Ab initio study of bilateral doping within the MoS2-NbS2 system

We present a systematic study on the stability and the structural and electronic properties of mixed molybdenum-niobium disulphides. Using density functional theory we investigate bilateral doping with up to 25 % of MoS2 (NbS2) by Nb (Mo) atoms, focusing on the precise arrangement of dopants within the host lattices. We find that over the whole range of considered concentrations, Nb doping of MoS2 occurs through a substitutional mechanism. For Mo in NbS2 both interstitial and substitutional doping can co-exist, depending upon the particular synthesis conditions. The analysis of the structural and electronic modifications of the perfect bulk systems due to the doping is presented. We show that substitutional Nb atoms introduce electron holes to the MoS2, leading to a semiconductor-metal transition. On the other hand, the Mo doping of Nb2, does not alter the metallic behavior of the initial system. The results of the present study are compared with available experimental data on mixed MoS2-NbS2 (bulk and nanoparticles).Comment: 7 pages, 6 figure

The universal Glivenko-Cantelli property

Let F be a separable uniformly bounded family of measurable functions on a standard measurable space, and let N_{[]}(F,\epsilon,\mu) be the smallest number of \epsilon-brackets in L^1(\mu) needed to cover F. The following are equivalent: 1. F is a universal Glivenko-Cantelli class. 2. N_{[]}(F,\epsilon,\mu)0 and every probability measure \mu. 3. F is totally bounded in L^1(\mu) for every probability measure \mu. 4. F does not contain a Boolean \sigma-independent sequence. It follows that universal Glivenko-Cantelli classes are uniformity classes for general sequences of almost surely convergent random measures.Comment: 26 page

Data Set Models and Exponential Families in Statistical Physics and Beyond

The exponential family of models is defined in a general setting, not relying on probability theory. Some results of information geometry are shown to remain valid. Exponential families both of classical and of quantum mechanical statistical physics fit into the new formalism. Other less obvious applications are predicted. For instance, quantum states can be modeled as points in a classical phase space and the resulting model belongs to the exponential family

Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur