CP Violation and Arrows of Time Evolution of a Neutral KK or BB Meson from an Incoherent to a Coherent State

We study the evolution of a neutral $K$ meson prepared as an incoherent equal mixture of $K^0$ and $\bar{K^0}$. Denoting the density matrix by \rho(t) = {1/2} N(t) [\1 + \vec{\zeta}(t) \cdot \vec{\sigma} ] , the norm of the state $N(t)$ is found to decrease monotonically from one to zero, while the magnitude of the Stokes vector $|\vec{\zeta}(t)|$ increases monotonically from zero to one. This property qualifies these observables as arrows of time. Requiring monotonic behaviour of $N(t)$ for arbitrary values of $\gamma_L, \gamma_S$ and $\Delta m$ yields a bound on the CP-violating overlap $\delta = \braket{K_L}{K_S}$, which is similar to, but weaker than, the known unitarity bound. A similar requirement on $|\vec{\zeta}(t)|$ yields a new bound, $\delta^2 < {1/2} (\frac{\Delta \gamma}{\Delta m}) \sinh (\frac{3\pi}{4} \frac{\Delta \gamma}{\Delta m})$ which is particularly effective in limiting the CP-violating overlap in the $B^0$-$\bar{B^0}$ system. We obtain the Stokes parameter $\zeta_3(t)$ which shows how the average strangeness of the beam evolves from zero to $\delta$. The evolution of the Stokes vector from $|\vec{\zeta}| = 0$ to $|\vec{\zeta}| = 1$ has a resemblance to an order parameter of a system undergoing spontaneous symmetry breaking.Comment: 13 pages, 6 figures. Inserted conon "." in title; minor change in text. To appear in Physical review

Performance and Stability of an Agile Tail-less MAV with Flexible Articulated Wings

This paper considers the problems of (a) modelling the ight mechanics of a tail-less MAV equipped with exible articulated wings, and (b) the analysis of its turning performance. The wings are assumed to have two degrees of freedom - heave and twist. They are assumed to be actuated from the root, which is the abstraction of an experimental control mechanism being developed by the authors. The dihedral and twist angles at the wing root are controlled. A novel actuator concept of axial tension to control wing stiffness has been explored in this paper. It is shown that axial tension in the wing has a significant effect on the turning performance of the aircraft, although the effect is not uniformly beneficial in nature. The effect of exibility on the steady state turning performance of the aircraft has been demonstrated by comparing it with that of a rigid aircraft, and with that of a similar aircraft possessing a wing with different elastic properties

Coordinate time and proper time in the GPS

The Global Positioning System (GPS) provides an excellent educational example as to how the theory of general relativity is put into practice and becomes part of our everyday life. This paper gives a short and instructive derivation of an important formula used in the GPS, and is aimed at graduate students and general physicists. The theoretical background of the GPS (see \cite{ashby}) uses the Schwarzschild spacetime to deduce the {\it approximate} formula, ds/dt\approx 1+V-\frac{|\vv|^2}{2}, for the relation between the proper time rate $s$ of a satellite clock and the coordinate time rate $t$. Here $V$ is the gravitational potential at the position of the satellite and \vv is its velocity (with light-speed being normalized as $c=1$). In this note we give a different derivation of this formula, {\it without using approximations}, to arrive at ds/dt=\sqrt{1+2V-|\vv|^2 -\frac{2V}{1+2V}(\n\cdot\vv)^2}, where \n is the normal vector pointing outward from the center of Earth to the satellite. In particular, if the satellite moves along a circular orbit then the formula simplifies to ds/dt=\sqrt{1+2V-|\vv|^2}. We emphasize that this derivation is useful mainly for educational purposes, as the approximation above is already satisfactory in practice.Comment: 5 pages, revised, over-over-simplified... Does anyone care that the GPS uses an approximate formula, while a precise one is available in just a few lines??? Physicists don'

Sum Rules for the Dirac Spectrum of the Schwinger Model

The inverse eigenvalues of the Dirac operator in the Schwinger model satisfy the same Leutwyler-Smilga sum rules as in the case of QCD with one flavor. In this paper we give a microscopic derivation of these sum rules in the sector of arbitrary topological charge. We show that the sum rules can be obtained from the clustering property of the scalar correlation functions. This argument also holds for other theories with a mass gap and broken chiral symmetry such as QCD with one flavor. For QCD with several flavors a modified clustering property is derived from the low energy chiral Lagrangian. We also obtain sum rules for a fixed external gauge field and show their relation with the bosonized version of the Schwinger model. In the sector of topological charge $\nu$ the sum rules are consistent with a shift of the Dirac spectrum away from zero by $\nu/2$ average level spacings. This shift is also required to obtain a nonzero chiral condensate in the massless limit. Finally, we discuss the Dirac spectrum for a closely related two-dimensional theory for which the gauge field action is quadratic in the the gauge fields. This theory of so called random Dirac fermions has been discussed extensively in the context of the quantum Hall effect and d-wave super-conductors.Comment: 41 pages, Late

