Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system $[ 1]$. We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states \`{a} la Gazeau-Klauder and those \`{a} la Klauder-Perelomov, we derive the generalized intelligent states in analytical ways

Generalized coherent and intelligent states for exact solvable quantum systems

The so-called Gazeau-Klauder and Perelomov coherent states are introduced for an arbitrary quantum system. We give also the general framework to construct the generalized intelligent states which minimize the Robertson-Schr\"odinger uncertainty relation. As illustration, the P\"oschl-Teller potentials of trigonometric type will be chosen. We show the advantage of the analytical representations of Gazeau-Klauder and Perelomov coherent states in obtaining the generalized intelligent states in analytical way

Views of the Universe

Man has been led to various views of the universe at various times in history. Here's how he sees it today

Are there any good digraph width measures?

Several different measures for digraph width have appeared in the last few years. However, none of them shares all the "nice" properties of treewidth: First, being \emph{algorithmically useful} i.e. admitting polynomial-time algorithms for all \MS1-definable problems on digraphs of bounded width. And, second, having nice \emph{structural properties} i.e. being monotone under taking subdigraphs and some form of arc contractions. As for the former, (undirected) \MS1 seems to be the least common denominator of all reasonably expressive logical languages on digraphs that can speak about the edge/arc relation on the vertex set.The latter property is a necessary condition for a width measure to be characterizable by some version of the cops-and-robber game characterizing the ordinary treewidth. Our main result is that \emph{any reasonable} algorithmically useful and structurally nice digraph measure cannot be substantially different from the treewidth of the underlying undirected graph. Moreover, we introduce \emph{directed topological minors} and argue that they are the weakest useful notion of minors for digraphs

SU(1,1)SU(1,1) and SU(2)SU(2) Perelomov number coherent states: algebraic approach for general systems

We study some properties of the $SU(1,1)$ Perelomov number coherent states. The Schr\"odinger's uncertainty relationship is evaluated for a position and momentum-like operators (constructed from the Lie algebra generators) in these number coherent states. It is shown that this relationship is minimized for the standard coherent states. We obtain the time evolution of the number coherent states by supposing that the Hamiltonian is proportional to the third generator $K_0$ of the $su(1,1)$ Lie algebra. Analogous results for the $SU(2)$ Perelomov number coherent states are found. As examples, we compute the Perelomov coherent states for the pseudoharmonic oscillator and the two-dimensional isotropic harmonic oscillator

Canonical Coherent States for the Relativistic Harmonic Oscillator

In this paper we construct manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given $SL(2,R)$ representation, once a change of variables $z\in C\rightarrow z_D \in$ unit disk is performed. We also introduce higher-order, relativistic creation and annihilation operators, \C,\Cc, with canonical commutation relation [\C,\Cc]=1 rather than the covariant one [\Z,\Zc]\approx Energy and naturally associated with the $SL(2,R)$ group. The canonical (relativistic) coherent states are then defined as eigenstates of \C. Finally, we construct a canonical, minimal representation in configuration space by mean of eigenstates of a canonical position operator.Comment: 11 LaTeX pages, final version, shortened and corrected, to appear in J. Math. Phy

Modern Michelson-Morley experiment using cryogenic optical resonators

We report on a new test of Lorentz invariance performed by comparing the resonance frequencies of two orthogonal cryogenic optical resonators subject to Earth's rotation over 1 year. For a possible anisotropy of the speed of light c, we obtain 2.6 +/- 1.7 parts in 10^15. Within the Robertson-Mansouri-Sexl test theory, this implies an isotropy violation parameter beta - delta - 1/2 of -2.2 +/- 1.5 parts in 10^9, about three times lower than the best previous result. Within the general extension of the standard model of particle physics, we extract limits on 7 parameters at accuracies down to a part in 10^15, improving the best previous result by about two orders of magnitude

Simultaneous minimum-uncertainty measurement of discrete-valued complementary observables

We have made the first experimental demonstration of the simultaneous minimum uncertainty product between two complementary observables for a two-state system (a qubit). A partially entangled two-photon state was used to perform such measurements. Each of the photons carries (partial) information of the initial state thus leaving a room for measurements of two complementary observables on every member in an ensemble.Comment: 4 pages, 4 figures, REVTeX, submitted to PR