C-Periodicity and the Physical Mass in the 3-State Potts Model

The standard infinite-volume definition of connected correlation function and particle mass in the 3-state Potts model can be implemented in Monte Carlo simulations by using C-periodic spatial boundary conditions. This avoids both the breaking of translation invariance (cold wall b.c.) and the phase-dependent and thus possibly biased evaluation of data (periodic boundary cconditions). The numerical feasibility of the standard definitions is demonstrated by sample computations on a 24*24*48 lattice.Comment: 13 pages + 5 figures Preprint Nos. IC/93/131 and TIFR/TH/93-2

First- and second-order charged particle optics

Since the invention of the alternating gradient principle there has been a rapid evolution of the mathematics and physics techniques applicable to charged particle optics. In this publication we derive a differential equation and a matrix algebra formalism valid to second-order to present the basic principles governing the design of charged particle beam transport systems. A notation first introduced by John Streib is used to convey the essential principles dictating the design of such beam transport systems. For example the momentum dispersion, the momentum resolution, and all second-order aberrations are expressed as simple integrals of the first-order trajectories (matrix elements) and of the magnetic field parameters (multipole components) characterizing the system. 16 references, 30 figures

QCD Phase Transition with Strange Quark in Wilson Formalism for Fermions

The nature of QCD phase transition is studied with massless up and down quarks and a light strange quark, using the Wilson formalism for quarks on a lattice with the temporal direction extension $N_t=4$. We find that the phase transition is first order in the cases of both about 150 MeV and 400 MeV for the strange quark mass. These results together with those for three degenerate quarks suggest that QCD phase transition in nature is first order.Comment: uuencoded compressed tar file, LaTeX, 13 pages, 9 figures, Minor errors for quoting references are corrected and a reference is adde

Entropy and the variational principle for actions of sofic groups

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants, and we establish the variational principle in this context. In the case of residually finite groups we use the variational principle to compute the topological entropy of principal algebraic actions whose defining group ring element is invertible in the full group C*-algebra.Comment: 44 pages; minor changes; to appear in Invent. Mat

Domain structure of bulk ferromagnetic crystals in applied fields near saturation

We investigate the ground state of a uniaxial ferromagnetic plate with perpendicular easy axis and subject to an applied magnetic field normal to the plate. Our interest is the asymptotic behavior of the energy in macroscopically large samples near the saturation field. We establish the scaling of the critical value of the applied field strength below saturation at which the ground state changes from the uniform to a branched domain magnetization pattern and the leading order scaling behavior of the minimal energy. Furthermore, we derive a reduced sharp-interface energy giving the precise asymptotic behavior of the minimal energy in macroscopically large plates under a physically reasonable assumption of small deviations of the magnetization from the easy axis away from domain walls. On the basis of the reduced energy, and by a formal asymptotic analysis near the transition, we derive the precise asymptotic values of the critical field strength at which non-trivial minimizers (either local or global) emerge. The non-trivial minimal energy scaling is achieved by magnetization patterns consisting of long slender needle-like domains of magnetization opposing the applied fieldComment: 38 pages, 7 figures, submitted to J. Nonlin. Sci

SCIENCECRAFT

The technological capabilities are now at hand to design an integrated system that combine science instruments, spacecraft and propulsion elements into a single system. The authors have called this a Sciencecraft since it is intended to provide automatic scientific observations of planetary and astrophysical objects. Integration of function allows lower mass and cost and supports a short development cycle. A specific science mission is described in this paper, a flyby of Neptune, Triton and an object in the Kuiper belt. The SCIENCECRAFT system is described. It has electric propulsion and is capable of measuring the surface constituents and morphology of the objects visited and characterizing their atmospheres both in emission and absorption (against the sun). Miniature fields and particles experiments are incorporated that will provide interplanetary information together with details of the magnetic and electric attributes of each object. The SCIENCECRAFT is Delta launched and has a flight time to the Kuiper belt of 7 years. The design is such that the craft functions in a largely autonomous mode to provide low cost mission operations

