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991.
992.
《Discrete Mathematics》2020,343(11):112018
Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is relevant in quantum information in particular for entanglement generation in spin networks. We study fractional revival in graphs whose adjacency matrices belong to the Bose–Mesner algebra of association schemes. A specific focus is a characterization of balanced fractional revival (which corresponds to maximal entanglement) in graphs that belong to the Hamming scheme. Our proofs exploit the intimate connections between algebraic combinatorics and orthogonal polynomials. 相似文献
993.
994.
Tetsuya Hattori 《Journal of statistical physics》2007,127(3):609-627
Let W(x,y) = ax
3+ bx
4+ f
5
x
5+ f
6
x
6+ (3 ax
2)2
y+ g
5
x
5
y + h
3
x
3
y
2 + h
4
x
4
y
2 + n
3
x
3
y
3+a
24
x
2
y
4+a
05
y
5+a
15
xy
5+a
06
y
6, and X = , , where the coefficients are non-negative constants, with a > 0, such that X
2(x,x
2)−Y(x,x
2) is a polynomial of x with non-negative coefficients.
Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding
paths on the 3 and 4 dimensional pre-gaskets.
We prove that there exists a unique fixed point (x
f
,y
f
) of Φ in the invariant set .
2000 Mathematics Subject Classification Numbers: 82B28; 60G99; 81T17; 82C41. 相似文献
995.
The emphasis of this review is both the geometric realization of the 2-point velocity correlation tensor field Bij (x,x′,t) and isometries of the correlation space K3 equipped with a (pseudo-) Riemannian metrics ds2(t) generated by the tensor field. The special form of this tensor field for homogeneous isotropic turbulence specifies ds2(t) as the semi-reducible pseudo-Riemannian metric. This construction presents the template for the application of methods of Riemannian geometry in turbulence to observe, in particular, the deformation of length scales of turbulent motion localized within a singled out fluid volume of the flow in time. This also allows to use common concepts and technics of Lagrangian mechanics for a Lagrangian system (Mt, ds2(t)), Mt ? K3. Here the metric ds2(t), whose components are the correlation functions, evolves due to the von Kármán-Howarth equation. We review the explicit geometric realization of ds2(t) in K3 and present symmetries (or isometric motions in K3) of the metric ds2(t) which coincide with the sliding deformation of a surface arising under the geometric realization of ds2(t). We expose the fine structure of a Lie algebra associated with this symmetry transformation and construct the basis of differential invariants. Minimal generating set of differential invariants is derived. We demonstrate that the well-known Taylor microscale λg is a second-order differential invariant and show how λg can be obtained by the minimal generating set of differential invariants and the operators of invariant differentiation. Finally, we establish that there exists a nontrivial central extension of the infinite-dimensional Lie algebra constructed wherein the central charge is defined by the same bilinear skew-symmetric form c as for the Witt algebra which measures the number of internal degrees of freedom of the system. For turbulence, we give the asymptotic expansion of the transversal correlation function for the geometry generated by a quadratic form. 相似文献
996.
Bao Cheng-guang 《Frontiers of Physics in China》2006,1(1):92-96
A very effective tool, namely, the analytical expression of the fractional parentage coefficients (FPC), is introduced in
this paper to deal with the total spin states of N-body spinor bosonic systems, where N is supposed to be large and the spin of each boson is one. In particular, the analytical forms of the one-body and two-body
FPC for the total spin states with {N} and {N−1,1} permutation symmetries have been derived. These coefficients facilitate greatly the calculation of related matrix elements,
and they can be used even in the case of N→∞. They appear as a powerful tool for the establishment of an improved theory of spinor Bose-Einstein condensation, where
the eigenstates have the total spin S and its Z-component being both conserved. 相似文献
997.
998.
Cao Li-ke Liang Hong Peng Dan-tao Yang Tao Yue Rui-hong 《Frontiers of Physics in China》2007,2(2):234-237
Gaudin model is a very important integrable model in both quantum field theory and condensed matter physics. The integrability
of Gaudin models is related to classical r-matrices of simple Lie algebras and semi-simple Lie algebra. Since most of the constructions of Gaudin models works concerned
mainly on rational and trigonometric Gaudin algebras or just in a particular Lie algebra as an alternative to the matrix entry
calculations often presented, in this paper we give our calculations in terms of a basis of the typical Lie algebra, A
n
, B
n
, C
n
, D
n
, and we calculate a classical r-matrix for the elliptic Gaudin system with spin.
相似文献
999.
Wide spectral white light emitting diodes have been designed and grown on a sapphire substrate by using a metal-organic chemical vapor deposition system. Three quantum wells with blue-light-emitting, green-light-emitting and red-light-emitting structures were grown according to the design. The surface morphology of the film was observed by using atomic force microscopy. The films were characterized by their photoluminescence measurements. X-ray diffraction θ/2θ scan spectroscopy was carried out on the multi-quantum wells. The secondary fringes of the symmetric ω/2θ X-ray diffraction scan peaks indicate that the thicknesses and the alloy compositions of the individual quantum wells are repeatable throughout the active region. The room temperature photoluminescence spectra of the structures indicate that the white light emission of the multi-quantum wells is obtained. The light spectrum covers 400-700 nm, which is almost the whole visible light spectrum. 相似文献
1000.
We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor symmetric mixing patterns (e.g., bi-maximal and tri-bimaximal mixing patterns) can be easily accommodated at relatively low energy scales, which is well within the reach of running and forthcoming experiments (e.g., the LHC). 相似文献