Stability in the instantaneous Bethe-Salpeter formalism: harmonic-oscillator reduced Salpeter equation

A popular three-dimensional reduction of the Bethe-Salpeter formalism for the description of bound states in quantum field theory is the Salpeter equation, derived by assuming both instantaneous interactions and free propagation of all bound-state constituents. Numerical (variational) studies of the Salpeter equation with confining interaction, however, observed specific instabilities of the solutions, likely related to the Klein paradox and rendering (part of the) bound states unstable. An analytic investigation of this problem by a comprehensive spectral analysis is feasible for the reduced Salpeter equation with only harmonic-oscillator confining interactions. There we are able to prove rigorously that the bound-state solutions correspond to real discrete energy spectra bounded from below and are thus free of any instabilities.Comment: 23 pages, 3 figures, extended conclusions, version to appear in Phys. Rev.

Quantum phase transitions in photonic cavities with two-level systems

Systems of coupled photonic cavities have been predicted to exhibit quantum phase transitions by analogy with the Hubbard model. To this end, we have studied topologies of few (up to six) photonic cavities each containing a single two-level system. Quantum phase space diagrams are produced for these systems, and compared to mean-field results. We also consider finite effective temperature, and compare this to the notion of disorder. We find the extent of the Mott lobes shrink analogously to the conventional Bose-Hubbard model.Comment: 11 pages, 11 figures, updated typo

Linking entanglement and quantum phase transitions via density functional theory

Density functional theory (DFT) is shown to provide a novel conceptual and computational framework for entanglement in interacting many-body quantum systems. DFT can, in particular, shed light on the intriguing relationship between quantum phase transitions and entanglement. We use DFT concepts to express entanglement measures in terms of the first or second derivative of the ground state energy. We illustrate the versatility of the DFT approach via a variety of analytically solvable models. As a further application we discuss entanglement and quantum phase transitions in the case of mean field approximations for realistic models of many-body systems.Comment: 6 pages, 2 figure

New Method to Calculate Electrical Forces Acting on a Sphere in an Electrorheological Fluid

We describe a method to calculate the electrical force acting on a sphere in a suspension of dielectric spheres in a host with a different dielectric constant, under the assumption that a spatially uniform electric field is applied. The method uses a spectral representation for the total electrostatic energy of the composite. The force is expressed as a certain gradient of this energy, which can be expressed in a closed analytic form rather than evaluated as a numerical derivative. The method is applicable even when both the spheres and the host have frequency-dependent dielectric functions and nonzero conductivities, provided the system is in the quasistatic regime. In principle, it includes all multipolar contributions to the force, and it can be used to calculate multi-body as well as pairwise forces. We also present several numerical examples, including host fluids with finite conductivities. The force between spheres approaches the dipole-dipole limit, as expected, at large separations, but departs drastically from that limit when the spheres are nearly in contact. The force may also change sign as a function of frequency when the host is a slightly conducting fluid.Comment: 29 pages, 8 figures, Accepted for Publication in Physical Review

Sampling of quantum dynamics at long time

The principle of energy conservation leads to a generalized choice of transition probability in a piecewise adiabatic representation of quantum(-classical) dynamics. Significant improvement (almost an order of magnitude, depending on the parameters of the calculation) over previous schemes is achieved. Novel perspectives for theoretical calculations in coherent many-body systems are opened.Comment: Revised versio

Point Interaction in two and three dimensional Riemannian Manifolds

We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac delta interactions on two and three dimensional Riemannian manifolds using the heat kernel. We formulate the problem in terms of a new operator called the principal or characteristic operator. In order to investigate the problem in more detail, we then restrict the problem to one particle sector. The lower bound of the ground state energy is found for general class of manifolds, e.g., for compact and Cartan-Hadamard manifolds. The estimate of the bound state energies in the tunneling regime is calculated by perturbation theory. Non-degeneracy and uniqueness of the ground state is proven by Perron-Frobenius theorem. Moreover, the pointwise bounds on the wave function is given and all these results are consistent with the one given in standard quantum mechanics. Renormalization procedure does not lead to any radical change in these cases. Finally, renormalization group equations are derived and the beta-function is exactly calculated. This work is a natural continuation of our previous work based on a novel approach to the renormalization of point interactions, developed by S. G. Rajeev.Comment: 43 page

Stability and phase coherence of trapped 1D Bose gases

We discuss stability and phase coherence of 1D trapped Bose gases and find that inelastic decay processes, such as 3-body recombination, are suppressed in the strongly interacting (Tonks-Girardeau) and intermediate regimes. This is promising for achieving these regimes with a large number of particles. "Fermionization" of the system reduces the phase coherence length, and at T=0 the gas is fully phase coherent only deeply in the weakly interacting (Gross-Pitaevskii) regime.Comment: published versio

Measuring Perceived Realistic Physical Threat Imposed by Migrants: Scale Development and Validation

Individuals differ in the extent to which they perceive threat imposed by out-groups like migrants. An established distinction in intergroup threat research is between symbolic and realistic threat. While symbolic threats concern a perceived menace against societal values, realistic threats jeopardize in-group members’ well-being more directly. Typically applied realistic threat conceptions explicitly include the aspect of physical integrity, but most empirical research captures only realistic economic threats, arguably also due to a lack of appropriate measures. Therefore, we have developed the Perceived Realistic Physical Threat scale (PRPT) with samples from Germany and the UK (total N = 1,391). Moreover, we conducted follow-up analyses with data from a subsample (N = 473) of the initial UK sample. Factor analyses indicated an 8-item one-factorial solution for the PRPT scale. We further identified measurement invariance across samples and over time and stability across 21 months. We found convincing evidence for its convergent and divergent validity and for its predictive and, importantly, incremental validity, above and beyond the prediction of relevant criteria by other threat types. The PRPT scale appears to be a distinct, comprehensive, and psychometrically sound measure of perceived realistic physical threat, complementing the existing body of available measures

Pion-delta sigma-term

We use a configuration space chiral model in order to evaluate nucleon and delta sigma-terms. Analytic expressions are consistent with chiral counting rules and give rise to expected non-analytic terms in the chiral limit. We obtain the results $\sigma_N=46$ MeV and $\sigma_{\Delta}=32$ MeV, which are very close to values extracted from experiment and produced by other groups.Comment: 18 pages, 4 figure