Local order parameters for use in driving homogeneous ice nucleation with all-atom models of water

We present a local order parameter based on the standard Steinhardt-Ten Wolde approach that is capable both of tracking and of driving homogeneous ice nucleation in simulations of all-atom models of water. We demonstrate that it is capable of forcing the growth of ice nuclei in supercooled liquid water simulated using the TIP4P/2005 model using overbiassed umbrella sampling Monte Carlo simulations. However, even with such an order parameter, the dynamics of ice growth in deeply supercooled liquid water in all-atom models of water are shown to be very slow, and so the computation of free energy landscapes and nucleation rates remains extremely challenging.Comment: This version incorporates the minor changes made to the paper following peer revie

Two-Point Functions of Coulomb Gauge Yang-Mills Theory

The functional approach to Coulomb gauge Yang-Mills theory is considered within the standard, second order, formalism. The Dyson-Schwinger equations and Slavnov-Taylor identities concerning the two-point functions are derived explicitly and one-loop perturbative results are presented.Comment: 12 pages, no figure

Nonlinear Performance of BAW Filters Including BST Capacitors

This paper evaluates the nonlinear effects occurring in a bulk acoustic wave (BAW) filter which includes barium strontium titanate (BST) capacitors to cancel the electrostatic capacitance of the BAW resonators. To do that we consider the nonlinear effects on the BAW resonators by use of a nonlinear Mason model. This model accounts for the distributed nonlinearities inherent in the materials forming the resonator. The whole filter is then implemented by properly connecting the resonators in a balanced configuration. Additional BST capacitors are included in the filter topology. The nonlinear behavior of the BST capacitors is also accounted in the overall nonlinear assessment. The whole circuit is then used to evaluate its nonlinear behavior. It is found that the nonlinear contribution arising from the ferroelectric nature of the BST capacitors makes it impractical to fulfill the linearity requirements of commercial filters

Heat-kernel expansion and counterterms of the Faddeev-Popov determinant in Coulomb and Landau gauge

The Faddeev-Popov determinant of Landau gauge in d dimensions and Coulomb gauge in d+1 dimensions is calculated in the heat-kernel expansion up to next-to-leading order. The UV-divergent parts in d=3,4 are isolated and the counterterms required for a non-perturbative treatment of the Faddeev-Popov determinant are determined.Comment: 7 page

On the temporal Wilson loop in the Hamiltonian approach in Coulomb gauge

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary transformations to take care of time evolution. We show how Coulomb gauge can be used for an alternative solution if the exact ground state wave functional is known. In the most interesting case of Yang-Mills theory in (3+1) dimensions, the vacuum wave functional is not known, but recent variational approaches in Coulomb gauge give a decent approximation. We use this formulation to compute the temporal Wilson loop and find that the Wilson and Coulomb string tension agree within our approximation scheme. Possible improvements of these findings are briefly discussed.Comment: 24 pages, 4 eps-figures; new version matches published on

SU(N)-Gauge Theories in Polyakov Gauge on the Torus

We investigate the Abelian projection with respect to the Polyakov loop operator for SU(N) gauge theories on the four torus. The gauge fixed $A_0$ is time-independent and diagonal. We construct fundamental domains for $A_0$. In sectors with non-vanishing instanton number such gauge fixings are always singular. The singularities define the positions of magnetically charged monopoles, strings or walls. These magnetic defects sit on the Gribov horizon and have quantized magnetic charges. We relate their magnetic charges to the instanton number.Comment: 11 pages, 2 figure

Continuum Singularities of a Mean Field Theory of Collisions

Consider a complex energy $z$ for a $N$-particle Hamiltonian $H$ and let $\chi$ be any wave packet accounting for any channel flux. The time independent mean field (TIMF) approximation of the inhomogeneous, linear equation $(z-H)|\Psi>=|\chi>$ consists in replacing $\Psi$ by a product or Slater determinant $\phi$ of single particle states $\phi_i.$ This results, under the Schwinger variational principle, into self consistent TIMF equations $(\eta_i-h_i)|\phi_i>=|\chi_i>$ in single particle space. The method is a generalization of the Hartree-Fock (HF) replacement of the $N$-body homogeneous linear equation $(E-H)|\Psi>=0$ by single particle HF diagonalizations $(e_i-h_i)|\phi_i>=0.$ We show how, despite strong nonlinearities in this mean field method, threshold singularities of the {\it inhomogeneous} TIMF equations are linked to solutions of the {\it homogeneous} HF equations.Comment: 21 pages, 14 figure

Variational solution of the Yang-Mills Schr\"odinger equation in Coulomb gauge

The Yang-Mills Schr\"odinger equation is solved in Coulomb gauge for the vacuum by the variational principle using an ansatz for the wave functional, which is strongly peaked at the Gribov horizon. A coupled set of Schwinger-Dyson equations for the gluon and ghost propagators in the Yang-Mills vacuum as well as for the curvature of gauge orbit space is derived and solved in one-loop approximation. We find an infrared suppressed gluon propagator, an infrared singular ghost propagator and a almost linearly rising confinement potential.Comment: 24 pages, revtex, 13 figure