Tunneling and the Spectrum of the Potts Model

The three-dimensional, three-state Potts model is studied as a paradigm for high temperature quantum chromodynamics. In a high statistics numerical simulation using a Swendson-Wang algorithm, we study cubic lattices of dimension as large as $64^3$ and measure correlation functions on long lattices of dimension $20^2\times 120$ and $30^2\times 120$. These correlations are controlled by the spectrum of the transfer matrix. This spectrum is studied in the vicinity of the phase transition. The analysis classifies the spectral levels according to an underlying $S_3$ symmetry. Near the phase transition the spectrum agrees nicely with a simple four-component hamiltonian model. In the context of this model, we find that low temperature ordered-ordered interfaces nearly always involve a disordered phase intermediate. We present a new spectral method for determining the surface tension between phases.Comment: 26 pages plus 13 Postscript figures (Axis versions also provided), UU-HEP-92/

Parity-Violating Interaction Effects I: the Longitudinal Asymmetry in pp Elastic Scattering

The proton-proton parity-violating longitudinal asymmetry is calculated in the lab-energy range 0--350 MeV, using a number of different, latest-generation strong-interaction potentials--Argonne V18, Bonn-2000, and Nijmegen-I--in combination with a weak-interaction potential consisting of rho- and omega-meson exchanges--the model known as DDH. The complete scattering problem in the presence of parity-conserving, including Coulomb, and parity-violating potentials is solved in both configuration- and momentum-space. The predicted parity-violating asymmetries are found to be only weakly dependent upon the input strong-interaction potential adopted in the calculation. Values for the rho- and omega-meson weak coupling constants $h^{pp}_\rho$ and $h^{pp}_\omega$ are determined by reproducing the measured asymmetries at 13.6 MeV, 45 MeV, and 221 MeV.Comment: 24 pages, 8 figures, submitted to Physical Review

The Nuclear Sigma Term in the Skyrme Model: Pion-Nucleus Interaction

The nuclear sigma term is calculated including the nuclear matrix element of the derivative of the NN interaction with respect to the quark mass, $m_q\frac{\partial V_{NN}}{\partial m_q}$. The NN potential is evaluated in the skyrmion-skyrmion picture within the quantized product ansatz. The contribution of the NN potential to the nuclear sigma term provides repulsion to the pion-nucleus interaction. The strength of the s-wave pion-nucleus optical potential is estimated including such contribution. The results are consistent with the analysis of the experimental data.Comment: 16 pages (latex), 3 figures (eps), e-mail: [email protected] and [email protected]

Black Hole Astrophysics in AdS Braneworlds

We consider astrophysics of large black holes localized on the brane in the infinite Randall-Sundrum model. Using their description in terms of a conformal field theory (CFT) coupled to gravity, deduced in Ref. [1], we show that they undergo a period of rapid decay via Hawking radiation of CFT modes. For example, a black hole of mass ${\rm few} \times M_\odot$ would shed most of its mass in $\sim 10^4 - 10^5$ years if the AdS radius is $L \sim 10^{-1}$ mm, currently the upper bound from table-top experiments. Since this is within the mass range of X-ray binary systems containing a black hole, the evaporation enhanced by the hidden sector CFT modes could cause the disappearance of X-ray sources on the sky. This would be a striking signature of RS2 with a large AdS radius. Alternatively, for shorter AdS radii, the evaporation would be slower. In such cases, the persistence of X-ray binaries with black holes already implies an upper bound on the AdS radius of L \la 10^{-2} mm, an order of magnitude better than the bounds from table-top experiments. The observation of primordial black holes with a mass in the MACHO range $M \sim 0.1 - 0.5 M_\odot$ and an age comparable to the age of the universe would further strengthen the bound on the AdS radius to L \la {\rm few} \times 10^{-6} mm.Comment: 14 pages, latex, no figures v2: added reference