اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGroup theoretical methods to construct the graphene
107
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, the tiling of the Euclidean plane with regular hexagons whose vertices are occupied by carbon atoms is called the graphene. We describe six different ways to generate the graphene by the means of group theory. There are two ways starting from the triangular lattice of Lie algebra $A_2$ and $G_2$, and one way for each of the Lie algebras $B_3$, $C_3$ and $A_3$, by projecting the weight system of their lowest representation to the hexagons of $A_2$. Colouring of the graphene is presented. Changing from one colouring to another is called phase transition. Multistep refinements of the graphene are described.
قيم البحث
اقرأ أيضاً
We utilize group-theoretical methods to develop a matrix representation of differential operators that act on tensors of any rank. In particular, we concentrate on the matrix formulation of the curl operator. A self-adjoint matrix of the curl operato
r is constructed and its action is extended to a complex plane. This scheme allows us to obtain properties, similar to those of the traditional curl operator.
Adopting a purely group-theoretical point of view, we consider the star product of functions which is associated, in a natural way, with a square integrable (in general, projective) representation of a locally compact group. Next, we show that for th
is (implicitly defined) star product explicit formulae can be provided. Two significant examples are studied in detail: the group of translations on phase space and the one-dimensional affine group. The study of the first example leads to the Groenewold-Moyal star product. In the second example, the link with wavelet analysis is clarified.
An integrable Hamiltonian system presents monodromy if the action-angle variables cannot be defined globally. We consider a classical system with azimuthal symmetry and explore the topology structure of its phase space. Based on the behavior of close
d orbits around singular points or regions of the energy-momentum plane, a semi-theoretical method is derived to detect classical monodromy. The validity of the monodromy test is numerically illustrated for several systems with azimuthal symmetry.
An overview is given on recent developments in the affine Weyl group approach to Painleve equations and discrete Painleve equations, based on the joint work with Y. Yamada and K. Kajiwara.
In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equation
s of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equation satisfies. Our result is a natural generalization of the paper {bf Chaturvedi et al} (arXiv : 0706.0964 [quant-ph]).
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
