category. The categorical analogues of the Fock states are some kind of 1-morphisms in our category, and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states. All the results in our categorical framework coincide exnetlv with those in normal quantum mechanics. 相似文献
84.
85.
86.
Jamila Douari 《International Journal of Theoretical Physics》2006,45(5):867-879
We construct a deformed C
λ-extended Heisenberg algebra in two-dimensional space using noncommuting coordinates which close an algebra depends on statistical parameter characterizing exotic particles. The obtained symmetry is nothing but an exotic particles algebra interpolating between bosonic and deformed fermionic algebras.
PACS numbers: 03.65.Fd, 02.40.Gh, 05.30.Pr 相似文献
87.
88.
We list characters (one-dimensional representations) of the reflection equation algebra associated with the fundamental vector representation of the Drinfeld–Jimbo quantum group
q
(gl(n)). 相似文献
89.
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
90.
Numerical Approximation of Hopf Bifurcation for Tumor-Immune System Competition Model with Two Delays 下载免费PDF全文
Jing-Jun Zhao Jing-Yu Xiao & Yang Xu 《advances in applied mathematics and mechanics.》2013,5(2):146-162
This paper is concerned with the Hopf bifurcation analysis of
tumor-immune system competition model with two delays. First, we
discuss the stability of state points with different kinds of
delays. Then, a sufficient condition to the existence of the Hopf
bifurcation is derived with parameters at different points.
Furthermore, under this condition, the stability and direction of
bifurcation are determined by applying the normal form method and
the center manifold theory. Finally, a kind of Runge-Kutta methods
is given out to simulate the periodic solutions numerically. At
last, some numerical experiments are given to match well with the
main conclusion of this paper. 相似文献