Frustrated collisions and unconventional pairing on a quantum superlattice

We solve the problem of scattering and binding of two spin-1/2 fermions on a one-dimensional superlattice with a period of twice the lattice spacing analytically. We find the exact bound states and the scattering states, consisting of a generalized Bethe ansatz augmented with an extra scattering product due to "asymptotic" degeneracy. If a Bloch band is doubly occupied, the extra wave can be a bound state in the continuum corresponding to a single-particle interband transition. In all other cases, it corresponds to a quasi-momentum changing, frustrated collision.Comment: 4 pages, 2 figure

Human and machine recognition of dynamic and static facial expressions: prototypicality, ambiguity, and complexity

A growing body of research suggests that movement aids facial expression recognition. However, less is known about the conditions under which the dynamic advantage occurs. The aim of this research was to test emotion recognition in static and dynamic facial expressions, thereby exploring the role of three featural parameters (prototypicality, ambiguity, and complexity) in human and machine analysis. In two studies, facial expression videos and corresponding images depicting the peak of the target and non-target emotion were presented to human observers and the machine classifier (FACET). Results revealed higher recognition rates for dynamic stimuli compared to non-target images. Such benefit disappeared in the context of target-emotion images which were similarly well (or even better) recognised than videos, and more prototypical, less ambiguous, and more complex in appearance than non-target images. While prototypicality and ambiguity exerted more predictive power in machine performance, complexity was more indicative of human emotion recognition. Interestingly, recognition performance by the machine was found to be superior to humans for both target and non-target images. Together, the findings point towards a compensatory role of dynamic information, particularly when static-based stimuli lack relevant features of the target emotion. Implications for research using automatic facial expression analysis (AFEA) are discussed

Parity violation in quasifree electron scattering off the deuteron

For deuteron electroweak disintegration, parity violating effects are investigated which arise from the interference of $\gamma$ and $Z$ exchange as well as from the hadronic sector via a small parity violating component in the deuteron. The general formalism for the differential cross section and polarization observables of electromagnetic deuteron disintegration is extended to incorporate parity violating contributions. Formal expressions for the additional structure functions are derived. Results are presented for these parity violating structure functions for quasifree kinematics neglecting final state interaction and two-body effects. Both types of parity violating contributions to the asymmetry of the inclusive reaction with respect to longitudinally polarized electrons are evaluated. The one from parity violating deuteron components is negligible over the whole range of momentum transfers considered.Comment: 21 pages revtex including 12 postscript figures, revised version, accepted for publication in Nucl. Phys.

Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy

The free energy of a multi-component scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys non-linear functional differential equations which are turned into recursion relations for the connected Greens functions in a loop expansion. These relations amount to a simple proof that W[G,J] generates only connected graphs and can be used to find all such graphs with their combinatoric weights. A Legendre transformation with respect to the external current converts the functional differential equations for the free energy into those for the effective energy Gamma[G,Phi], which is considered as a functional of the free correlation function G and the field expectation Phi. These equations are turned into recursion relations for the one-particle irreducible Greens functions. These relations amount to a simple proof that Gamma[G,J] generates only one-particle irreducible graphs and can be used to find all such graphs with their combinatoric weights. The techniques used also allow for a systematic investigation into resummations of classes of graphs. Examples are given for resumming one-loop and multi-loop tadpoles, both through all orders of perturbation theory. Since the functional differential equations derived are non-perturbative, they constitute also a convenient starting point for other expansions than those in numbers of loops or powers of coupling constants. We work with general interactions through four powers in the field.Comment: 34 pages; abstract expanded; section IV.E about absorption of tadpoles and one related reference added; eqs. (20) and (23) corrected; further references added; some minor beautifications; to be published by Phys.Rev.

Spontaneous symmetry breaking and the p→0p \to 0 limit

We point out a basic ambiguity in the $p \to 0$ limit of the connected propagator in a spontaneously broken phase. This may represent an indication that the conventional singlet Higgs boson, rather than being a purely massive field, might have a gap-less branch. This would dominate the energy spectrum for ${\bf{p}} \to 0$ and give rise to a very weak, long-range force. The natural interpretation is in terms of density fluctuations of the `Higgs condensate': in the region of very long wavelengths, infinitely larger than the Fermi scale, it cannot be treated as a purely classical c-number field.Comment: 17 pages, LaTex, small changes and some comments adde