Diffusion Process in a Flow

We establish circumstances under which the dispersion of passive contaminants in a forced, deterministic or random, flow can be consistently interpreted as a Markovian diffusion process. In case of conservative forcing the repulsive case only, $\vec{F}=\vec{\nabla }V$ with $V(\vec{x},t)$ bounded from below, is unquestionably admitted by the compatibility conditions. A class of diffusion processes is exemplified, such that the attractive forcing is allowed as well, due to an appropriate compensation coming from the "pressure" term. The compressible Euler flows form their subclass, when regarded as stochastic processes. We establish circumstances under which the dispersion of passive contaminants in a forced, deterministic or random, flow can be consistently interpreted as a Markovian diffusion process. In case of conservative forcing the repulsive case only, $\vec{F}=\vec{\nabla }V$ with $V(\vec{x},t)$ bounded from below, is unquestionably admitted by the compatibility conditions. A class of diffusion processes is exemplified, such that the attractive forcing is allowed as well, due to an appropriate compensation coming from the "pressure" term. The compressible Euler flows form their subclass, when regarded as stochastic processes.Comment: 10 pages, Late

Decays of metastable vacua in SQCD

The decay rates of metastable SQCD vacua in ISS-type models, both towards supersymmetric vacua as well as towards other nonsupersymmetric configurations arising in theories with elementary spectators, are estimated numerically in the semiclassical approximation by computing the corresponding multifield bounce configurations. The scaling of the bounce action with respect to the most relevant dimensionless couplings and ratios of scales is analyzed. In the case of the decays towards the susy vacua generated by nonperturbative effects, the results confirm previous analytical estimations of this scaling, obtained by assuming a triangular potential barrier. The decay rates towards susy vacua generated by R-symmetry breaking interactions turn out to be more than sufficiently suppressed for the phenomenologically relevant parameter range, and their behavior in this regime differs from analytic estimations valid for parametrically small scale ratios. It is also shown that in models with spectator fields, even though the decays towards vacua involving nonzero spectator VEVs don't have a strong parametric dependence on the scale ratios, the ISS vacuum can still be made long-lived in the presence of R-symmetry breaking interactions.Comment: 22 pages, 7 figure

L\'evy-Schr\"odinger wave packets

We analyze the time--dependent solutions of the pseudo--differential L\'evy--Schr\"odinger wave equation in the free case, and we compare them with the associated L\'evy processes. We list the principal laws used to describe the time evolutions of both the L\'evy process densities, and the L\'evy--Schr\"odinger wave packets. To have self--adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible L\'evy noises with laws symmetric under change of sign of the independent variable. We then show several examples of the characteristic behavior of the L\'evy--Schr\"odinger wave packets, and in particular of the bi-modality arising in their evolutions: a feature at variance with the typical diffusive uni--modality of both the L\'evy process densities, and the usual Schr\"odinger wave functions.Comment: 41 pages, 13 figures; paper substantially shortened, while keeping intact examples and results; changed format from "report" to "article"; eliminated Appendices B, C, F (old names); shifted Chapters 4 and 5 (old numbers) from text to Appendices C, D (new names); introduced connection between Relativistic q.m. laws and Generalized Hyperbolic law

Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of {\it Genius loci}. Global structural properties of a city can be characterized by the thermodynamical parameters calculated in the random walks problem.Comment: 44 pages, 22 figures, 2 table

Acute gastroenteritis in Hong Kong: A population-based telephone survey

A population-based telephone survey of acute gastroenteritis (AG) was conducted in Hong Kong from August 2006 to July 2007. Study subjects were recruited through random digit-dialling with recruitments evenly distributed weekly over the 1-year period. In total, 3743 completed questionnaires were obtained. An AG episode is defined as diarrhoea 3 times or any vomiting in a 24-h period during the 4 weeks prior to interview, in the absence of known non-infectious causes. The prevalence of AG reporting was 7%. An overall rate of 091 (95% CI 081-101) episodes per person-year was observed with women having a slightly higher rate (094, 95% CI 079-108) than men (088, 95% CI 073-104). The mean duration of illness was 36 days (s.d.=552). Thirty-nine percent consulted a physician, 19% submitted a stool sample for testing, and 26% were admitted to hospital. Of the subjects aged 15 ≥ years, significantly more of those with AG reported eating raw oysters (OR 24, 95% CI 13-44), buffet meals (OR 18, 95% CI 13-25), and partially cooked beef (OR 18, 95% CI 12-27) in the previous 4 weeks compared to the subjects who did not report AG. AG subjects were also more likely to have had hot pot, salad, partially cooked or raw egg or fish, sushi, sashimi, and snacks bought at roadside in the previous 4 weeks. This first population-based study on the disease burden of AG in Asia showed that the prevalence of AG in Hong Kong is comparable to that experienced in the West. The study also revealed some risky eating practices that are more prevalent in those affected with AG. Copyright © 2009 Cambridge University Press.published_or_final_versio

