Conditional Symmetries and Riemann Invariants for Hyperbolic Systems of PDEs

This paper contains an analysis of rank-k solutions in terms of Riemann invariants, obtained from interrelations between two concepts, that of the symmetry reduction method and of the generalized method of characteristics for first order quasilinear hyperbolic systems of PDEs in many dimensions. A variant of the conditional symmetry method for obtaining this type of solutions is proposed. A Lie module of vector fields, which are symmetries of an overdetermined system defined by the initial system of equations and certain first order differential constraints, is constructed. It is shown that this overdetermined system admits rank-k solutions expressible in terms of Riemann invariants. Finally, examples of applications of the proposed approach to the fluid dynamics equations in (k+1) dimensions are discussed in detail. Several new soliton-like solutions (among them kinks, bumps and multiple wave solutions) have been obtained

Microscopic spectral density in random matrix models for chiral and diquark condensation

We examine random matrix models of QCD which are capable of supporting both chiral and diquark condensation. A numerical study of the spectral densities near zero virtuality shows that the introduction of color in the interactions does not alter the one-body results imposed by chiral symmetry. A model with three colors has the spectral density predicted for the chiral ensemble with a Dyson index beta = 2; a pseudoreal model with two colors exhibits the spectral density of the chiral ensemble with beta = 1.Comment: 6 pages, 3 eps figures, uses revtex4 and graphicx. v2 : minor editions, Fig. 3 shows relative deviations rather than absolute. Version to appear in PR

Random matrix models for chiral and diquark condensation

We consider random matrix models for the thermodynamic competition between chiral symmetry breaking and diquark condensation in QCD at finite temperature and finite baryon density. The models produce mean field phase diagrams whose topology depends solely on the global symmetries of the theory. We discuss the block structure of the interactions that is imposed by chiral, spin, and color degrees of freedom and comment on the treatment of density and temperature effects. Extension of the coupling parameters to a larger class of theories allows us to investigate the robustness of the phase topology with respect to variations in the dynamics of the interactions. We briefly study the phase structure as a function of coupling parameters and the number of colors.Comment: 6 pages, 2 figures, proceedings of the workshop "Three Days of Hadronic Physics", Joint Meeting Heidelberg-Liege-Paris-Rostock, 16/12/2004-18/12/2004, Sol Cress, Spa, Belgium. v2: typographical errors corrected in reference

Random matrix model for antiferromagnetism and superconductivity on a two-dimensional lattice

We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that describe the exchange of density and spin-fluctuations. A block structure dictated by spin, time-reversal, and bipartite symmetries is imposed on the single-particle Hamiltonian. The detailed dynamics of the interactions are neglected and replaced by a normal distribution of random matrix elements. The resulting partition function can be calculated exactly. The thermodynamic potential has a structure which depends only on the spectrum of quasiparticles propagating in fixed condensation fields, with coupling constants that can be related directly to the variances of the microscopic processes. The resulting phase diagram reveals a fixed number of phase topologies whose realizations depend on a single coupling-parameter ratio, alpha. Most phase topologies are realized for a broad range of values of alpha and can thus be considered robust with respect to moderate variations in the detailed description of the underlying interactions.Comment: 21 pages, 8 figures, RevTex 4. Minor grammatical errors corrected in the last versio

Vibrational anharmonicity of small gold and silver clusters using the VSCF method

We study the vibrational spectra of small neutral gold (Au2–Au10) and silver (Ag2–Au5) clusters using the vibrational self-consistent field method (VSCF) in order to account for anharmonicity. We report harmonic, VSCF, and correlation-corrected VSCF calculations obtained using a vibrational configuration interaction approach (VSCF/VCI). Our implementation of the method is based on an efficient calculation of the potential energy surfaces (PES), using periodic density functional theory (DFT) with a plane-wave pseudopotential basis. In some cases, we use an efficient technique (fast-VSCF) assisted by the Voter–Chen potential in order to get an efficient reduction of the number of pair-couplings between modes. This allows us to efficiently reduce the computing time of 2D-PES without degrading the accuracy. We found that anharmonicity of the gold clusters is very small with maximum rms deviations of about 1 cm−1, although for some particular modes anharmonicity reaches values slightly larger than 2 cm−1. Silver clusters show slightly larger anharmonicity. In both cases, large differences between calculated and experimental vibrational frequencies (when available) stem more likely from the quality of the electronic structure method used than from vibrational anharmonicity. We show that noble gas embedding often affects the vibrational properties of these clusters more than anharmonicity, and discuss our results in the context of experimental studies

The nature and role of the gold-krypton interactions in small neutral gold clusters

© 2015 American Chemical Society. We investigate the nature and role of krypton embedding in small neutral gold clusters. For some of these clusters, we observe a particular site-dependent character of the Kr binding that does not completely follow the criterion of binding at low-coordinated sites, widely accepted for interaction of a noble gas with closed-shell metal systems such as metal surfaces. We aim at understanding the effect of low dimensionality and open-shell electronic structure of the odd-numbered clusters on the noble gas-metal cluster interaction. First, we investigate the role of attractive and repulsive forces, and the frontier molecular orbitals. Second, we investigate the Au-Kr interaction in terms of reactivity and bonding character. We use a reactivity index derived from Fukui formalism, and criteria provided by the electron localization function (ELF), in order to classify the type of bonding. We carry out this study on the minimum energy structures of neutral gold clusters, as obtained using pseudo potential plane-wave density functional theory (DFT). A model is proposed that includes the effect of attractive electrostatic, van der Waals and repulsive forces, together with effects originating from orbital overlap. This satisfactorily explains minimum configurations of the noble gas-gold cluster systems, the site preference of the noble gas atoms, and changes in electronic properties

Metastable spontaneous breaking of N=2 supersymmetry

We show that contrary to the common lore it is possible to spontaneously break N=2 supersymmetry even in simple theories without constant Fayet-Iliopoulos terms. We consider the most general N=2 supersymmetric theory with one hypermultiplet and one vector multiplet without Fayet-Iliopoulos terms, and show that metastable supersymmetry breaking vacua can arise if both the hyper-Kahler and the special-Kahler geometries are suitably curved. We then also prove that while all the scalars can be massive, the lightest one is always lighter than the vector boson. Finally, we argue that these results also directly imply that metastable de Sitter vacua can exist in N=2 supergravity theories with Abelian gaugings and no Fayet-Iliopoulos terms, again contrary to common lore, at least if the cosmological constant is sufficiently large.Comment: 16 pages, no figures; v2 improved introduction and conclusions; v3 minor correction

Elliptic solutions of isentropic ideal compressible fluid flow in (3 + 1) dimensions

A modified version of the conditional symmetry method, together with the classical method, is used to obtain new classes of elliptic solutions of the isentropic ideal compressible fluid flow in (3+1) dimensions. We focus on those types of solutions which are expressed in terms of the Weierstrass P-functions of Riemann invariants. These solutions are of special interest since we show that they remain bounded even when these invariants admit the gradient catastrophe. We describe in detail a procedure for constructing such classes of solutions. Finally, we present several examples of an application of our approach which includes bumps, kinks and multi-wave solutions