On the resistivity at low temperatures in electron-doped cuprate superconductors

We measured the magnetoresistance as a function of temperature down to 20mK and magnetic field for a set of underdoped PrCeCuO (x=0.12) thin films with controlled oxygen content. This allows us to access the edge of the superconducting dome on the underdoped side. The sheet resistance increases with increasing oxygen content whereas the superconducting transition temperature is steadily decreasing down to zero. Upon applying various magnetic fields to suppress superconductivity we found that the sheet resistance increases when the temperature is lowered. It saturates at very low temperatures. These results, along with the magnetoresistance, cannot be described in the context of zero temperature two dimensional superconductor-to-insulator transition nor as a simple Kondo effect due to scattering off spins in the copper-oxide planes. We conjecture that due to the proximity to an antiferromagnetic phase magnetic droplets are induced. This results in negative magnetoresistance and in an upturn in the resistivity.Comment: Accepted in Phys. Rev.

Flight Mechanics of a Tail-less Articulated Wing Aircraft

This paper explores the flight mechanics of a Micro Aerial Vehicle (MAV) without a vertical tail. The key to stability and control of such an aircraft lies in the ability to control the twist and dihedral angles of both wings independently. Specifically, asymmetric dihedral can be used to control yaw whereas antisymmetric twist can be used to control roll. It has been demonstrated that wing dihedral angles can regulate sideslip and speed during a turn maneuver. The role of wing dihedral in the aircraft's longitudinal performance has been explored. It has been shown that dihedral angle can be varied symmetrically to achieve limited control over aircraft speed even as the angle of attack and flight path angle are varied. A rapid descent and perching maneuver has been used to illustrate the longitudinal agility of the aircraft. This paper lays part of the foundation for the design and stability analysis of an agile flapping wing aircraft capable of performing rapid maneuvers while gliding in a constrained environment

Practice pointer: Using the new UK-WHO growth charts

The new UK growth charts for children aged 0-4 years (designed using data from the new WHO standards) describe the optimal pattern of growth for all children, rather than the prevailing pattern in the UK (as with previous charts). The new charts are suitable for all ethnic groups and set breast feeding as the norm. UK children match the new charts well for length and height, but after age 6 months fewer children will be below the 2nd centile for weight or show weight faltering, and more will be above the 98th centile. The new charts look different: they have a separate preterm section, no lines between 0 and 2 weeks, and the 50th percentile is no longer emphasised. The charts give clear instructions on gestational correction, and there is a new chart for infants born before 32 weeks’ gestation. The instructions advise on when and how to measure and when a measurement or growth pattern is outside the normal range. The charts include a “look-up” tool for determining the body mass index centile from height and weight centiles without calculation and aid for predicting adult height. The charts and supporting educational materials can be downloaded from www.growthcharts.rcpch.ac.u

Akns Hierarchy, Self-Similarity, String Equations and the Grassmannian

In this paper the Galilean, scaling and translational self--similarity conditions for the AKNS hierarchy are analysed geometrically in terms of the infinite dimensional Grassmannian. The string equations found recently by non--scaling limit analysis of the one--matrix model are shown to correspond to the Galilean self--similarity condition for this hierarchy. We describe, in terms of the initial data for the zero--curvature 1--form of the AKNS hierarchy, the moduli space of these self--similar solutions in the Sato Grassmannian. As a byproduct we characterize the points in the Segal--Wilson Grassmannian corresponding to the Sachs rational solutions of the AKNS equation and to the Nakamura--Hirota rational solutions of the NLS equation. An explicit 1--parameter family of Galilean self--similar solutions of the AKNS equation and the associated solution to the NLS equation is determined.Comment: 25 pages in AMS-LaTe

A Riemann-Hilbert Problem for an Energy Dependent Schr\"odinger Operator

\We consider an inverse scattering problem for Schr\"odinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct symmetry classes. As an application we prove global existence theorems for the two distinct systems of partial differential equations $u_t+(u^2/2+w)_x=0, w_t\pm u_{xxx}+(uw)_x=0$ for suitably restricted, complementary classes of initial data