A Class of Nonperturbative Configurations in Abelian-Higgs Models: Complexity from Dynamical Symmetry Breaking

We present a numerical investigation of the dynamics of symmetry breaking in both Abelian and non-Abelian $[S U (2)]$ Higgs models in three spatial dimensions. We find a class of time-dependent, long-lived nonperturbative field configurations within the range of parameters corresponding to type-1 superconductors, that is, with vector masses ($m_v$) larger than scalar masses ($m_s$). We argue that these emergent nontopological configurations are related to oscillons found previously in other contexts. For the Abelian-Higgs model, our lattice implementation allows us to map the range of parameter space -- the values of $\beta = (m_s /m_v)^2$ -- where such configurations exist and to follow them for times t \sim \O(10^5) m^{-1}. An investigation of their properties for $\hat z$-symmetric models reveals an enormously rich structure of resonances and mode-mode oscillations reminiscent of excited atomic states. For the SU(2) case, we present preliminary results indicating the presence of similar oscillonic configurations.Comment: 21 pages, 19 figures, prd, revte

Information Content of Spontaneous Symmetry Breaking

We propose a measure of order in the context of nonequilibrium field theory and argue that this measure, which we call relative configurational entropy (RCE), may be used to quantify the emergence of coherent low-entropy configurations, such as time-dependent or time-independent topological and nontopological spatially-extended structures. As an illustration, we investigate the nonequilibrium dynamics of spontaneous symmetry-breaking in three spatial dimensions. In particular, we focus on a model where a real scalar field, prepared initially in a symmetric thermal state, is quenched to a broken-symmetric state. For a certain range of initial temperatures, spatially-localized, long-lived structures known as oscillons emerge in synchrony and remain until the field reaches equilibrium again. We show that the RCE correlates with the number-density of oscillons, thus offering a quantitative measure of the emergence of nonperturbative spatiotemporal patterns that can be generalized to a variety of physical systems.Comment: LaTeX, 9 pages, 5 figures, 1 tabl

Magnetic and optical studies on an <i>S</i>=6 ground-state cluster [Cr₁₂O₉(OH)₃(O₂CCMe₃)₁₅]: Determination of, and the relationship between, single-ion and cluster spin Hamiltonian parameters

The dodecametallic Cr(III) cluster [Cr12O9(OH)(3)(O2CCMe3)(15)] has a ground spin state of S = 6 characterized by the spin Hamiltonian parameters g(ZZ) = 1.965, g(XX) = g(YY) = 1.960, D-S=6 = +0.088 cm(-1), and E-S=6 = 0 (where D and E are the axial and rhombic zero-field splitting parameters, respectively) as determined by multifrequency EPR spectroscopy and magnetization studies. Micro-SQUID magnetization studies reveal steps due to the fine structure of the ground state, with the spacing between the steps in excellent agreement with the D-S=6 value determined by EPR. Analysis of high-resolution optical data (MCD) allows us to determine the single-ion g values and D value (= -1.035 cm(-1)) of the constituent Cr(III) ions directly. A vector coupling analysis demonstrates that the cluster ZFS is almost entirely due to the single-ion component. Thus, the relative orientations of the local and cluster magnetic axes can lead to a cluster ZFS of opposite sign to the single-ion value, even when this is the only significant contribution.</p

Measuring and computing database inconsistency via repairs

We propose a generic numerical measure of inconsistency of a database with respect to a set of integrity constraints. It is based on an abstract repair semantics. A particular inconsistency measure associated to cardinality-repairs is investigated; and we show that it can be computed via answer-set programs