Ab initio Quantum and ab initio Molecular Dynamics of the Dissociative Adsorption of Hydrogen on Pd(100)

The dissociative adsorption of hydrogen on Pd(100) has been studied by ab initio quantum dynamics and ab initio molecular dynamics calculations. Treating all hydrogen degrees of freedom as dynamical coordinates implies a high dimensionality and requires statistical averages over thousands of trajectories. An efficient and accurate treatment of such extensive statistics is achieved in two steps: In a first step we evaluate the ab initio potential energy surface (PES) and determine an analytical representation. Then, in an independent second step dynamical calculations are performed on the analytical representation of the PES. Thus the dissociation dynamics is investigated without any crucial assumption except for the Born-Oppenheimer approximation which is anyhow employed when density-functional theory calculations are performed. The ab initio molecular dynamics is compared to detailed quantum dynamical calculations on exactly the same ab initio PES. The occurence of quantum oscillations in the sticking probability as a function of kinetic energy is addressed. They turn out to be very sensitive to the symmetry of the initial conditions. At low kinetic energies sticking is dominated by the steering effect which is illustrated using classical trajectories. The steering effects depends on the kinetic energy, but not on the mass of the molecules. Zero-point effects lead to strong differences between quantum and classical calculations of the sticking probability. The dependence of the sticking probability on the angle of incidence is analysed; it is found to be in good agreement with experimental data. The results show that the determination of the potential energy surface combined with high-dimensional dynamical calculations, in which all relevant degrees of freedon are taken into account, leads to a detailed understanding of the dissociation dynamics of hydrogen at a transition metal surface.Comment: 15 pages, 9 figures, subm. to Phys. Rev.

The open-charm radiative and pionic decays of molecular charmonium Y(4274)

In this work, we investigate the decay widths and the line shapes of the open-charm radiative and pionic decays of Y(4274) with the $D_s\bar{D}_{s0}(2317)$ molecular charmonium assignment. Our calculation indicates that the decay widths of $Y(4274)\to D^{+}_{s}D^{*-}_{s}\gamma$ and $Y(4274)\to D^+_{s}D^-_{s}\pi^0$ can reach up to 0.05 keV and 0.75 keV, respectively. In addition, the result of the line shape of the photon spectrum of $Y(4274)\to D_s^+ {D}_s^{*-} \gamma$ shows that there exists a very sharp peak near the large end point of photon energy. The line shape of the pion spectrum of $Y(4274)\to D_s^+ {D}_s^{*-} \pi^0$ is similar to that of the pion spectrum of $Y(4274)\to D_s^+ {D}_s^{*-} \gamma$, where we also find a very sharp peak near the large end point of pion energy. According to our calculation, we suggest further experiments to carry out the search for the open-charm radiative and pionic decays of Y(4274).Comment: 7 pages, 6 figures, 1 table. Published versio

Anomaly-matching and Higgs-less effective theories

We reconsider the low-energy effective theory for Higgs-less electroweak symmetry breaking: we study the anomaly-matching in the situation where all Goldstone fields disappear from the spectrum as a result of the Higgs mechanism. We find that the global SU(2)_L x SU(2)_R x U(1)_{B-L} symmetry of the underlying theory, which is spontaneously broken to SU(2)_{L+R} x U(1)_{B-L} has to be anomaly-free. For the sake of generality, we include the possibility of light spin-1/2 bound states resulting from the dynamics of the strongly-interacting symmetry-breaking sector, in addition to the Goldstone bosons. Such composite fermions may have non-standard couplings at the leading order, and an arbitrary total B-L charge. In order to perform the anomaly-matching in that case, we generalize the construction of the Wess-Zumino effective lagrangian. Composite fermions beyond the three known generations are theoretically allowed, and there are no restrictions from the anomaly-matching on their couplings nor on their U(1)_{B-L} charge. Absence of global anomalies for the composite sector as a whole does not preclude anomalous triple gauge boson couplings arising from composite fermion triangular diagrams. On the other hand, the trace of B-L over elementary fermions must vanish if all Goldstone modes are to disappear from the spectrum.Comment: Keywords: Anomalies in Field and String Theories, Spontaneous Symmetry Breaking, Beyond the Standard Model, Chiral Lagrangians. 33 pages, 7 figure

Semilinear mixed problems on Hilbert complexes and their numerical approximation

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing variational crimes (a la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk [Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J. Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold-Falk-Winther results in the linear case. We also consider the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces.Comment: 22 pages; v2: major revision, particularly sharpening of error estimates in Section

