In this work, we study the photonic band of cumulative Fibonacci lattices, of which the structure is composed of all generated units in a Fibonacci sequence. The results are compared with distributed Bragg reflector(D...In this work, we study the photonic band of cumulative Fibonacci lattices, of which the structure is composed of all generated units in a Fibonacci sequence. The results are compared with distributed Bragg reflector(DBR)structures with the same numbers of layers. Photonic bandgaps are found at two characteristic frequencies, symmetrically separated from the central bandgap in the DBR counterpart. Field amplitude and phase distribution in the Fibonacci lattice indicates an interferential origin of the bandgaps. Fourier transform on the refractive index profile is carried out, and the result confirms a determinate long-range periodicity that agrees well with the photonic band structure.展开更多
In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio <span style="font-family:Verdana;">...In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio <span style="font-family:Verdana;">φ<span style="font-family:Verdana;"> respectively its fifth power <span style="font-family:Verdana;">φ<sup><span style="font-family:Verdana;">5</sup><span style="font-family:Verdana;">. The research fields cover model calculations of statistical physics associated with phase transitions, the quantum probability of two particles, new physics of everything suggested by the information relativity theory (<span style="font-family:Verdana;">IRT<span style="font-family:Verdana;">) including explanations of cosmological relevance, the <span style="font-family:Verdana;">ε<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-<span style="font-family:;" "=""><span style="font-family:Verdana;">infinity theory, superconductivity, and the <span style="font-family:Verdana;">Tammes<span style="font-family:Verdana;"> problem of the largest diameter of <span style="font-family:Verdana;">N<span style="font-family:Verdana;"> non-overlapping circles on the surface of a sphere with its connection to viral morphology and crystallography. Finally, <span style="font-family:Verdana;">Fibo<span style="font-family:Verdana;">nacci<span style="font-family:Verdana;"> anyons proposed for topological quantum<span style="font-family:Verdana;"> computation (<span style="font-family:Verdana;">TQC<span style="font-family:Verdana;">) were briefly described in comparison to the recently formulated reverse <span style="font-family:Verdana;">Fibonacci<span style="font-family:Verdana;"> approach using the <span style="font-family:Verdana;">Jani<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="white-space:nowrap;">čko<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> number sequence. An architecture applicable for a quantum computer is proposed consisting of 13-step twisted microtubules similar to tubulin microtubules of living matter. Most topics point to the omnipresence of the golden mean as the numerical dominator of our world.展开更多
This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same prop...This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.展开更多
基金National Natural Science Foundation of China(NSFC)(11574166)Science and Technology Foundation for Youth Talents of the Educational Commission of Hubei Province of China(Q2015002)
文摘In this work, we study the photonic band of cumulative Fibonacci lattices, of which the structure is composed of all generated units in a Fibonacci sequence. The results are compared with distributed Bragg reflector(DBR)structures with the same numbers of layers. Photonic bandgaps are found at two characteristic frequencies, symmetrically separated from the central bandgap in the DBR counterpart. Field amplitude and phase distribution in the Fibonacci lattice indicates an interferential origin of the bandgaps. Fourier transform on the refractive index profile is carried out, and the result confirms a determinate long-range periodicity that agrees well with the photonic band structure.
文摘In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio <span style="font-family:Verdana;">φ<span style="font-family:Verdana;"> respectively its fifth power <span style="font-family:Verdana;">φ<sup><span style="font-family:Verdana;">5</sup><span style="font-family:Verdana;">. The research fields cover model calculations of statistical physics associated with phase transitions, the quantum probability of two particles, new physics of everything suggested by the information relativity theory (<span style="font-family:Verdana;">IRT<span style="font-family:Verdana;">) including explanations of cosmological relevance, the <span style="font-family:Verdana;">ε<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-<span style="font-family:;" "=""><span style="font-family:Verdana;">infinity theory, superconductivity, and the <span style="font-family:Verdana;">Tammes<span style="font-family:Verdana;"> problem of the largest diameter of <span style="font-family:Verdana;">N<span style="font-family:Verdana;"> non-overlapping circles on the surface of a sphere with its connection to viral morphology and crystallography. Finally, <span style="font-family:Verdana;">Fibo<span style="font-family:Verdana;">nacci<span style="font-family:Verdana;"> anyons proposed for topological quantum<span style="font-family:Verdana;"> computation (<span style="font-family:Verdana;">TQC<span style="font-family:Verdana;">) were briefly described in comparison to the recently formulated reverse <span style="font-family:Verdana;">Fibonacci<span style="font-family:Verdana;"> approach using the <span style="font-family:Verdana;">Jani<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="white-space:nowrap;">čko<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> number sequence. An architecture applicable for a quantum computer is proposed consisting of 13-step twisted microtubules similar to tubulin microtubules of living matter. Most topics point to the omnipresence of the golden mean as the numerical dominator of our world.
基金Project supported by the National Natural Science Foundation of China(Grant No19674046)the Cheung Kong Scholars Programme of Chinathe Construct Program of the Key Discipline in Hunan Province,China
文摘This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.
