论文标题
斐波那契分隔线的量子计算和玻色含量金黄色量子振荡器的无限层次结构
Quantum Calculus of Fibonacci Divisors and Infinite Hierarchy of Bosonic-Fermionic Golden Quantum Oscillators
论文作者
论文摘要
从斐波那契数的划分问题开始，我们引入了斐波那契，黄金比例的黄金衍生物相关层次结构，并发展了相应的量子计算。通过这种演算，具有整数频谱的金量子振荡器的无限层次结构由纤维纤维分隔确定，在复杂分析功能的空间中，金色相干状态的层次结构和相关的Fock-Bargman表示。结果表明，具有均匀和奇数$ k $的斐波那契分隔符相应地描述了金色变形的骨气和费米子量子振荡器。通过一组翻译操作员，我们发现了金色二项式和相关的黄金分析功能的层次结构，共轭到fibonacci Number $ f_k $。在限制k-> 0中，黄金分析函数将斐波那契分隔剂的经典全体形态函数和量子计算减少到通常的函数。讨论了微积分对骨气和费米振荡器代数的量子变形，R型，流体动力图像和量子计算的几种应用。
Starting from divisibility problem for Fibonacci numbers we introduce Fibonacci divisors, related hierarchy of Golden derivatives in powers of the Golden Ratio and develop corresponding quantum calculus. By this calculus, the infinite hierarchy of Golden quantum oscillators with integer spectrum determined by Fibonacci divisors, the hierarchy of Golden coherent states and related Fock-Bargman representations in space of complex analytic functions are derived. It is shown that Fibonacci divisors with even and odd $k$ describe Golden deformed bosonic and fermionic quantum oscillators, correspondingly. By the set of translation operators we find the hierarchy of Golden binomials and related Golden analytic functions, conjugate to Fibonacci number $F_k$. In the limit k -> 0, Golden analytic functions reduce to classical holomorphic functions and quantum calculus of Fibonacci divisors to the usual one. Several applications of the calculus to quantum deformation of bosonic and fermionic oscillator algebras, R-matrices, hydrodynamic images and quantum computations are discussed.
