15,574 research outputs found
Quantum stochastic cocycles and completely bounded semigroups on operator spaces
An operator space analysis of quantum stochastic cocycles is undertaken.
These are cocycles with respect to an ampliated CCR flow, adapted to the
associated filtration of subspaces, or subalgebras. They form a noncommutative
analogue of stochastic semigroups in the sense of Skorohod. One-to-one
correspondences are established between classes of cocycle of interest and
corresponding classes of one-parameter semigroups on associated matrix spaces.
Each of these 'global' semigroups may be viewed as the expectation semigroup of
an associated quantum stochastic cocycle on the corresponding matrix space. The
classes of cocycle covered include completely positive contraction cocycles on
an operator system, or C*-algebra; completely contractive cocycles on an
operator space; and contraction operator cocycles on a Hilbert space. As
indicated by Accardi and Kozyrev, the Schur-action matrix semigroup viewpoint
circumvents technical (domain) limitations inherent in the theory of quantum
stochastic differential equations. An infinitesimal analysis of quantum
stochastic cocycles from the present wider perspective is given in a sister
paper.Comment: 32 page
Further Representations of the Canonical Commutation Relations
We construct a new class of representations of the canonical commutation
relations, which generalizes previously known classes. We perturb the
infinitesimal generator of the initial Fock representation (i.e. the free
quantum field) by a function of the field which is square-integrable with
respect to the associated Gaussian measure. We characterize which such
perturbations lead to representations of the canonical commutation relations.
We provide conditions entailing the irreducibility of such representations,
show explicitly that our class of representations subsumes previously studied
classes, and give necessary and sufficient conditions for our representations
to be unitarily equivalent, resp. quasi-equivalent, with Fock, coherent or
quasifree representations
Active cooling design for scramjet engines using optimization methods
A methodology for using optimization in designing metallic cooling jackets for scramjet engines is presented. The optimal design minimizes the required coolant flow rate subject to temperature, mechanical-stress, and thermal-fatigue-life constraints on the cooling-jacket panels, and Mach-number and pressure contraints on the coolant exiting the panel. The analytical basis for the methodology is presented, and results for the optimal design of panels are shown to demonstrate its utility
Self-shrinkers with a rotational symmetry
In this paper we present a new family of non-compact properly embedded,
self-shrinking, asymptotically conical, positive mean curvature ends
that are hypersurfaces of revolution with
circular boundaries. These hypersurface families interpolate between the plane
and half-cylinder in , and any rotationally symmetric
self-shrinking non-compact end belongs to our family. The proofs involve the
global analysis of a cubic-derivative quasi-linear ODE. We also prove the
following classification result: a given complete, embedded, self-shrinking
hypersurface of revolution is either a hyperplane ,
the round cylinder of radius , the
round sphere of radius , or is diffeomorphic to an (i.e. a "doughnut" as in [Ang], which when is a torus). In
particular for self-shrinkers there is no direct analogue of the Delaunay
unduloid family. The proof of the classification uses translation and rotation
of pieces, replacing the method of moving planes in the absence of isometries.Comment: Trans. Amer. Math. Soc. (2011), to appear; 23 pages, 1 figur
Mean curvature self-shrinkers of high genus: Non-compact examples
We give the first rigorous construction of complete, embedded self-shrinking
hypersurfaces under mean curvature flow, since Angenent's torus in 1989. The
surfaces exist for any sufficiently large prescribed genus , and are
non-compact with one end. Each has symmetries and comes from
desingularizing the intersection of the plane and sphere through a great
circle, a configuration with very high symmetry. Each is at infinity asymptotic
to the cone in over a -periodic graph on an equator
of the unit sphere , with the shape of a
periodically "wobbling sheet". This is a dramatic instability phenomenon, with
changes of asymptotics that break much more symmetry than seen in minimal
surface constructions. The core of the proof is a detailed understanding of the
linearized problem in a setting with severely unbounded geometry, leading to
special PDEs of Ornstein-Uhlenbeck type with fast growth on coefficients of the
gradient terms. This involves identifying new, adequate weighted H\"older
spaces of asymptotically conical functions in which the operators invert, via a
Liouville-type result with precise asymptotics.Comment: 41 pages, 1 figure; minor typos fixed; to appear in J. Reine Angew.
Mat
Geometric Modular Action and Spacetime Symmetry Groups
A condition of geometric modular action is proposed as a selection principle
for physically interesting states on general space-times. This condition is
naturally associated with transformation groups of partially ordered sets and
provides these groups with projective representations. Under suitable
additional conditions, these groups induce groups of point transformations on
these space-times, which may be interpreted as symmetry groups. The
consequences of this condition are studied in detail in application to two
concrete space-times -- four-dimensional Minkowski and three-dimensional de
Sitter spaces -- for which it is shown how this condition characterizes the
states invariant under the respective isometry group. An intriguing new
algebraic characterization of vacuum states is given. In addition, the logical
relations between the condition proposed in this paper and the condition of
modular covariance, widely used in the literature, are completely illuminated.Comment: 83 pages, AMS-TEX (format changed to US letter size
Three-loop corrections to the lightest Higgs scalar boson mass in supersymmetry
I evaluate the largest three-loop corrections to the mass of the lightest
Higgs scalar boson in the Minimal Supersymmetric Standard Model in a
mass-independent renormalization scheme, using effective field theory and
renormalization group methods. The contributions found here are those that
depend only on strong and Yukawa interactions and on the leading and
next-to-leading logarithms of the ratio of a typical superpartner mass scale to
the top quark mass. The approximation assumes that all superpartners and the
other Higgs bosons can be treated as much heavier than the top quark, but does
not assume their degeneracy. I also discuss the consistent addition of the
three-loop corrections to a complete two-loop calculation.Comment: 9 page
The Many Faces of Heterogeneous Ice Nucleation: Interplay Between Surface Morphology and Hydrophobicity
What makes a material a good ice nucleating agent? Despite the importance of
heterogeneous ice nucleation to a variety of fields, from cloud science to
microbiology, major gaps in our understanding of this ubiquitous process still
prevent us from answering this question. In this work, we have examined the
ability of generic crystalline substrates to promote ice nucleation as a
function of the hydrophobicity and the morphology of the surface. Nucleation
rates have been obtained by brute-force molecular dynamics simulations of
coarse-grained water on top of different surfaces of a model fcc crystal,
varying the water-surface interaction and the surface lattice parameter. It
turns out that the lattice mismatch of the surface with respect to ice,
customarily regarded as the most important requirement for a good ice
nucleating agent, is at most desirable but not a requirement. On the other
hand, the balance between the morphology of the surface and its hydrophobicity
can significantly alter the ice nucleation rate and can also lead to the
formation of up to three different faces of ice on the same substrate. We have
pinpointed three circumstances where heterogeneous ice nucleation can be
promoted by the crystalline surface: (i) the formation of a water overlayer
that acts as an in-plane template; (ii) the emergence of a contact layer
buckled in an ice-like manner; and (iii) nucleation on compact surfaces with
very high interaction strength. We hope that this extensive systematic study
will foster future experimental work aimed at testing the physiochemical
understanding presented herein.Comment: Main + S
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