Temperature dependence of photoluminescence in amorphous Si1-xCx:H films

We have investigated the temperature dependence of photoluminescence in hydrogenated amorphous silicon-carbon alloys a-Si_1-xC_x:H prepared by glow discharge in the low-power regime. The radiative recombination process, due to photocarriers trapped on band-edge states, is in competition with the thermal escape of the photocarriers into the mobility bands. The model gives a quantitative fit with experiment, without any adjustable parameter, provided the width of the band-edge distribution of states is taken as the width of the conduction band only (measured by “photo-induced infra-red spectroscopy”) and not as the Urbach energy, as it is usually assumed.     

A lightning initiation mechanism: application to a thunderstorm electrification model

The use of numerical models has greatly increased our understanding of the electrical and microphysical process within electrified clouds. We use the University of Washington, 1.5-dimensional thunderstorm model to examine the effects of including a runaway electron based lightning initiation mechanism. We find that this mechanism can significantly alter the electrification history of modeled storms and produce vertical electric field profiles that are very similar to those of observed storms. To cite this article: R. Solomon et al., C. R. Physique 3 (2002) 1325–1333.     

Combinatorial solutions to normal ordering of bosons

We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions — the Stirling and Bell numbers, Bell polynomials and Dobinski relations — lead to calculational tools, which allow to find explicitly normally ordered forms for a large class of operator functions. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Dobiński relations and ordering of boson operators

We introduce a generalization of the Dobiński relation, through which we define a family of Bell-type numbers and polynomials. Such generalized Dobiński relations are coherent state matrix elements of expressions involving boson ladder operators. This may be used in order to obtain normally ordered forms of polynomials in creation and annihilation operators, both if the latter satisfy canonical and deformed commutation relations.     

Group Theoretic Properties of the Group of Computable Automorphisms of a Countable Dense Linear Order

We compare Aut(Q), the classical automorphism group of a countable dense linear order, with Aut _c (Q), the group of all computable automorphisms of such an order. They have a number of similarities, including the facts that every element of each group is a commutator and each group has exactly three nontrivial normal subgroups. However, the standard proofs of these facts in Aut(Q) do not work for Aut _c (Q). Also, Aut(Q) has three fundamental properties which fail in Aut _c (Q): it is divisible, every element is a commutator of itself with some other element, and two elements are conjugate if and only if they have isomorphic orbital structures.     

Theta function transformation formulas and the Weil representation

A short proof is given that the theta functional is invariant under the Weil representation, and the explicit determination of the eighth root of unity which arises is also shown. Namely, the action of the Weil representation on the theta functional is described as the limit of integration against a specialization of the symplectic theta function as the symplectic variable approaches a cusp. The invariance is then a consequence of the automorphic nature of this theta function, coupled with the fact that in the limit it acts as the reproducing kernel for a certain lattice. Using results of Stark and Styer, this also allows one to determine the root of unity involved.