Significance of Ghost Orbit Bifurcations in Semiclassical Spectra

Gutzwiller's trace formula for the semiclassical density of states in a chaotic system diverges near bifurcations of periodic orbits, where it must be replaced with uniform approximations. It is well known that, when applying these approximations, complex predecessors of orbits created in the bifurcation ("ghost orbits") can produce pronounced signatures in the semiclassical spectra in the vicinity of the bifurcation. It is the purpose of this paper to demonstrate that these ghost orbits themselves can undergo bifurcations, resulting in complex, nongeneric bifurcation scenarios. We do so by studying an example taken from the Diamagnetic Kepler Problem, viz. the period quadrupling of the balloon orbit. By application of normal form theory we construct an analytic description of the complete bifurcation scenario, which is then used to calculate the pertinent uniform approximation. The ghost orbit bifurcation turns out to produce signatures in the semiclassical spectrum in much the same way as a bifurcation of real orbits would.Comment: 20 pages, 6 figures, LATEX (IOP style), submitted to J. Phys.

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

Duality between quantum and classical dynamics for integrable billiards

We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the quantum wave vector spectrum. A semiclassical derivation and numerical calculations are presented in support of the results. These classical eigenmodes can be observed in physical experiments through the auto-correlation of the transmission coefficient of waves in quantum billiards. Exact classical trace formulas of the resolvent are derived for the rectangle, equilateral triangle, and circle billiards. We also establish a correspondence between the classical periodic orbit length spectrum and the quantum spectrum for integrable polygonal billiards.Comment: 12 pages, 4 figure

Congruences associated with inverse transversals

An inverse transversal of a regular semigroup $S$ is an inverse subsemigroup of $S$ that contains a unique inverse $x^\circ$ of every element $x$ of $S$. Here we consider the congruences on such a semigroup, considered as an algebra of type (2, 1). The structure of such semigroups being known, with 'building bricks' the inverse subsemigroup $S^\circ$ and the sub-bands $I = \{xx^\circ; x\in S\},\Lambda = \{x^\circ x; x\in S\}$, we investigate how congruences on $S$ are related to congruences on these building bricks

Application of two-parameter dynamical replica theory to retrieval dynamics of associative memory with non-monotonic neurons

The two-parameter dynamical replica theory (2-DRT) is applied to investigate retrieval properties of non-monotonic associative memory, a model which lacks thermodynamic potential functions. 2-DRT reproduces dynamical properties of the model quite well, including the capacity and basin of attraction. Superretrieval state is also discussed in the framework of 2-DRT. The local stability condition of the superretrieval state is given, which provides a better estimate of the region in which superretrieval is observed experimentally than the self-consistent signal-to-noise analysis (SCSNA) does.Comment: 16 pages, 19 postscript figure

The Optical System for the Large Size Telescope of the Cherenkov Telescope Array

The Large Size Telescope (LST) of the Cherenkov Telescope Array (CTA) is designed to achieve a threshold energy of 20 GeV. The LST optics is composed of one parabolic primary mirror 23 m in diameter and 28 m focal length. The reflector dish is segmented in 198 hexagonal, 1.51 m flat to flat mirrors. The total effective reflective area, taking into account the shadow of the mechanical structure, is about 368 m$^2$. The mirrors have a sandwich structure consisting of a glass sheet of 2.7 mm thickness, aluminum honeycomb of 60 mm thickness, and another glass sheet on the rear, and have a total weight about 47 kg. The mirror surface is produced using a sputtering deposition technique to apply a 5-layer coating, and the mirrors reach a reflectivity of $\sim$94% at peak. The mirror facets are actively aligned during operations by an active mirror control system, using actuators, CMOS cameras and a reference laser. Each mirror facet carries a CMOS camera, which measures the position of the light spot of the optical axis reference laser on the target of the telescope camera. The two actuators and the universal joint of each mirror facet are respectively fixed to three neighboring joints of the dish space frame, via specially designed interface plate.Comment: In Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherlands. All CTA contributions at arXiv:1508.0589

Pair of Heavy-Exotic-Quarks at LHC

We study the production and signatures of heavy exotic quarks pairs at LHC in the framework of the vector singlet model (VSM), vector doublet model (VDM) and fermion-mirror-fermion (FMF) model. The pair production cross sections for the electroweak and strong sector are computed.Comment: 7 pages, 6 figures. accept at Int. Jour. of Mod. Phy