Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space

We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips $S$-matrix is unitarily related to the $S$-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable $\sigma$ of the Lax-Phillips theory. Analytic continuation in $\sigma$ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.Comment: Plain TeX, 26 pages. Minor revision

Measurement Theory in Lax-Phillips Formalism

It is shown that the application of Lax-Phillips scattering theory to quantum mechanics provides a natural framework for the realization of the ideas of the Many-Hilbert-Space theory of Machida and Namiki to describe the development of decoherence in the process of measurement. We show that if the quantum mechanical evolution is pointwise in time, then decoherence occurs only if the Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in Liouville space), then the decoherence may occur even for closed systems. These conclusions apply as well to the general problem of mixing of states.Comment: 14 pages, IASSNS-HEP 93/6

The Index Of Narrative Microstructure: A Clinical Tool For Analyzing School-Age Children's Narrative Performances

Purpose: This research was conducted to develop a clinical tool-the Index of Narrative Microstructure (INMIS)-that would parsimoniously account for important microstructural aspects of narrative production for school-age children. The study provides field test age- and grade-based INMIS values to aid clinicians in making normative judgments about microstructural aspects of pupils' narrative performance. Method: Narrative samples using a single-picture elicitation context were collected from 250 children age 5-12 years and then transcribed and segmented into T-units. A T-unit consists of a single main clause and any dependent constituents. The narrative transcripts were then coded and analyzed to document a comprehensive set of microstructural indices. Results: Factor analysis indicated that narrative microstructure consisted of 2 moderately related factors. The Productivity factor primarily comprised measures of word output, lexical diversity, and T-unit output. The Complexity factor comprised measures of syntactic organization, with mean length of T-units in words and proportion of complex T-units loading most strongly. Principal components analysis was used to provide a linear combination of 8 variables to approximate the 2 factors. Formulas for calculating a student's performance on the 2 factors using 8 narrative measures are provided. Conclusions: This study provided a method for professionals to calculate INMIS scores for narrative Productivity and Complexity for comparison against field test data for age (5- to 12-year-old) or grade (kindergarten to Grade 6) groupings. INMIS scores complement other tools in evaluating a child's narrative performance specifically and language abilities more generally.Communication Sciences and Disorder

Glassy states in lattice models with many coexisting crystalline phases

We study the emergence of glassy states after a sudden cooling in lattice models with short range interactions and without any a priori quenched disorder. The glassy state emerges whenever the equilibrium model possesses a sufficient number of coexisting crystalline phases at low temperatures, provided the thermodynamic limit be taken before the infinite time limit. This result is obtained through simulations of the time relaxation of the standard Potts model and some exclusion models equipped with a local stochastic dynamics on a square lattice.Comment: 12 pages, 4 figure

Approximate resonance states in the semigroup decomposition of resonance evolution

The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.Comment: LaTex 22 pages 3 figure

Hypercomplex quantum mechanics

The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective geometry of the weakly modular orthocomplemented lattice of propositions may be imbedded in a complex Hilbert space; this is the structure which has traditionally been used. This paper reviews some work which has been devoted to generalizing the target space of this imbedding to Hilbert modules of a more general type. In particular, detailed discussion is given of the simplest generalization of the complex Hilbert space, that of the quaternion Hilbert module.Comment: Plain Tex, 11 page

The biaxial nonlinear crystal BiB3O6 as a polarization entangled photon source using non-collinear type-II parametric down-conversion

We describe the full characterization of the biaxial nonlinear crystal BiB3O6 (BiBO) as a polarization entangled photon source using non-collinear type-II parametric down-conversion. We consider the relevant parameters for crystal design, such as cutting angles, polarization of the photons, effective nonlinearity, spatial and temporal walk-offs, crystal thickness and the effect of the pump laser bandwidth. Experimental results showing entanglement generation with high rates and a comparison to the well investigated beta-BaB2O4 (BBO) crystal are presented as well. Changing the down-conversion crystal of a polarization entangled photon source from BBO to BiBO enhances the generation rate as if the pump power was increased by more than three times. Such an improvement is currently required for the generation of multiphoton entangled states.Comment: 15 pages, 13 figures, published versio

Interplay of the volume and surface plasmons in the electron energy loss spectra of C60_{60}

The results of a joint experimental and theoretical investigation of the C60 collective excitations in the process of inelastic scattering of electrons are presented. The shape of the electron energy loss spectrum is observed to vary when the scattering angle increases. This variation arising due to the electron diffraction of the fullerene shell is described by a new theoretical model which treats the fullerene as a spherical shell of a finite width and accounts for the two modes of the surface plasmon and for the volume plasmon as well. It is shown that at small angles, the inelastic scattering cross section is determined mostly by the symmetric mode of the surface plasmon, while at larger angles, the contributions of the antisymmetric surface plasmon and the volume plasmon become prominent.Comment: 11 pages, 3 figure