Asymptotic States and the Definition of the S-matrix in Quantum Gravity

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energy-momentum naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space. The generalized asymptotic free scalar, Dirac and gauge fields in that theory are canonically quantized, the Fock spaces of stationary states are constructed and the gravitational limit - mapping the gravitational energy-momentum onto the inertial energy-momentum to account for their observed equality - is introduced. Next the S-matrix in quantum gravity is defined as the gravitational limit of the transition amplitudes of asymptotic in- to out-states in the gauge theory of volume-preserving diffeormorphisms. The so defined S-matrix relates in- and out-states of observable particles carrying gravitational equal to inertial energy-momentum. Finally generalized LSZ reduction formulae for scalar, Dirac and gauge fields are established which allow to express S-matrix elements as the gravitational limit of truncated Fourier-transformed vacuum expectation values of time-ordered products of field operators of the interacting theory. Together with the generating functional of the latter established in an earlier paper [8] any transition amplitude can in principle be computed to any order in perturbative quantum gravity.Comment: 35 page

Unified model of voltage/current mode control to predict saddle-node bifurcation

A unified model of voltage mode control (VMC) and current mode control (CMC) is proposed to predict the saddle-node bifurcation (SNB). Exact SNB boundary conditions are derived, and can be further simplified in various forms for design purpose. Many approaches, including steady-state, sampled-data, average, harmonic balance, and loop gain analyses are applied to predict SNB. Each approach has its own merits and complement the other approaches.Comment: Submitted to International Journal of Circuit Theory and Applications on December 23, 2010; Manuscript ID: CTA-10-025

Quantum stochastic integrals as operators

We construct quantum stochastic integrals for the integrator being a martingale in a von Neumann algebra, and the integrand -- a suitable process with values in the same algebra, as densely defined operators affiliated with the algebra. In the case of a finite algebra we allow the integrator to be an $L^2$--martingale in which case the integrals are $L^2$--martingales too

Heat-treatment of metal parts facilitated by sand embedment

Embedding metal parts of complex shape in sand contained in a steel box prevents strains and warping during heat treatment. The sand not only provides a simple, inexpensive support for the parts but also ensures more uniform distribution of heat to the parts

Magnetic field dependence of the antiferromagnetic phase transitions in Co-doped YbRh_2Si_2

We present first specific-heat data of the alloy Yb(Rh_(1-x)Co_x)_2Si_2 at intermediate Co-contents x=0.18, 0.27, and 0.68. The results already point to a complex magnetic phase diagram as a function of composition. Co-doping of YbRh_2Si_2 (T_N^{x=0}=72 mK) stabilizes the magnetic phase due to the volume decrease of the crystallographic unit cell. The magnetic phase transitions are clearly visible as pronounced anomalies in C^{4f}(T)/T and can be suppressed by applying a magnetic field. Going from x=0.18 to x=0.27 we observe a change from two mean-field (MF) like magnetic transitions at T_N^{0.18}=1.1 K and T_L^{0.18}=0.65 K to one sharp \lambda-type transition at T_N^{0.27}=1.3 K. Preliminary measurements under magnetic field do not confirm the field-induced first-order transition suggested in the literature. For x=0.68 we find two transitions at T_N^{0.68}=1.14 K and T_L^{0.68}=1.06 K.Comment: Accepted for the ICM proceedings 200

Solving the Poisson equation on small aspect ratio domains using unstructured meshes

We discuss the ill conditioning of the matrix for the discretised Poisson equation in the small aspect ratio limit, and motivate this problem in the context of nonhydrostatic ocean modelling. Efficient iterative solvers for the Poisson equation in small aspect ratio domains are crucial for the successful development of nonhydrostatic ocean models on unstructured meshes. We introduce a new multigrid preconditioner for the Poisson problem which can be used with finite element discretisations on general unstructured meshes; this preconditioner is motivated by the fact that the Poisson problem has a condition number which is independent of aspect ratio when Dirichlet boundary conditions are imposed on the top surface of the domain. This leads to the first level in an algebraic multigrid solver (which can be extended by further conventional algebraic multigrid stages), and an additive smoother. We illustrate the method with numerical tests on unstructured meshes, which show that the preconditioner makes a dramatic improvement on a more standard multigrid preconditioner approach, and also show that the additive smoother produces better results than standard SOR smoothing. This new solver method makes it feasible to run nonhydrostatic unstructured mesh ocean models in small aspect ratio domains.Comment: submitted to Ocean Modellin

Center motions of nonoverlapping condensates coupled by long-range dipolar interaction in bilayer and multilayer stacks

We investigate the effect of anisotropic and long-range dipole-dipole interaction (DDI) on the center motions of nonoverlapping Bose-Einstein condensates (BEC) in bilayer and multilayer stacks. In the bilayer, it is shown analytically that while DDI plays no role in the in-phase modes of center motions of condensates, out-of-phase mode frequency ($\omega_o$) depends crucially on the strength of DDI ($a_d$). At the small-$a_d$ limit, $\omega_o^2(a_d)-\omega_o^2(0)\propto a_d$. In the multilayer stack, transverse modes associated with center motions of coupled condensates are found to be optical phonon like. At the long-wavelength limit, phonon velocity is proportional to $\sqrt a_d$.Comment: 7 pages, 5 figure