Quantum corrections to conductivity for semiconductors with various structures

We study the magnetic field dependences of the conductivity in heavily doped, strongly disordered 2D quantum well structures within wide conductivity and temperature ranges. We show that the exact analytical expression derived in our previous paper [1], is in better agreement than the existing equation i.e. Hikami(et.al.,) expression [2,3], with the experimental data even in low magnetic field for which the diffusion approximation is valid. On the other hand from theoretical point of view we observe that our equation is also rich because it establishes a strong relationship between quantum corrections to the conductivity and the quantum symmetry su_{q}(2). It is shown that the quantum corrections to the conductivity is the trace of Green function made by a generator of su_{q}(2)algebra. Using this fact we show that the quantum corrections to the conductivity can be expressed as a sum of an infinite number of Feynman diagrams.Comment: 15 pages, 6 figures. To appear in International journal of modern physics

Large subgroups of simple groups

Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies the bound $|H|^3 \ge |G|$. In this note we determine all the large maximal subgroups of finite simple groups, and we establish an analogous result for simple algebraic groups (in this context, largeness is defined in terms of dimension). An application to triple factorisations of simple groups (both finite and algebraic) is discussed.Comment: 37 page