Controlling Phase Space Caustics in the Semiclassical Coherent State Propagator

The semiclassical formula for the quantum propagator in the coherent state representation $$ is not free from the problem of caustics. These are singular points along the complex classical trajectories specified by $\mathbf{z}'$, $\mathbf{z}''$ and $T$ where the usual quadratic approximation fails, leading to divergences in the semiclassical formula. In this paper we derive third order approximations for this propagator that remain finite in the vicinity of caustics. We use Maslov's method and the dual representation proposed in Phys. Rev. Lett. {\bf 95}, 050405 (2005) to derive uniform, regular and transitional semiclassical approximations for coherent state propagator in systems with two degrees of freedom.Comment: 24 pages, to appear in Ann. of Phy

On the propagation of semiclassical Wigner functions

We establish the difference between the propagation of semiclassical Wigner functions and classical Liouville propagation. First we re-discuss the semiclassical limit for the propagator of Wigner functions, which on its own leads to their classical propagation. Then, via stationary phase evaluation of the full integral evolution equation, using the semiclassical expressions of Wigner functions, we provide the correct geometrical prescription for their semiclassical propagation. This is determined by the classical trajectories of the tips of the chords defined by the initial semiclassical Wigner function and centered on their arguments, in contrast to the Liouville propagation which is determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the one set to print and differs from the previous one (07 Nov 2001) by the addition of two references, a few extra words of explanation and an augmented figure captio

The Automobile Industry and The Mexico-Us Free Trade Agreement

This paper considers the likely effect on the automobile industry of a free trade agreement between the U.S. and Mexico. As there are currently large restrictions on imports into Mexico, one important outcome of a free trade agreement would be the opening of the Mexican market to U.S. producers. This is consistent with the history of the international auto industry and the fact that the U.S.-Canada Auto Pact opened a new, large market to U.S. manufacturers. The current state of the Mexican auto industry is considered in great detail, suggesting that the Mexican industry will continue to prosper, increasing output but also relying heavily on production from U.S. owned plants and on inputs imported from the U.S. and Canada. However, much of the existing domestically oriented industry is likely to be replaced by other North American producers. Finally, an econometric demand analysis implies that economic growth together with declines in prices to world levels could rapidly expand the size of the Mexican auto market. The free trade agreement represents an opportunity for product diversification and rationalization in the auto industry.

Qcompiler: quantum compilation with CSD method

In this paper, we present a general quantum computation compiler, which maps any given quantum algorithm to a quantum circuit consisting a sequential set of elementary quantum logic gates based on recursive cosine-sine decomposition. The resulting quantum circuit diagram is provided by directly linking the package output written in LaTex to Qcircuit.tex $$. We illustrate the use of the Qcompiler package through various examples with full details of the derived quantum circuits. Besides its generality and simplicity, Qcompiler produces quantum circuits which reflect the symmetry of the systems under study

Una perspectiva del Banco Mundial

El Banco Mundial aporta cualidades características al papel que puede desempeñar en promover la transición del ámbito humanitario al del desarrollo y está aumentando de manera significativa su compromiso con el desplazamiento forzado

Decoherence of Semiclassical Wigner Functions

The Lindblad equation governs general markovian evolution of the density operator in an open quantum system. An expression for the rate of change of the Wigner function as a sum of integrals is one of the forms of the Weyl representation for this equation. The semiclassical description of the Wigner function in terms of chords, each with its classically defined amplitude and phase, is thus inserted in the integrals, which leads to an explicit differential equation for the Wigner function. All the Lindblad operators are assumed to be represented by smooth phase space functions corresponding to classical variables. In the case that these are real, representing hermitian operators, the semiclassical Lindblad equation can be integrated. There results a simple extension of the unitary evolution of the semiclassical Wigner function, which does not affect the phase of each chord contribution, while dampening its amplitude. This decreases exponentially, as governed by the time integral of the square difference of the Lindblad functions along the classical trajectories of both tips of each chord. The decay of the amplitudes is shown to imply diffusion in energy for initial states that are nearly pure. Projecting the Wigner function onto an orthogonal position or momentum basis, the dampening of long chords emerges as the exponential decay of off-diagonal elements of the density matrix.Comment: 23 pg, 2 fi

Genetic parameters for milk mineral content and acidity predicted by mid-infrared spectroscopy in Holstein–Friesian cows

peer-reviewedThis article was first published in animal, Volume 9, Issue 05, May 2015, pp 775-780 © The Animal Consortium 2015The aim of the present study was to estimate genetic parameters for calcium (Ca), phosphorus (P) and titratable acidity (TA) in bovine milk predicted by mid-IR spectroscopy (MIRS). Data consisted of 2458 Italian Holstein−Friesian cows sampled once in 220 farms. Information per sample on protein and fat percentage, pH and somatic cell count, as well as test-day milk yield, was also available. (Co)variance components were estimated using univariate and bivariate animal linear mixed models. Fixed effects considered in the analyses were herd of sampling, parity, lactation stage and a two-way interaction between parity and lactation stage; an additive genetic and residual term were included in the models as random effects. Estimates of heritability for Ca, P and TA were 0.10, 0.12 and 0.26, respectively. Positive moderate to strong phenotypic correlations (0.33 to 0.82) existed between Ca, P and TA, whereas phenotypic weak to moderate correlations (0.00 to 0.45) existed between these traits with both milk quality and yield. Moderate to strong genetic correlations (0.28 to 0.92) existed between Ca, P and TA, and between these predicted traits with both fat and protein percentage (0.35 to 0.91). The existence of heritable genetic variation for Ca, P and TA, coupled with the potential to predict these components for routine cow milk testing, imply that genetic gain in these traits is indeed possible

Solovay-Kitaev Decomposition Strategy for Single-Qubit Channels

Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using single-qubit gates and the controlled-NOT (CNOT). Our approach uses the decomposition of the single-qubit channel into a convex combination of "quasiextreme" channels. Previous techniques for simulating general single-qubit channels would require as many as 20 CNOT gates, whereas ours only needs one, bringing it within the range of current experiments

A semiclassical approach to the Dirac equation

We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the transport of the spin degrees of freedom along the trajectories which can be understood geometrically as parallel transport in a vector bundle with SU(2) holonomy. Furthermore, we give an interpretation in terms of a classical spin vector that is transported along the trajectories and whose dynamics, dictated by the equation of Thomas precession, gives rise to dynamical and geometric phases every orbit is weighted by. We also present an analogous approach to the Pauli equation which we analyse in two different limits