A time-dependent perturbative analysis for a quantum particle in a cloud chamber

We consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \in \mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.Comment: 23 page

On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles

We consider a non relativistic quantum system consisting of $K$ heavy and $N$ light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential $\alpha V$. No interaction is assumed among particles of the same kind. Choosing an initial state in a product form and assuming $\alpha$ sufficiently small we characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. In the case K=1 the result is extended to arbitrary $\alpha$. The proof relies on a perturbative analysis and exploits a generalized version of the standard dispersive estimates for the Schr\"{o}dinger group. Exploiting the asymptotic formula, it is also outlined an application to the problem of the decoherence effect produced on a heavy particle by the interaction with the light ones.Comment: 38 page

An intuitive introduction to the evolution of physical systems

We outline a unified introduction to the general problem of dynamics intended for a high-school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of 1) geometric diagrams, 2) a discretized version of the equations of motion and 3) a simplified form of computation and analysis of their solutions. The aim is to allow students to approach theoretical features as well as computational aspects of the evolution equations through the use of spreadsheets, a work environment students are usually familiar with and an ideal tool for an intuitive approach to recursive algorithms. The proposal was presented to an audience composed of students of University courses of Physics teaching and to high-school Science teachers

Mesoscale models and approximate solutions for solids containing clouds of voids

For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of mesoscale approximations. There are no assumptions of periodicity involved in the description of the geometry of the domain. The size of the perforations is small compared to the minimal separation between neighboring defects and here we discuss a class of problems in perforated domains, which are not covered by the homogenization approximations. The mesoscale approximations presented here are uniform. Explicit asymptotic formulas are supplied with the remainder estimates. Numerical illustrations, demonstrating the efficiency of the asymptotic approach developed here, are also given

Sindbad: A new operational service for a safer leisure and boating navigation

The SINDBAD- Leisure and Boating Safety Navigation - project goal is the development of an advanced operational service to support navigation in a specific area. The first prototype covers the Ligurian Sea (a very busy touristic area in the North Mediterranean Sea) It develops an ICT Service Infrastructure to provide innovative intelligent automation functions and to develop customized services, accessible by your mobile device, for conducting a boat and avoiding any kind of risk ensuring the best degree of comfort

Gentle Perturbations of the Free Bose Gas I

It is demonstrated that the thermal structure of the noncritical free Bose Gas is completely described by certain periodic generalized Gaussian stochastic process or equivalently by certain periodic generalized Gaussian random field. Elementary properties of this Gaussian stochastic thermal structure have been established. Gentle perturbations of several types of the free thermal stochastic structure are studied. In particular new models of non-Gaussian thermal structures have been constructed and a new functional integral representation of the corresponding euclidean-time Green functions have been obtained rigorously.Comment: 51 pages, LaTeX fil

Cretaceous intraplate contraction in Southern Patagonia: A far-field response to changing subduction dynamics?

The origin, extent, and timing of intraplate contraction in Patagonia are among the least understood geological processes of southern South America. Particularly, the intraplate Deseado fold-thrust belt (FTB), located in the Patagonian broken foreland (47°–48°300 S), is one of the most enigmatic areas. In this belt, time constraints on tectonic events are limited and synorogenic deposits have not been documented so far. Furthermore, the driving mechanism for intraplate contraction remains unknown. In this study, we carried out a structural and sedimentological analysis. We report the first syntectonic deposits in this area in the Baqueró (Aptian) and Chubut (Cenomanian/Campanian) groups and a newly found unit referred to as the Albian beds (109.9 ± 1.5 Ma). Thus, several contractional stages in late Aptian, Albian, and Cenomanian-Campanian are then inferred. We suggest that the Deseado FTB constituted the southernmost expression of the early Patagonian broken foreland in Cretaceous times. Additionally, we analyzed the spatiotemporal magmatic arc behavior as a proxy of dynamic changes in the Andean subduction during determined stages of intraplate contraction. We observe a significant arc broadening from ~121 to 82 Myr and magmatic quiescence after ~67 Ma. This is interpreted as a slab shallowing to flattening process. Far-field tectonic forces would have been produced by increased plate coupling linked to the slab flattening as indirectly indicated by the correlation between Cretaceous arc expansion and intraplate contraction. Finally, the tectonic evolution of the Deseado FTB favors studies supporting inception of Andean shortening since Cretaceous times.Fil: Gianni, Guido Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto Geofísico Sismológico Volponi; ArgentinaFil: Navarrete Granzotto, César Rodrigo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de la Patagonia "San Juan Bosco"; ArgentinaFil: Liendo, Ingrid Florencia. Universidad Nacional de la Patagonia "San Juan Bosco"; ArgentinaFil: Díaz, Marianela Ximena Yasmin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Geología; ArgentinaFil: Gimenez, Mario Ernesto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto Geofísico Sismológico Volponi; ArgentinaFil: Encinas, Alfonso. Universidad de Concepción; ChileFil: Folguera Telichevsky, Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Estudios Andinos "Don Pablo Groeber". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Estudios Andinos "Don Pablo Groeber"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias Geológicas; Argentin

Convergence to SPDEs in Stratonovich form

We consider the perturbation of parabolic operators of the form $\partial_t+P(x,D)$ by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the solution to the random equation is affected by the randomness at the leading order. We show that, when the dimension is smaller than the order of the elliptic pseudo-differential operator $P(x,D)$, the perturbed parabolic equation admits a solution given by a Duhamel expansion. Moreover, as the correlation length of the potential vanishes, we show that the latter solution converges in distribution to the solution of a stochastic parabolic equation with a multiplicative term that should be interpreted in the Stratonovich sense. The theory of mild solutions for such stochastic partial differential equations is developed. The behavior described above should be contrasted to the case of dimensions that are larger than or equal to the order of the elliptic pseudo-differential operator $P(x,D)$. In the latter case, the solution to the random equation converges strongly to the solution of a homogenized (deterministic) parabolic equation as is shown in the companion paper [2]. The stochastic model is therefore valid only for sufficiently small space dimensions in this class of parabolic problems.Comment: 21 page

Aspects of Quantum Gravity in de Sitter Spaces

In these lectures we give a review of recent attempts to understand quantum gravity on de Sitter spaces. In particular, we discuss the holographic correspondence between de Sitter gravity and conformal field theories proposed by Hull and by Strominger, and how this may be reconciled with the finite-dimensional Hilbert space proposal by Banks and Fischler. Furthermore we review the no-go theorems that forbid an embedding of de Sitter spaces in string theory, and discuss how they can be circumvented. Finally, some curious issues concerning the thermal nature of de Sitter space are elucidated.Comment: 36+1 pages, 5 Postscript figures, introduction and section 6 extended, further references, final version to appear in JCA