Multi-parametric deformed Heisenberg algebras: a route to complexity
Multi-parametric deformed Heisenberg algebras: a route to complexity
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DOI：
10.1088/0305-4470/34/15/304
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发表时间：
2000-11
期刊：
影响因子：
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通讯作者：
E. Curado;M. Rego-Monteiro
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文献类型：
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作者：
E. Curado;M. Rego-Monteiro
我们介绍了一个推广的海森堡代数，这是书面的代数，f（J 0），可以是任何分析功能的一个发电机的功能。当f与斜率θ呈线性时，我们证明这种情况下的代数对应于q2 = tan θ的q-振子。f是J 0中n阶多项式的情况对应于n-参数变形海森堡代数。当f为任意解析函数时，通过研究f及其组合函数的不动点的稳定性，得到了该代数的表示.的情况下，当f是一个二次多项式在J 0，最简单的非线性计划，这是能够创造混乱的行为，进行了详细的分析和特殊区域的参数空间表示，不能连续变形的海森堡代数表示。
We introduce a generalization of the Heisenberg algebra which is written in terms of a functional of one generator of the algebra, f (J0), that can be any analytical function. When f is linear with slope θ, we show that the algebra in this case corresponds to q-oscillators for q2 = tan θ. The case where f is a polynomial of order n in J0 corresponds to an n-parameter deformed Heisenberg algebra. The representations of the algebra, when f is any analytical function, are shown to be obtained through the study of the stability of the fixed points of f and their composed functions. The case when f is a quadratic polynomial in J0, the simplest nonlinear scheme which is able to create chaotic behaviour, is analysed in detail and special regions in the parameter space give representations that cannot be continuously deformed to representations of Heisenberg algebra.