Bounds on Localized Modes in the Crystal Impurity Problem

Using general properties of the crystal site representation normal mode matrix, we provide some very simple bounds on localized modes in simple, body-centered and face-centered cubic crystals with substitutional point defects. We derive a trace condition constraint on the net change in crystal eigenfrequencies caused by the introduction of a defect, with the condition being a completely general one which holds for any combination of central and non-central crystal force-constants and for all-neighbor interactions. Using this condition we show that the sufficient condition for producing localized modes in an arbitrary cubic crystal by a mass change at the defect site is that the defect mass be less than one half of that of the host atom mass which it replaces, and that the sufficient condition for producing localized modes in an arbitrary cubic crystal by force-constant changes alone is that the defect site self force-constant be greater than twice that of the pure crystal self force-constant of the host atom which it replaces.Comment: 25 pages, 3 figures, revtex4. Updated version contains much more general bounds than original versio

Bose-Einstein Correlations for Mixed Neutral Mesons

Correlations are shown to arise in nonidentical mixed-particle pairs like $K^o \bar K^o$ when observed in identical decay modes like $K_S K_S$ in multiparticle final states containing many partial waves. No enhancement is found in any single partial wave and all partial wave analyses of the s-wave threshold resonance $a_o$ and $f_o$ should give the same results for all decay modes. In CP violation experiments where $B^o - \bar B^o$ pairs are inclusively produced and correlated decays into $\psi K_S$ and leptonic modes are observed, the CP-violating lepton asymmetry is enhanced by a factor of two in the kinematic region where Bose enhancement occurs.Comment: 11 page

Framework for Identification of Neutral B Mesons

We introduce a method for the study of CP-violating asymmetries in tagged states of neutral $B$ mesons with arbitrary coherence properties. A set of time-dependent measurements is identified which completely specifies the density matrix of the initial state in a two-component space with basis vectors $B^0$ and $\overline B^0$, and permits a determination of phases in the Cabibbo-Kobayashi-Maskawa matrix. For a given tagging configuration, the measurement of decays both to flavor eigenstates and to CP eigenstates provides the necessary information.Comment: Submitted to Phys. Rev. Letters. 8 pages, LaTeX, Technion-PH-93-31 / EFI 93-3

Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model

We introduce a novel semiclassical approach to the Lipkin model. In this way the well-known phase transition arising at the critical value of the coupling is intuitively understood. New results -- showing for strong couplings the existence of a threshold energy which separates deformed from undeformed states as well as the divergence of the density of states at the threshold energy -- are explained straightforwardly and in quantitative terms by the appearance of a double well structure in a classical system corresponding to the Lipkin model. Previously unnoticed features of the eigenstates near the threshold energy are also predicted and found to hold.Comment: 4 pages, 2 figures, to appear in PR

The Ursinus Weekly, April 27, 1936

Plans completed for open house • Junior week-end is great success • Ball team takes two during week • Glee Club to present annual spring concert • Coaches select cast for Curtain Club play • Installation of WSGA officers held last week • York alumni hold annual banquet and choose officers • E.C. Wagner, Ursinus alumnus, addresses chemical society • Yost\u27s review of Lantern continued from last week • Music clubs to give opera during commencement week • Pageant groups to rehearse according to given schedule • Brotherhood of St. Paul elects new officers for coming year • Herrick B. Young to speak to IRC to-morrow eve • Muhlenberg easily defeats grizzly tennis team, 6-1 • Grizzly J.V.\u27s lose first game of season to Hill School, 7-6 • Track records corrections • Brodbeck tops ball league • TKA names new membershttps://digitalcommons.ursinus.edu/weekly/1959/thumbnail.jp

The Ursinus Weekly, February 22, 1937

Men debaters go on tour of four colleges; women are busy at home throughout week • Student council lays penalties • Sororities pledge flushed freshmen after hectic week • Congressman Ditter to speak at forum • Large crowd hails Curtain Club show • Try-outs for junior play to be held this evening • College receives $18,000 in Sarah Leiphart will • Y panel group discusses negro-versus-white topic • Sociological survey journey is planned for after Easter • Professor Baker speaks at vespers in Bomberger • Yost reviews McClure-Holzknecht Shakespeare set; second vol., just printed, wins graphic arts award • Philadelphia alumni plan banquet; committee meets • Placement bureau reports jobs for seniors, grads • Contest for radio script writing is opened to all major colleges • Hedgerow, praised before, comes to perform again • Lehigh begins new course named general education • Lantern issue will appear in March; copy is solicited • Don Kellett\u27s cubs defeat Penn, 36-30 • Haverford gets close one, Hopkins wins, as injuries still plague bear matmen • Mules hand varsity team its eighth league defeat • Drexel six go down, 34-7, before co-eds\u27 onslaught • Both teams lose battles at Albright on Wednesday • Brotherhood of St. Paul meets; appoints two deputationshttps://digitalcommons.ursinus.edu/weekly/1922/thumbnail.jp

The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond

There have been many discussions of two-mode models for Bose condensates in a double well potential, but few cases in which parameters for these models have been calculated for realistic situations. Recent experiments lead us to use the Gross-Pitaevskii equation to obtain optimum two-mode parameters. We find that by using the lowest symmetric and antisymmetric wavefunctions, it is possible to derive equations for a more exact two-mode model that provides for a variable tunneling rate depending on the instantaneous values of the number of atoms and phase differences. Especially for larger values of the nonlinear interaction term and larger barrier heights, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in 1D and 3D, as compared with previous models with constant tunneling, and better agreement with experimental results for the tunneling oscillation frequency [Albiez et al., cond-mat/0411757]. We also show how this approach can be used to obtain modified equations for a second quantized version of the Bose double well problem.Comment: RevTeX, 14 pages, 14 figure

Beyond the relativistic mean-field approximation (II): configuration mixing of mean-field wave functions projected on angular momentum and particle number

The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field + Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent $\delta$-interaction in the pairing channel. Illustrative calculations are performed for $^{24}$Mg, $^{32}$S and $^{36}$Ar, and compared with results obtained employing the model developed in the first part of this work, i.e. without particle-number projection, as well as with the corresponding non-relativistic models based on Skyrme and Gogny effective interactions.Comment: 37 pages, 10 figures, submitted to Physical Review