Quantum measurement in a family of hidden-variable theories

The measurement process for hidden-configuration formulations of quantum mechanics is analysed. It is shown how a satisfactory description of quantum measurement can be given in this framework. The unified treatment of hidden-configuration theories, including Bohmian mechanics and Nelson's stochastic mechanics, helps in understanding the true reasons why the problem of quantum measurement can succesfully be solved within such theories.Comment: 16 pages, LaTeX; all special macros are included in the file; a figure is there, but it is processed by LaTe

Comment on "Why quantum mechanics cannot be formulated as a Markov process"

In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie's "measurement probabilities" \it are \rm the transition probabilities of a stochastic process, then the process must have an invariant (time independent) probability measure. Alternatively, if we demand the probability measure of the process to follow the quantally implemented (via the Born statistical postulate) evolution, then we arrive at the jump process which \it can \rm be interpreted as a Markov process if restricted to a suitable duration time. However, there is no corresponding Markov process consistent with the $Z_2$ event space assumption, if we require its existence for all times $t\in R_+$.Comment: Latex file, resubm. to Phys. Rev.

Burgers velocity fields and dynamical transport processes

We explore a connection of the forced Burgers equation with the Schr\"{o}dinger (diffusive) interpolating dynamics in the presence of deterministic external forces. This entails an exploration of the consistency conditions that allow to interpret dispersion of passive contaminants in the Burgers flow as a Markovian diffusion process. In general, the usage of a continuity equation $\partial_t\rho =-\nabla (\vec{v}\rho)$, where $\vec{v}=\vec{v}(\vec{x},t)$ stands for the Burgers field and $\rho$ is the density of transported matter, is at variance with the explicit diffusion scenario. Under these circumstances, we give a complete characterisation of the diffusive matter transport that is governed by Burgers velocity fields. The result extends both to the approximate description of the transport driven by an incompressible fluid and to motions in an infinitely compressible medium.Comment: Latex fil

Dynamical Evolution in Noncommutative Discrete Phase Space and the Derivation of Classical Kinetic Equations

By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generators of motion and transition probability distributions on the lattice; (b) the emergence of the time direction on the basis of the encoding of probabilities in the lattice structure; (c) the general prescription for the observables' evolution in analogy with classical dynamics. We show that, in the limit of a continuous description, these results lead to the time evolution of observables in terms of (the adjoint of) generalized Fokker-Planck equations having: (1) a diffusion coefficient given by the limit of the correlation matrix of the lattice coordinates with respect to the probability distribution associated with the generator of motion; (2) a drift term given by the microscopic average of the dynamical equations in the present context. These results are applied to 1D and 2D problems. Specifically, we derive: (I) The equations of diffusion, Smoluchowski and Fokker-Planck in velocity space, thus indicating the way random walk models are incorporated in the present context; (II) Kramers' equation, by further assuming that, motion is deterministic in coordinate spaceComment: LaTeX2e, 40 pages, 1 Postscript figure, uses package epsfi

Controlled quantum evolutions and transitions

We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or nonstationary quantum states. In particular we discuss the stationary states of quantum systems with singular velocity fields. We introduce a technique that allows to realize arbitrary evolutions ruled by these equations, to account for controlled quantum transitions. The method is illustrated by presenting the detailed treatment of the transition probabilities and of the controlling time-dependent potentials associated to the transitions between the stationary, the coherent, and the squeezed states of the harmonic oscillator. Possible extensions to anharmonic systems and mixed states are briefly discussed and assessed.Comment: 24 pages, 4 figure