Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive

We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose positive partial transpose and e) are superpositive. Working with the Hilbert-Schmidt (Euclidean) measure we derive tight explicit two-sided bounds for the volumes of all five sets. A sample consequence is the fact that, as N increases, a generic positive map becomes not decomposable and, a fortiori, not completely positive. Due to the Jamiolkowski isomorphism, the results obtained for quantum maps are closely connected to similar relations between the volume of the set of quantum states and the volumes of its subsets (such as states with positive partial transpose or separable states) or supersets. Our approach depends on systematic use of duality to derive quantitative estimates, and on various tools of classical convexity, high-dimensional probability and geometry of Banach spaces, some of which are not standard.Comment: 34 pages in Latex including 3 figures in eps, ver 2: minor revision

On stochasticity in nearly-elastic systems

Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to stochasticity of its long-time behavior. Various ways to give a rigorous meaning to the last statement are considered. All of them, if applicable, lead to the same stochasticity which is described explicitly. So that the stochasticity of the long-time behavior is an intrinsic property of the deterministic systems.Comment: 35 pages, 12 figures, already online at Stochastics and Dynamic

Cauchy's formulas for random walks in bounded domains

Cauchy's formula was originally established for random straight paths crossing a body $B \subset \mathbb{R}^{n}$ and basically relates the average chord length through $B$ to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length travelled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in $B$. Similar results are obtained also for the average number of collisions performed by the walker in $B$, and an extension to absorbing media is discussed.Comment: 12 pages, 6 figure

Inicis de la radiologia odontoestomatológica a Catalunya

Un avens important en el camp de les Ciències de la Salut va ser la investigació sobre els raigs X, així com la seva posterior aplicació en l'odontologia. En aquest treball ens vàrem plantejar el fer un recull de les dades històriques de la Radiologia en l'Odontologia, centrant-nos a Catalunya, des dels inicis -a finals del segle XIX- fins el primer ters de l'actual segle, encara que la individualització del tema és totalment impossible i més en una matèria com aquesta tant interrelacionada

Evolució técnica dels raigs X i la seva influencia en la radiologia odonto-estomatologia a Catalunya (1895-1935)

El descobriment dels raigs X és un dels fets més importants de la història de les ciències, en el camp de la medicina suposa un nou camí diagnòstic, que ens permet explorar tot allò que no veiem. Un fet individual, que es convertí ben aviat en un model de col·laboració multidisciplinària. Aquest treball vol ser un modest homenatge a tots aquells homes, pioners, 'molts dels quals deixaren la seva vida en l'empresa', sense diferenciar l'especialitat que professaven de forma individual, tots eren simultàniament físics, enginyers, metges ... que gracies a la seva obra facilitaren i' evolució del radiodiagnòsti

Josep Boniquet i Colobrans, anys 1856-1914, en l'odontologia catalana de fa un segle

Va néixer a Girona I'any 1856 (existeixen dubtes repecte d'aquesta data: en alguns escrits consta 1858 i en altres 1860). El seu entorn familiar podríem catalogar-10 de classe mitjana. Pensem que es tracta del gran de dos germans, i fill de Ramon Boniquet