Macroscopic Quantum Fluctuations in the Josephson Dynamics of Two Weakly Linked Bose-Einstein Condensates

We study the quantum corrections to the Gross-Pitaevskii equation for two weakly linked Bose-Einstein condensates. The goals are: 1) to investigate dynamical regimes at the borderline between the classical and quantum behaviour of the bosonic field; 2) to search for new macroscopic quantum coherence phenomena not observable with other superfluid/superconducting systems. Quantum fluctuations renormalize the classical Josephson oscillation frequencies. Large amplitude phase oscillations are modulated, exhibiting collapses and revivals. We describe a new inter-well oscillation mode, with a vanishing (ensemble averaged) mean value of the observables, but with oscillating mean square fluctuations. Increasing the number of condensate atoms, we recover the classical Gross-Pitaevskii (Josephson) dynamics, without invoking the symmetry-breaking of the Gauge invariance.Comment: Submitte

Higgs Bundles, Gauge Theories and Quantum Groups

The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions of the corresponding two-dimensional topological U(N) gauge theory reproduce quantum wave functions of the Nonlinear Schr\"{o}dinger equation in the $N$-particle sector. This implies the full equivalence between the above gauge theory and the $N$-particle sub-sector of the quantum theory of Nonlinear Schr\"{o}dinger equation. This also implies the explicit correspondence between the gauge theory and the representation theory of degenerate double affine Hecke algebra. We propose similar construction based on the $G/G$ gauged WZW model leading to the representation theory of the double affine Hecke algebra. The relation with the Nahm transform and the geometric Langlands correspondence is briefly discussed.Comment: 48 pages, typos corrected, one reference adde

Four-point correlator constraints on electromagnetic chiral parameters and resonance effective Lagrangians

We pursue the analysis of a set of generalized DGMLY sum rules for the electromagnetic chiral parameters at order $e^2p^2$ and discuss implications for effective Lagrangians with resonances. We exploit a formalism in which charge spurions are introduced and treated as sources. We show that no inconsistency arises from anomalies up to quadratic order in the spurions. We focus on the sum rules associated with QCD 4-point correlators which were not analyzed in detail before. Convergence properties of the sum rules are deduced from a general analysis of the form of the counterterms in the presence of electromagnetic spurions. Following the approach in which vector and axial-vector resonances are described with antisymmetric tensor fields and have a chiral order, we show that the convergence constraints are violated at chiral order four and can be satisfied by introducing a set of terms of order six. The relevant couplings get completely and uniquely determined from a set of generalized Weinberg sum-rule relations. An update on the corrections to Dashen's low-energy theorem is given.Comment: 42 pages, 1 figure. v2: references adde

Mass Parameterizations and Predictions of Isotopic Observables

We discuss the accuracy of mass models for extrapolating to very asymmetric nuclei and the impact of such extrapolations on the predictions of isotopic observables in multifragmentation. We obtain improved mass predictions by incorporating measured masses and extrapolating to unmeasured masses with a mass formula that includes surface symmetry and Coulomb terms. We find that using accurate masses has a significant impact on the predicted isotopic observables.Comment: 12 pages, 4 figure

Efimov Trimers near the Zero-crossing of a Feshbach Resonance

Near a Feshbach resonance, the two-body scattering length can assume any value. When it approaches zero, the next-order term given by the effective range is known to diverge. We consider the question of whether this divergence (and the vanishing of the scattering length) is accompanied by an anomalous solution of the three-boson Schr\"odinger equation similar to the one found at infinite scattering length by Efimov. Within a simple zero-range model, we find no such solutions, and conclude that higher-order terms do not support Efimov physics.Comment: 8 pages, no figures, final versio

Comparisons of Statistical Multifragmentation and Evaporation Models for Heavy Ion Collisions

The results from ten statistical multifragmentation models have been compared with each other using selected experimental observables. Even though details in any single observable may differ, the general trends among models are similar. Thus these models and similar ones are very good in providing important physics insights especially for general properties of the primary fragments and the multifragmentation process. Mean values and ratios of observables are also less sensitive to individual differences in the models. In addition to multifragmentation models, we have compared results from five commonly used evaporation codes. The fluctuations in isotope yield ratios are found to be a good indicator to evaluate the sequential decay implementation in the code. The systems and the observables studied here can be used as benchmarks for the development of statistical multifragmentation models and evaporation codes.Comment: To appear on Euorpean Physics Journal A as part of the Topical Volume "Dynamics and Thermodynamics with Nuclear Degrees of Freedo