Hamilton's turns as visual tool-kit for designing of single-qubit unitary gates

Unitary evolutions of a qubit are traditionally represented geometrically as rotations of the Bloch sphere, but the composition of such evolutions is handled algebraically through matrix multiplication [of SU(2) or SO(3) matrices]. Hamilton's construct, called turns, provides for handling the latter pictorially through the as addition of directed great circle arcs on the unit sphere S$^2 \subset \mathbb{R}^3$, resulting in a non-Abelian version of the parallelogram law of vector addition of the Euclidean translation group. This construct is developed into a visual tool-kit for handling the design of single-qubit unitary gates. As an application, it is shown, in the concrete case wherein the qubit is realized as polarization states of light, that all unitary gates can be realized conveniently through a universal gadget consisting of just two quarter-wave plates (QWP) and one half-wave plate (HWP). The analysis and results easily transcribe to other realizations of the qubit: The case of NMR is obtained by simply substituting $\pi/2$ and $\pi$ pulses respectively for QWPs and HWPs, the phases of the pulses playing the role of the orientation of fast axes of these plates.Comment: 16 Pages, 14 Figures, Published versio

Dynamics of some constrained lattices

We consider the dynamics of lattices which have constrained constitutive units flexible in only their mutual orientations. A continuum description is derived through which it is shown that the models have zero shear velocity, free-particle like internal rotational modes and volume decreasing linearly with temperature. The relevance of modelsto a range of problems is pointed out.Comment: 5 pages, 2 EPS figure

A nonlinear-coherence receiver

Mathematical analysis and detailed study of generic model for coherent receiver has demonstrated that nonlinear coherence between given biphase-modulated input signal and supplied reference signal can be used in receivers to improve telecommunication systems

Data-aided carrier tracking loops

Power in composite signal sidebands is used to enhance signal-to-noise ratio in carrier tracking loop, thereby reducing radio loss and decreasing probability of receiver error. By adding quadrature channel to phase-lock-loop detector circuit of receiver, dc component can be fed back into carrier tracking loop

Coherent receiver employing nonlinear coherence detection for carrier tracking

The concept of nonlinear coherence employed in carrier tracking to improve telecommunications efficiency is disclosed. A generic tracking loop for a coherent receiver is shown having seven principle feedback signals which may be selectively added and applied to a voltage controlled oscillator to produce a reference signal that is phase coherent with a received carrier. An eighth feedback signal whose nonrandom components are coherent with the phase detected and filtered carrier may also be added to exploit the sideband power of the received signal. A ninth feedback signal whose nonrandom components are also coherent with the quadrature phase detected and filtered carrier could be additionally or alternatively included in the composite feedback signal to the voltage controlled oscillator

Detection and Implications of a Time-reversal breaking state in underdoped Cuprates

We present general symmetry considerations on how a Time-reversal breaking state may be detected by angle-resolved photoemission using circularly polarized photons as has been proposed earlier. Results of recent experiments utilizing the proposal in underdoped cuprates are analysed and found to be consistent in their symmetry and magnitude with a theory of the Copper-Oxides. These togather with evidence for a quantum critical point and marginal Fermi-liquid properties near optimum doping suggest that a valid microscopic theory of the phenomena in the cuprates has been found.Comment: A statement on detecting the Anyon state is added and some typos are subtracte

Status of the ILC Main Linac BPM R&D

An introduction and the status of R&D activities for a high-resolution, "cold" beam position monitor (BPM) and the related read-out electronics are discussed. Two different BPM detector concepts, to be attached to the SC quadrupole and located inside the ILC cryomodule, are currently under investigation: A resonant dipole-mode cavity-style BPM pickup, developed at Fermilab, and a re-entrant resonant coaxial waveguide BPM, designed by CEA-Saclay. While the 1.5 GHz dipole-mode cavity BPM is still in the R&D phase, the re-entrant BPM has already passed first beam tests, including its read-out system. Furthermore, the LAPP group is developing radiation tolerant digital read-out systems, which are tested at the CLIC test facility (CTF).Comment: LCWS / ILC08 conference contribution, 6 pages, 6 figure

Majoranas with and without a 'character': hybridization, braiding and Majorana number

In this paper we demonstrate under what conditions a pseudo-spin degree of freedom or character can be ascribed to the Majorana bound states (MBS) which can be created at the end of one dimensional non-interacting systems, corresponding to D, DIII and BDI in the usual classification scheme. We have found that such a character is directly related to the class of the topological superconductor and its description by a $\mathbb{Z}$, rather than a $\mathbb{Z}_2$, invariant which corresponds to the BDI class. We have also found that the DIII case with mirror symmetry, which supports multiple MBS, is in fact equivalent to the BDI class with an additional time-reversal symmetry. In all cases where a character can be given to the Majorana states we show how to construct the appropriate operator explicitly in various examples. We also examine the consequences of the Majorana character by considering possible hybridization of MBS brought into proximity and find that two MBS with the same character do not hybridize. Finally, we show that having this character or not has no consequence on the braiding properties of MBS.Comment: 10 pages, 1 figur

Perceptions and correlates of peer-victimization and bullying

The experiences of peer-victimization and bullying are often treated empirically as though they are conceptually indistinct. Both involve repeated aggression,but definitions of bullying additionally emphasize the importance of aggressor intent and imbalance of power between the aggressor and the victim (Olweus, 1978; Whitney & Smith, 1993). The present study aimed to examine the extent to which peer-victimization and bullying are empirically similar. The sample comprised 1,429 pupils (50.2% male) aged between 8 and 13 years attending mainstream Scottish schools. Self-report questionnaire assessing peer-victimization and bullying, copingstrategy use (WCCL: Hunter, 2000), situational appraisal and depressive symptomatology (Birleson, 1981). Almost one-third (30.7%) of pupils reported experiencing peer-victimization, and of these 38.1% (11.7% of whole sample) were categorized as victims of bullying. Victims of bullying perceived higher levels of threat and lower levels of perceived control. They also reported using more Wishful Thinking and Social Support coping strategies, but did not differ on Problem Focused coping. Bullied pupils also reported higher levels of depressive symptomatology. Peer-victimization and bullying appear to be qualitatively different experiences for children and adolescents, with bullying being the more serious phenomenon

Cellular automata models of traffic flow along a highway containing a junction

We examine various realistic generalizations of the basic cellular automaton model describing traffic flow along a highway. In particular, we introduce a {\em slow-to-start} rule which simulates a possible delay before a car pulls away from being stationary. Having discussed the case of a bare highway, we then consider the presence of a junction. We study the effects of acceleration, disorderness, and slow-to-start behavior on the queue length at the entrance to the highway. Interestingly, the junction's efficiency is {\it improved} by introducing disorderness along the highway, and by imposing a speed limit.Comment: to appear in J. Phys. A:Math.& General. 15 pages, RevTeX, 3 Postscript figure