7,628,866 research outputs found
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
--martingale in which case the integrals are --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 () depends
crucially on the strength of DDI (). At the small- limit,
. 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 .Comment: 7 pages, 5 figure
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