16,195 research outputs found
On The Capacity of Surfaces in Manifolds with Nonnegative Scalar Curvature
Given a surface in an asymptotically flat 3-manifold with nonnegative scalar
curvature, we derive an upper bound for the capacity of the surface in terms of
the area of the surface and the Willmore functional of the surface. The
capacity of a surface is defined to be the energy of the harmonic function
which equals 0 on the surface and goes to 1 at infinity. Even in the special
case of Euclidean space, this is a new estimate. More generally, equality holds
precisely for a spherically symmetric sphere in a spatial Schwarzschild
3-manifold. As applications, we obtain inequalities relating the capacity of
the surface to the Hawking mass of the surface and the total mass of the
asymptotically flat manifold.Comment: 18 page
Absolute Value Boundedness, Operator Decomposition, and Stochastic Media and Equations
The research accomplished during this period is reported. Published abstracts and technical reports are listed. Articles presented include: boundedness of absolute values of generalized Fourier coefficients, propagation in stochastic media, and stationary conditions for stochastic differential equations
A Two-Person Dynamic Equilibrium under Ambiguity
This paper describes a pure-exchange, continuous-time economy with two heterogeneous agents and complete markets. A novel feature of the economy is that agents perceive some security returns as ambiguous in the sense often attributed to frank Knight. The equilibrium is described completely in closed-form. In particular, closed-form solutions are obtained for the equilibrium processes describing individual consumption, the interest rate, the market price of uncertainty, security prices and trading strategies. After identifying agents as countries, the model is applied to address the consumption home-bias puzzles.ambiguity, risk, continuous-time, asset returns, Knightian uncertainty, dynamic equilibrium, home bias
B-Physics Observables and Electroweak Precision Data in the CMSSM, mGMSB and mAMSB
We explore electroweak precision observables (EWPO) and -physics
observables (BPO) in the CMSSM, the mGMSB and the mAMSB. We perform a chi^2
analysis based on the combination of current EWPO and BPO data. For the first
time this allows the comparison of the mGMSB and mAMSB in terms of EWPO and BPO
with the CMSSM. We find that relatively low mass scales in all three scenarios
are favored. However, the current data from EWPO and BPO can hardly exclude any
parameters at the level of Delta chi^2 = 9. Remarkably the mAMSB scenario,
despite having one free GUT scale parameter less than the other two scenarios,
has a somewhat lower total minimum chi^2. We present predictions for the
lightest Higgs boson mass, based on the chi^2 analysis of current data, where
relatively good compatibility with the bounds from Higgs searches at LEP is
found. We also present the predictions for other Higgs sector parameters and
SUSY mass scales, allowing to compare the reach of the LHC and the ILC in the
three scenarios. We furthermore explore the future sensitivities of the EWPO
and BPO for the current best-fit results and for a hypothetical point with
somewhat higher mass scales that results in a similar Higgs and SUSY spectrum
in the three scenarios. We find that the future improvement of the accuracy of
the EWPO and BPO will lead to a significant gain in the indirect parameter
determination. The improvement is similar in the CMSSM, mGMSB and mAMSB and
will yield constraints to the parameter space even for heavy Higgs and SUSY
mass scales.Comment: 53 pages, 27 figures, discussion extended. Version to appear in JHE
Dual Actions for Born-Infeld and Dp-Brane Theories
Dual actions with respect to U(1) gauge fields for Born-Infeld and -brane
theories are reexamined. Taking into account an additional condition, i.e. a
corollary to the field equation of the auxiliary metric, one obtains an
alternative dual action that does not involve the infinite power series in the
auxiliary metric given by ref. \cite{s14}, but just picks out the first term
from the series formally. New effective interactions of the theories are
revealed. That is, the new dual action gives rise to an effective interaction
in terms of one interaction term rather than infinite terms of different
(higher) orders of interactions physically. However, the price paid for
eliminating the infinite power series is that the new action is not quadratic
but highly nonlinear in the Hodge dual of a -form field strength. This
non-linearity is inevitable to the requirement the two dual actions are
equivalent.Comment: v1: 11 pages, no figures; v2: explanation of effective interactions
added; v3: concision made; v4: minor modification mad
A Remark on Boundary Effects in Static Vacuum Initial Data sets
Let (M, g) be an asymptotically flat static vacuum initial data set with
non-empty compact boundary. We prove that (M, g) is isometric to a spacelike
slice of a Schwarzschild spacetime under the mere assumption that the boundary
of (M, g) has zero mean curvature, hence generalizing a classic result of
Bunting and Masood-ul-Alam. In the case that the boundary has constant positive
mean curvature and satisfies a stability condition, we derive an upper bound of
the ADM mass of (M, g) in terms of the area and mean curvature of the boundary.
Our discussion is motivated by Bartnik's quasi-local mass definition.Comment: 10 pages, to be published in Classical and Quantum Gravit
Quantum ground-state cooling and tripartite entanglement with three-mode optoacoustic interactions
We present a quantum analysis of three-mode optoacoustic parametric
interactions in an optical cavity, in which two orthogonal transverse
optical-cavity modes are coupled to one acoustic mode through radiation
pressure. Due to the optimal frequency matching -- the frequency separation of
two cavity modes is equal to the acoustic-mode frequency -- the carrier and
sideband fields simultaneously resonate and coherently build up. This mechanism
significantly enhances the optoacoustic couplings in the quantum regime. It
allows exploration of quantum behavior of optoacoustic interactions in
small-scale table-top experiments. We show explicitly that given an
experimentally achievable parameter, three-mode scheme can realize quantum
ground-state cooling of milligram scale mechanical oscillators and create
robust stationary tripartite optoacoustic quantum entanglements.Comment: 20 pages, 5 figure
- …