Two-particle scattering theory for anyons

We consider potential scattering theory of a nonrelativistic quantum mechanical 2-particle system in R^2 with anyon statistics. Sufficient conditions are given which guarantee the existence of wave operators and the unitarity of the S-matrix. As examples the rotationally invariant potential well and the delta-function potential are discussed in detail. In case of a general rotationally invariant potential the angular momentum decomposition leads to a theory of Jost functions. The anyon statistics parameter gives rise to an interpolation for angular momenta analogous to the Regge trajectories for complex angular momenta. Levinson's theorem is adapted to the present context. In particular we find that in case of a zero energy resonance the statistics parameter can be determined from the scattering phase.Comment: 42 pages of RevTex and 5 figures (included

Apparatus for aiding a pilot in avoiding a midair collision between aircraft

An apparatus for aiding a pilot in avoiding a midair collision between aircraft is described. A protected aircraft carries a transmitter, a transponder, a receiver, and a data processor; and an intruding cooperating aircraft carries a transponder. The transmitter of the protected aircraft continuously transmits a signal to the transponders of all intruding aircraft. The transponder of each of the intruding aircraft adds the altitude of the intruding aircraft to the signal and transmits it back to the receiver of the protected aircraft. The receiver selects only the signal from the most hazardous intruding aircraft and applies it to the data processor. From this selected signal the data processor determines the closing velocity between the protected and intruding aircraft, the range between the two aircraft, their altitude difference and the time to a possible collision

Perturbative test of single parameter scaling for 1D random media

Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance is equal to the Lyapunov exponent. We settle discussions about its validity for a wide class of models by proving that, away from anomalies, single parameter scaling holds to lowest order perturbation theory in the disorder strength. However, it is generically violated at higher order. This is explicitely exhibited for the Anderson model.Comment: minor corrections to previous version, to appear in Annales H. Poincar

Stabilization not for certain and the usefulness of bounds

Stabilization is still a somewhat controversial issue concerning its very existence and also the precise conditions for its occurrence. The key quantity to settle these questions is the ionization probability, for which hitherto no computational method exists which is entirely agreed upon. It is therefore very useful to provide various consistency criteria which have to be satisfied by this quantity, whose discussion is the main objective of this contribution. We show how the scaling behaviour of the space leads to a symmetry in the ionization probability, which can be exploited in the mentioned sense. Furthermore, we discuss how upper and lower bounds may be used for the same purpose. Rather than concentrating on particular analytical expressions we obtained elsewhere for these bounds, we focus in our discussion on the general principles of this method. We illustrate the precise working of this procedure, its advantages, shortcomings and range of applicability. We show that besides constraining possible values for the ionization probability these bounds, like the scaling behaviour, also lead to definite statements concerning the physical outcome. The pulse shape properties which have to be satitisfied for the existence of asymptotical stabilization is the vanishing of the total classical momentum transfer and the total classical displacement and not smoothly switched on and off pulses. Alternatively we support our results by general considerations in the Gordon-Volkov perturbation theory and explicit studies of various pulse shapes and potentials including in particular the Coulomb- and the delta potential.Comment: 12 pages Late

Analytical treatment of stabilization

We present a summarizing account of a series of investigations whose central topic is to address the question whether atomic stabilization exists in an analytical way. We provide new aspects on several issues of the matter in the theoretical context when the dynamics is described by the Stark Hamiltonian. The main outcome of these studies is that the governing parameters for this phenomenon are the total classical momentum transfer and the total classical displacement. Whenever these two quantities vanish, asymptotically weak stabilization does exist. For all other situations we did not find any evidence for stabilization. We found no evidence that strong stabilization might occur. Our results agree qualitatively with the existing experimental findings

An FPGA-Based System for Tracking Digital Information Transmitted via Peer-to-Peer Protocols

This thesis addresses the problem of identifying and tracking digital information that is shared using peer-to-peer file transfer and Voice over IP (VoIP) protocols. The goal of the research is to develop a system for detecting and tracking the illicit dissemination of sensitive government information using file sharing applications within a target network, and tracking terrorist cells or criminal organizations that are covertly communicating using VoIP applications. A digital forensic tool is developed using an FPGA-based embedded software application. The tool is designed to process file transfers using the BitTorrent peer-to-peer protocol and VoIP phone calls made using the Session Initiation Protocol (SIP). The tool searches a network for selected peer-to-peer control messages using payload analysis and compares the unique identifier of the file being shared or phone number being used against a list of known contraband files or phone numbers. If the identifier is found on the list, the control packet is added to a log file for later forensic analysis. Results show that the FPGA tool processes peer-to-peer packets of interest 92% faster than a software-only configuration and is 99.0% accurate at capturing and processing BitTorrent Handshake messages under a network traffic load of at least 89.6 Mbps. When SIP is added to the system, the probability of intercept for BitTorrent Handshake messages remains at 99.0% and the probability of intercept for SIP control packets is 97.6% under a network traffic load of at least 89.6 Mbps, demonstrating that the tool can be expanded to process additional peer-to-peer protocols with minimal impact on overall performance