Optimal asymptotic cloning machines

We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at the single-clone level, still holds when all clones are examined globally. We conjecture that the answer is affirmative and present a large amount of evidence supporting our conjecture, developing techniques to derive optimal asymptotic cloners and proving their equivalence with estimation in virtually all scenarios considered in the literature. Our analysis covers the case of arbitrary finite sets of states, arbitrary families of coherent states, arbitrary phase- and multiphase-covariant sets of states, and two-qubit maximally entangled states. In all these examples we observe that the optimal asymptotic fidelity enjoys a universality property, as its scaling does not depend on the specific details of the set of input states, but only on the number of parameters needed to specify them.Comment: 27 + 9 pages, corrected one observation about cloning of maximally entangled state

Adiabatic Cooling with Non-Abelian Anyons

We show in this Letter that the ground state degeneracy associated with the presence of non-Abelian anyons can be probed by using an adiabatic cooling process based on the non-Abelian entropy. In particular, we show that when the number of such anyons is increased adiabatically at sufficiently low temperatures, the non-Abelian liquid undergoes cooling, whereas heating occurs in the Abelian case. Estimates are provided for the cooling power produced by the non-Abelian anyon refrigerator, and its implementation in non-Abelian fractional quantum Hall liquids is discussed

Diffusion-convection function of cosmic rays

The fundamental properties and some numerical results of the solution of the diffusion equation of an impulsive cosmic-ray point source in an uniform, unbounded and spherically symmetrical moving medium is presented. The diffusion-convection(D-C) function is an elementary composite function of the solution of the D-C equation for the particles injected impulsively from a diffusive point source into the medium. It is the analytic solution derived by the dimensional method for the propagation equation of solar cosmic rays in the heliosphere, i.e. the interplanetary space. Because of the introduction of convection effect of solar wind, a nonhomogeneous term appears in the propagation equation, it is difficult to express its solution in terms of the ordinary special functions. The research made so far has led to a solution containing only the first order approximation of the convection effect

Intention recognition for gaze controlled robotic minimally invasive laser ablation

Eye tracking technology has shown promising results for allowing hands-free control of robotically-mounted cameras and tools. However existing systems present only limited capabilities in allowing the full range of camera motions in a safe, intuitive manner. This paper introduces a framework for the recognition of surgeon intention, allowing activation and control of the camera through natural gaze behaviour. The system is resistant to noise such as blinking, while allowing the surgeon to look away safely at any time. Furthermore, this paper presents a novel approach to control the translation of the camera along its optical axis using a combination of eye tracking and stereo reconstruction. Combining eye tracking and stereo reconstruction allows the system to determine which point in 3D space the user is fixating, enabling a translation of the camera to achieve the optimal viewing distance. In addition, the eye tracking information is used to perform automatic laser targeting for laser ablation. The desired target point of the laser, mounted on a separate robotic arm, is determined with the eye tracking thus removing the need to manually adjust the laser's target point before starting each new ablation. The calibration methodology used to obtain millimetre precision for the laser targeting without the aid of visual servoing is described. Finally, a user study validating the system is presented, showing clear improvement with median task times under half of those of a manually controlled robotic system

The Effective Lagrangian of Three Dimensional Quantum Chromodynamics

We consider the low energy limit of three dimensional Quantum Chromodynamics with an even number of flavors. We show that Parity is not spontaneously broken, but the global (flavor) symmetry is spontaneously broken. The low energy effective lagrangian is a nonlinear sigma model on the Grassmannian. Some Chern--Simons terms are necessary in the lagrangian to realize the discrete symmetries correctly. We consider also another parametrization of the low energy sector which leads to a three dimensional analogue of the Wess--Zumino--Witten--Novikov model. Since three dimensional QCD is believed to be a model for quantum anti--ferromagnetism, our effective lagrangian can describe their long wavelength excitations (spin waves).Comment: 18 page

Three Dimensional Quantum Chromodynamics

The subject of this talk was the review of our study of three ($2+1$) dimensional Quantum Chromodynamics. In our previous works, we showed the existence of a phase where parity is unbroken and the flavor group $U(2n)$ is broken to a subgroup $U(n)\times U(n)$. We derived the low energy effective action for the theory and showed that it has solitonic excitations with Fermi statistic, to be identified with the three dimensional ``baryon''. Finally, we studied the current algebra for this effective action and we found a co-homologically non trivial generalization of Kac-Moody algebras to three dimensions.Comment: 7 pages, Plain TEX, talk presented by S.G. Rajeev at the XXVI INTERNATIONAL CONFERENCE ON HIGH ENERGY PHYSICS, DALLAS TX AUG. 199

Baryons as Solitons in Three Dimensional Quantum Chromodynamics

We show that baryons of three dimensional Quantum Chromodynamics can be understood as solitons of its effective lagrangian. In the parity preserving phase we study, these baryons are fermions for odd $N_c$ and bosons for even $N_c$, never anyons. We quantize the collective variables of the solitons and there by calculate the flavor quantum numbers, magnetic moments and mass splittings of the baryon. The flavor quantum numbers are in agreement with naive quark model for the low lying states. The magnetic moments and mass splittings are smaller in the soliton model by a factor of $\log {F_\pi\over N_c m_\pi}$. We also show that there is a dibaryon solution that is an analogue of the deuteron. These solitons can describe defects in a quantum anti--ferromagnet.Comment: 22 pages + 4 figures (figures not included, postscript files available upon request

The Longitudinal Variation of Equatorial Waves due to Propagation on a Varying Zonal Flow

The general 1D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behavior are found, depending on the sign of the group velocity cg and a wave property B. For B positive, the wave energy and the wavenumber vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang occurs where cg goes to zero. However, for B negative, they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analyzed in detail using the theory. For nondispersive Kelvin waves, B reduces to 2, and an analytic solution is possible. For all the waves considered, B is positive, except for the westward-moving mixed Rossby–gravity (WMRG) wave, which can have negative B as well as positive B. Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper-tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However, the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic Oceans are generally not in accord with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher-latitude wave activity