The Exact Correspondence between Phase Times and Dwell Times in a Symmetrical Quantum Tunneling Configuration

The general and explicit relation between the phase time and the dwell time for quantum tunneling or scattering is investigated. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, here we demonstrate that these two distinct transit time definitions give connected results where, however, the phase time (group delay) accurately describes the exact position of the scattered particles. The analytical difficulties that arise when the stationary phase method is employed for obtaining phase (traversal) times are all overcome. Multiple wave packet decomposition allows us to recover the exact position of the reflected and transmitted waves in terms of the phase time, which, in addition to the exact relation between the phase time and the dwell time, leads to right interpretation for both of them.Comment: 11 pages, 2 figure

Waiting times between orders and trades in double-auction markets

In this paper, the survival function of waiting times between orders and the corresponding trades in a double-auction market is studied both by means of experiments and of empirical data. It turns out that, already at the level of order durations, the survival function cannot be represented by a single exponential, thus ruling out the hypothesis of constant activity during trading. This fact has direct consequences for market microstructural models. They must include such a non-exponential behaviour to be realistic.Comment: 19 pages, 3 figures, paper presented at the WEHIA 2005, Colchester, U

Predicting vehicular travel times by modeling heterogeneous influences between arterial roads

Predicting travel times of vehicles in urban settings is a useful and tangible quantity of interest in the context of intelligent transportation systems. We address the problem of travel time prediction in arterial roads using data sampled from probe vehicles. There is only a limited literature on methods using data input from probe vehicles. The spatio-temporal dependencies captured by existing data driven approaches are either too detailed or very simplistic. We strike a balance of the existing data driven approaches to account for varying degrees of influence a given road may experience from its neighbors, while controlling the number of parameters to be learnt. Specifically, we use a NoisyOR conditional probability distribution (CPD) in conjunction with a dynamic bayesian network (DBN) to model state transitions of various roads. We propose an efficient algorithm to learn model parameters. We propose an algorithm for predicting travel times on trips of arbitrary durations. Using synthetic and real world data traces we demonstrate the superior performance of the proposed method under different traffic conditions.Comment: 13 pages, conferenc

Modeling the connection between ultraviolet and infrared galaxy populations across cosmic times

Using a phenomenological approach, we self-consistently model the redshift evolution of the ultraviolet (UV) and infrared (IR) luminosity functions across cosmic time, as well as a range of observed IR properties of UV-selected galaxy population. This model is an extension of the 2SFM (2 star-formation modes) formalism, which is based on the observed "main-sequence" of star-forming galaxies, i.e. a strong correlation between their stellar mass and their star formation rate (SFR), and a secondary population of starbursts with an excess of star formation. The balance between the UV light from young, massive stars and the dust-reprocessed IR emission is modeled following the empirical relation between the attenuation (IRX for IR excess hereafter) and the stellar mass, assuming a scatter of 0.4\,dex around this relation. We obtain a good overall agreement with the measurements of the IR luminosity function up to z~3 and the UV luminosity functions up to z~6, and show that a scatter on the IRX-M relation is mandatory to reproduce these observables. We also naturally reproduce the observed, flat relation between the mean IRX and the UV luminosity at LUV>109.5 L⊙. Finally, we perform predictions of the UV properties and detectability of IR-selected samples and the vice versa, and discuss the results in the context of the UV-rest-frame and sub-millimeter surveys of the next decade

the in-between times

I have grown up around cameras. My parents are documentary filmmakers. Early on, I understood how a photograph can capture reality. As a child, I also spent time in my grandfather’s darkroom, watching him as he went through the process of printing negatives. I watched as the images emerged in the chemicals. It seemed magical to me. A gnarled tree limb, a snow drift, a strange image emerging out of a series of torn papers on a wall. I remember him explaining the steps of making a picture. However, it was only when I arrived at Bard College that I began to think about how each step in the photographic process can affect the content and intention of an image. It was more than simply capturing reality. In The View Camera class I took with An My-Lê I learned how to split-filter print (a printing technique that allows for separate exposure of highlights and shadows). This opened my eyes to the ability of the printing process as a means to express artistically. I realized that this is the process by which night photography is possible, as well as other high-contrast instances. Once I had this foundation, I found myself thinking, while I was actually shooting, about the photograph in its final form – a print object. Instead of trying to document the world exactly how it was, I was interested in creating a different world, a transformed world, within my photographs. The word photography, translates in Greek to, ‘drawing with light’. In my practice, I use light to shape space as a way to develop and observe found mysteries. I am interested in seemingly mundane moments that can be elevated by the light. How can I use what already exists in the world to my advantage? I have always been curious about weather and, consequently, the shape-shifting of light weather can cause. In the winter, after a snowfall, the entire ground becomes an indirect light source. Through the rain, the light gets refracted, distorted, and softened. And on foggy days, digital imaging technology is able to see objects in the distance much easier than the human eye. There is something beautiful about the fact that the digital camera is sometimes better at seeing in certain weather conditions than our eyes. The photograph has the ability to transform, flatten, and decontextualize space. I use this to create instances of disorientation within my work. the in-between times is about the relationship between light, the world, and the unique way the camera sees. I have chosen to photograph these moments that feel in-between reality, latency, and an unknown magical possibility. My goal was to use my new understanding and control over the photographic process and lighting to move beyond simple documentation toward creating emotional experiences for myself and the viewer

Escape from the potential well: competition between long jumps and long waiting times

Within a concept of the fractional diffusion equation and subordination, the paper examines the influence of a competition between long waiting times and long jumps on the escape from the potential well. Applying analytical arguments and numerical methods, we demonstrate that the presence of long waiting times distributed according to a power-law distribution with a diverging mean leads to very general asymptotic properties of the survival probability. The observed survival probability asymptotically decays like a power-law whose form is not affected by the value of the exponent characterizing the power-law jump length distribution. It is demonstrated that this behavior is typical of and generic for systems exhibiting long waiting times. We also show that the survival probability has a universal character not only asymptotically but also at small times. Finally, it is indicated which properties of the first passage time density are sensitive to the exact value of the exponent characterizing the jump length distribution.Comment: 8 pages, 10 figure