Entangling power of baker's map: Role of symmetries

The quantum baker map possesses two symmetries: a canonical "spatial" symmetry, and a time-reversal symmetry. We show that, even when these features are taken into account, the asymptotic entangling power of the baker's map does not always agree with the predictions of random matrix theory. We have verified that the dimension of the Hilbert space is the crucial parameter which determines whether the entangling properties of the baker are universal or not. For power-of-two dimensions, i.e., qubit systems, an anomalous entangling power is observed; otherwise the behavior of the baker is consistent with random matrix theories. We also derive a general formula that relates the asymptotic entangling power of an arbitrary unitary with properties of its reduced eigenvectors.Comment: 5 page

Quantum revival patterns from classical phase-space trajectories

A general semiclassical method in phase space based on the final value representation of the Wigner function is considered that bypasses caustics and the need to root-search for classical trajectories. We demonstrate its potential by applying the method to the Kerr Hamiltonian, for which the exact quantum evolution is punctuated by a sequence of intricate revival patterns. The structure of such revival patterns, lying far beyond the Ehrenfest time, is semiclassically reproduced and revealed as a consequence of constructive and destructive interferences of classical trajectories.Comment: 7 pages, 6 figure

Quantum Baker Maps for Spiraling Chaotic Motion

We define a coupling of two baker maps through a pi/2 rotation both in position and in momentum. The classical trajectories thus exhibit spiraling, or loxodromic motion, which is only possible for conservative maps of at least two degrees of freedom. This loxodromic baker map is still hyperbolic, that is, fully chaotic. Quantization of this map follows on similar lines to other generalized baker maps. It is found that the eigenvalue spectrum for quantum loxodromic baker map is far removed from those of the canonical random matrix ensembles. An investigation of the symmetries of the loxodromic baker map reveals the cause of this deviation from the Bohigas-Giannoni-Schmit conjecture

Periodic orbit bifurcations and scattering time delay fluctuations

We study fluctuations of the Wigner time delay for open (scattering) systems which exhibit mixed dynamics in the classical limit. It is shown that in the semiclassical limit the time delay fluctuations have a distribution that differs markedly from those which describe fully chaotic (or strongly disordered) systems: their moments have a power law dependence on a semiclassical parameter, with exponents that are rational fractions. These exponents are obtained from bifurcating periodic orbits trapped in the system. They are universal in situations where sufficiently long orbits contribute. We illustrate the influence of bifurcations on the time delay numerically using an open quantum map.Comment: 9 pages, 3 figures, contribution to QMC200

Statistical bounds on the dynamical production of entanglement

We present a random-matrix analysis of the entangling power of a unitary operator as a function of the number of times it is iterated. We consider unitaries belonging to the circular ensembles of random matrices (CUE or COE) applied to random (real or complex) non-entangled states. We verify numerically that the average entangling power is a monotonic decreasing function of time. The same behavior is observed for the "operator entanglement" --an alternative measure of the entangling strength of a unitary. On the analytical side we calculate the CUE operator entanglement and asymptotic values for the entangling power. We also provide a theoretical explanation of the time dependence in the CUE cases.Comment: preprint format, 14 pages, 2 figure

On the classical-quantum correspondence for the scattering dwell time

Using results from the theory of dynamical systems, we derive a general expression for the classical average scattering dwell time, tau_av. Remarkably, tau_av depends only on a ratio of phase space volumes. We further show that, for a wide class of systems, the average classical dwell time is not in correspondence with the energy average of the quantum Wigner time delay.Comment: 5 pages, 1 figur

Comparación de fórmulas chilenas e internacionales para valorar el arbolado urbano

Ponce-Donoso, M (reprint author), Univ Talca, Fac Ciencias Forestales, Casilla 747, Talca, Chile.The appraisal of urban trees is a practice adopted in diverse cities of world. This survey compared international formulae: Council of Tree Landscape Appraiser (CTLA), Burnley, Helliwell and Standard Tree Evaluation Method (STEM) and three Chilean methods applied in municipalities of Concepcion, La Pintana, Maip (COPIMA), Nunoa and Penalolen, in 14 different trees located in Talca city (Chile). The objective was to identify the differences and similarities of the monetary result in the application of these formulae, which was realized by a professional. These were analyzed using a non parametric variance test of Kruskal - Wallis and the multiple comparisons Duncan test. It was possible to determine that the Chilean formulae did not present statistically significant differences with the international formulae of Burnley and CTLA; whereas Penalolen and COPIMA formulae did not present any difference when contrasted with Helliwell. In addition, the STEM formula presented differences with all the Chilean analyzed formulae. In the valuation by tree, statistically significant differences were obtained, which showed the independence of the used formula. The exception was when being applied to emblematic species or to species that stand-out in some amenity. Likewise, it was observed that the basic value continues having a high impact in the appraisal final result and the use of the statistical test applied allows extending this type of analyses