Existence, uniqueness and approximation of a stochastic Schr\"odinger equation: the diffusive case

Recent developments in quantum physics make heavy use of so-called "quantum trajectories." Mathematically, this theory gives rise to "stochastic Schr\"odinger equations", that is, perturbation of Schr\"odinger-type equations under the form of stochastic differential equations. But such equations are in general not of the usual type as considered in the literature. They pose a serious problem in terms of justifying the existence and uniqueness of a solution, justifying the physical pertinence of the equations. In this article we concentrate on a particular case: the diffusive case, for a two-level system. We prove existence and uniqueness of the associated stochastic Schr\"odinger equation. We physically justify the equations by proving that they are a continuous-time limit of a concrete physical procedure for obtaining a quantum trajectory.Comment: Published in at http://dx.doi.org/10.1214/08-AOP391 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

1/f noise in graphene

We present a novel and comprehensive model of 1/f noise in nanoscale graphene devices that accounts for the unusual and so far unexplained experimental characteristics. We find that the noise power spectral density versus carrier concentration of single-layer sheet devices has a behavior characterized by a shape going from the M to the Gamma type as the material inhomogeneity increases, whereas the shape becomes of V type in bilayer sheet devices for any inhomogeneity, or of M type at high carrier concentration. In single-layer nanoribbons, instead, the ratio of noise to resistance versus the latter quantity is approximately constant, whereas in the bilayer case it exhibits a linear decrease on a logarithmic scale as resistance increases and its limit for zero resistance equals the single-layer value. Noise at the Dirac point is much greater in single-layer than in bilayer devices and it increases with temperature. The origin of 1/f noise is attributed to the traps in the device and to their relaxation time dispersion. The coupling of trap charge fluctuations with the electrode current is computed according to the electrokinematics theorem, by taking into account their opposite effects on electrons and holes as well as the device inhomogeneities. The results agree well with experiments.Comment: 27 pages, 5 figures. The final publication is available at link.springer.co

Optimizing memory management for optimistic simulation with reinforcement learning

Simulation is a powerful technique to explore complex scenarios and analyze systems related to a wide range of disciplines. To allow for an efficient exploitation of the available computing power, speculative Time Warp-based Parallel Discrete Event Simulation is universally recognized as a viable solution. In this context, the rollback operation is a fundamental building block to support a correct execution even when causality inconsistencies are a posteriori materialized. If this operation is supported via checkpoint/restore strategies, memory management plays a fundamental role to ensure high performance of the simulation run. With few exceptions, adaptive protocols targeting memory management for Time Warp-based simulations have been mostly based on a pre-defined analytic models of the system, expressed as a closed-form functions that map system's state to control parameters. The underlying assumption is that the model itself is optimal. In this paper, we present an approach that exploits reinforcement learning techniques. Rather than assuming an optimal control strategy, we seek to find the optimal strategy through parameter exploration. A value function that captures the history of system feedback is used, and no a-priori knowledge of the system is required. An experimental assessment of the viability of our proposal is also provided for a mobile cellular system simulation

Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case

In quantum physics, recent investigations deal with the so-called "quantum trajectory" theory. Heuristic rules are usually used to give rise to "stochastic Schrodinger equations" which are stochastic differential equations of non-usual type describing the physical models. These equations pose tedious problems in terms of mathematical justification: notion of solution, existence, uniqueness, justification... In this article, we concentrate on a particular case: the Poisson case. Random measure theory is used in order to give rigorous sense to such equations. We prove existence and uniqueness of a solution for the associated stochastic equation. Furthermore, the stochastic model is physically justified by proving that the solution can be obtained as a limit of a concrete discrete time physical model.Comment: 35 page

X-ray emission from early-type galaxies

The past decade has seen a large progress in the X-ray investigation of early-type galaxies of the local universe, and first attempts have been made to reach redshifts z>0 for these objects, thanks to the high angular resolution and sensitivity of the satellites Chandra and XMM-Newton. Major advances have been obtained in our knowledge of the three separate contributors to the X-ray emission, that are the stellar sources, the hot gas and the galactic nucleus. Here a brief outline of the main results is presented, pointing out the questions that remain open, and finally discussing the prospects to solve them with a wide area X-ray survey mission such as WFXT.Comment: 6 pages, 4 figures; to appear in the Proceedings of "The Wide Field X-ray Telescope Workshop", held in Bologna, Italy, Nov. 25-26 2009, published by Memorie della Societ\`a Astronomica Italiana 2010 (arXiv:1010.5889

Hijacker: Efficient static software instrumentation with applications in high performance computing: Poster paper

Static Binary Instrumentation is a technique that allows compile-time program manipulation. In particular, by relying on ad-hoc tools, the end user is able to alter the program's execution flow without affecting its overall semantic. This technique has been effectively used, e.g., to support code profiling, performance analysis, error detection, attack detection, or behavior monitoring. Nevertheless, efficiently relying on static instrumentation for producing executables which can be deployed without affecting the overall performance of the application still presents technical and methodological issues. In this paper, we present Hijacker, an open-source customizable static binary instrumentation tool which is able to alter a program's execution flow according to some user-specified rules, limiting the execution overhead due to the code snippets inserted in the original program, thus enabling for the exploitation in high performance computing. The tool is highly modular and works on an internal representation of the program which allows to perform complex instrumentation tasks efficiently, and can be additionally extended to support different instruction sets and executable formats without any need to modify the instrumentation engine. We additionally present an experimental assessment of the overhead induced by the injected code in real HPC applications. © 2013 IEEE