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在简介斐波那契类(Fibonacci-class)准晶(FC(n))的特征基础上,在小信号、平面波近似下详细地研究了通过N层按斐波那契类准周期系列排布的铁电畴超晶格的二次谐波光场的谱性质.发现其谱的极强峰在实空间,在不考虑介质色散效应的情况下,具有完美的自相似性;对于具有线性色散效应的铁电晶体,其谱在实空间也具有相同的结论;而对于具有非线性色散效应的铁电介质,极强峰的这种自相似性将被破坏.另外,二次谐波光的暗线处将存在缺级效应;亮线处则无缺级效应.
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斐波那契数列具有许多有趣的性质,广泛见于理论分析和实际应用中。电容器、电感器和电阻器是电路中基本的无源元件。本文应用基尔霍夫定律对梯形结构的纯电容和纯电阻网络进行了分析,指出它们可以清晰而简洁地实现斐波那契数列,并给出了斐波那契数列的若干性质在电阻电路中的反映和体现。最后用电路仿真软件和实际电路给出具体的测量数值,结果与理论分析完全一致。 相似文献
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In this paper we study the
splitting rules of energy spectra for two-dimensional
Fibonacci-class quasilattices (FC(n)) with three kinds of atoms
(A, B, and C) and one bond length by means of a
decomposition-decimation method, and find that the sublattices of
B atoms and C atoms are different from those of normal
two-dimensional FC(n) and the corresponding splitting manners
are new and interesting. B atom forms a kind of two-dimensional
so-called FC(n)’, which structure is some different from that of
normal FC(n-1) (n≥2), but the spectra lines are as the
same as that of the latter. C atom forms two kinds of
interesting one-dimensional periodic chains: n-atom chain and
(n-1)-atom chain, which spectra will both tend to become
continuous, respectively. The analytical results are confirmed by
numerical simulations. 相似文献
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On the basis of our former work and by means of the decomposition-decimation method, we study the splitting rules for the second hierarchy of the electronic energy spectra for two-dimensional Fibonacci-class quasicrystals with one kind of atom and two bond lengths. It is found that every line of the sub-spectra for n x n and (n + 1) x (n + 1) clusters of FC(n)
splits according to the type Y(n-1)-2-1 and type Y
n-2-1 respectively. The one for n x (n + 1) clusters of FC(n) consists of three sub-subbands when
, and five sub-subbranches when
. The general formulae of the number of energy levels for the spectra of the second hierarchy are obtained. The analytical results are confirmed by numerical simulations.Received: 18 March 2004, Published online: 23 July 2004PACS:
71.23.Ft Quasicrystals - 63.90. + t Other topics in lattice dynamics (restricted to new topics in section 63) - 33.70.Jg Line and band widths, shapes, and shifts 相似文献
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A.?Fledderjohann A.?Klümper K.-H.?Mütter 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,72(4):541
The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix ΔS (n+1) of 4 neighbouring “n clusters” of size 2n × 2n, n = 1,2,3,... from the corresponding quantities ΔS (n). Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies ES (n+1), S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S’,m’;n+1|Sq *|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2n+1 × 2n+1, mediated by the staggered spin operator Sq *. 相似文献
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A. Fledderjohann A. Klümper K.-H. Mütter 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,72(4):559-565
The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins
S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix ΔS
(n+1) of 4 neighbouring “n clusters” of size 2n × 2n, n = 1,2,3,... from the corresponding quantities ΔS
(n). Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies
ES
(n+1), S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices
are generated by the transitions 〈S’,m’;n+1|Sq
*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2n+1 × 2n+1, mediated by the staggered spin operator Sq
*. 相似文献
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A simple vibronic coupling model involving two electronic states and two vibrational modes is considered. The model is based on harmonic diabatic potentials and linear coupling of the diabatic electronic states. It is shown that the adiabatic electronic potential energy surfaces exhibit, in general, a conical intersection. The well known E × E and E × B Jahn-Teller problems are contained as special cases. Using numerical methods the optical absorption spectrum is calculated exactly. Extremely complex vibronic spectra are obtained when the conical intersection occurs within the Franck-Condon (FC) zone. The exact vibronic spectra are compared with spectra calculated in the adiabatic and FC approximation. The genuine spectroscopic effects of conical intersections are revealed by a comparison with the results of standard one-dimensional vibronic coupling calculations. The presence of a conical intersection limits the applicability of the adiabatic and FC approximations much more strongly than in the one-dimensional case. The upper adiabatic electronic state is strongly affected by non-adiabatic coupling even when the point of intersection lies outside the FC zone. The relevance of these results for the calculation of molecular electronic spectra is briefly discussed. 相似文献
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Single vibronic level fluorescence spectra of sulfur dioxide have been recorded throughout most of the region corresponding to the absorption. These spectra show progressions in the symmetric stretching mode of at least five members. Twelve origins between 30 972 and 31 776 cm?1 show remarkably similar Franck-Condon (FC) patterns for this progression. Seven origins between 31 840 and 32 257 cm?1 show another distinct FC pattern. This behavior is repeated for three more regions of excitation, each with a different distinct FC pattern and each containing numerous origins spread throughout a region of about 700 cm?1. The progressions in the symmetric bending mode are essentially absent in the lowest energy excitation spectra and then slowly increase in length as the excitation energy increases. There is limited activity in both even and odd quanta of the antisymmetric stretching mode. These results are interpreted in terms of the levels of a zero-order 1B1 electronic state (with zero-order origin at around 31 240 cm?1) that are very strongly vibronically coupled to many more 1A2 levels (with lower energy zero-order origin). The bulk of the emission is what would be expected from the zero-order 1B1 levels spread among the 1A2 levels. 相似文献
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The many-body properties of the strongly correlated two-dimensional dangling bond electron gas of a (1 × 1)-Si surface have been analysed by means of an accurate solution of a Hubbard Hamiltonian. The experimental similarity between the (1 × 1) and the (7 × 7) faces allows us to extend our analysis to the latter surface. A peak appearing near the Fermi energy for the (7 × 7) face at low temperatures is related to a kind of “Kondo-peak” for the Hubbard Hamiltonian. Photoemission spectra for the (1 × 1) surface of highly doped Si can be understood in terms of our model. 相似文献