3,376 research outputs found
Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces
We discuss various infinite-dimensional configuration spaces that carry
measures quasiinvariant under compactly-supported diffeomorphisms of a manifold
M corresponding to a physical space. Such measures allow the construction of
unitary representations of the diffeomorphism group, which are important to
nonrelativistic quantum statistical physics and to the quantum theory of
extended objects in d-dimensional Euclidean space. Special attention is given
to measurable structure and topology underlying measures on generalized
configuration spaces obtained from self-similar random processes (both for d =
1 and d > 1), which describe infinite point configurations having accumulation
points
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Mast cell clones: a model for the analysis of cellular maturation.
Cloned mouse mast cells resemble, by ultrastructure, immature mast cells observed in vivo. These mast cell clones can be grown in the absence of any other cells, facilitating direct investigations of their biochemistry and function. We find that cloned mast cells express plasma membrane receptors (Fc epsilon R) that bind mouse IgE with an equilibrium constant (KA) similar to that of normal mouse peritoneal mast cells. In addition, cloned mast cells do not display detectable la antigens and cannot enhance lg secretion when added to lymphocyte cultures or mediate natural killer lysis. In the presence of 1 mM sodium butyrate, cloned mast cells stop dividing and acquire abundant electron-dense cytoplasmic granules similar to those of mature mast cells. Their histamine content increases concomitant with cytoplasmic granule maturation and may exceed that of untreated mast cells by 50-fold. Unlike peritoneal mast cells, cloned mast cells incorporate 35SO4 into chondroitin sulfates rather than heparin. These findings demonstrate that, unlike fully differentiated mouse peritoneal mast cells, cloned immature mouse mast cells contain no heparin and low levels of histamine. In addition, they establish that high-affinity Fc epsilon R are expressed early in mast cell maturation, well before completion of cytoplasmic granule synthesis and mediator storage
Bicrossproduct approach to the Connes-Moscovici Hopf algebra
We give a rigorous proof that the (codimension one) Connes-Moscovici Hopf
algebra H_CM is isomorphic to a bicrossproduct Hopf algebra linked to a group
factorisation of the group of positively-oriented diffeomorphisms of the real
line. We construct a second bicrossproduct U_CM equipped with a nondegenerate
dual pairing with H_CM. We give a natural quotient Hopf algebra of H_CM and
Hopf subalgebra of U_CM which again are in duality. All these Hopf algebras
arise as deformations of commutative or cocommutative Hopf algebras that we
describe in each case. Finally we develop the noncommutative differential
geometry of the quotient of H_CM by studying covariant first order differential
calculi of small dimension over this algebra.Comment: 21 page
Equivariant cohomology and analytic descriptions of ring isomorphisms
In this paper we consider a class of connected closed -manifolds with a
non-empty finite fixed point set, each of which is totally non-homologous
to zero in (or -equivariantly formal), where . With the
help of the equivariant index, we give an explicit description of the
equivariant cohomology of such a -manifold in terms of algebra, so that we
can obtain analytic descriptions of ring isomorphisms among equivariant
cohomology rings of such -manifolds, and a necessary and sufficient
condition that the equivariant cohomology rings of such two -manifolds are
isomorphic. This also leads us to analyze how many there are equivariant
cohomology rings up to isomorphism for such -manifolds in 2- and
3-dimensional cases.Comment: 20 pages, updated version with two references adde
Signaling, Entanglement, and Quantum Evolution Beyond Cauchy Horizons
Consider a bipartite entangled system half of which falls through the event
horizon of an evaporating black hole, while the other half remains coherently
accessible to experiments in the exterior region. Beyond complete evaporation,
the evolution of the quantum state past the Cauchy horizon cannot remain
unitary, raising the questions: How can this evolution be described as a
quantum map, and how is causality preserved? What are the possible effects of
such nonstandard quantum evolution maps on the behavior of the entangled
laboratory partner? More generally, the laws of quantum evolution under extreme
conditions in remote regions (not just in evaporating black-hole interiors, but
possibly near other naked singularities and regions of extreme spacetime
structure) remain untested by observation, and might conceivably be non-unitary
or even nonlinear, raising the same questions about the evolution of entangled
states. The answers to these questions are subtle, and are linked in unexpected
ways to the fundamental laws of quantum mechanics. We show that terrestrial
experiments can be designed to probe and constrain exactly how the laws of
quantum evolution might be altered, either by black-hole evaporation, or by
other extreme processes in remote regions possibly governed by unknown physics.Comment: Combined, revised, and expanded version of quant-ph/0312160 and
hep-th/0402060; 13 pages, RevTeX, 2 eps figure
Anharmonicity of flux lattices and thermal fluctuations in layered superconductors
We study elasticity of a perpendicular flux lattice in a layered
superconductor with Josephson coupling between layers. We find that the energy
contains ln(flux displacement) terms, so that elastic constants cannot be
strictly defined. Instead we define effective elastic constants by a thermal
average. The tilt modulus has terms with ln(T) which for weak fields, i.e.
Josephson length smaller than the flux line spacing, lead to displacement
square average proportional to T/ln(T). The expansion parameter indicates that
the dominant low temperature phase transition is either layer decoupling at
high fields or melting at low fields.Comment: 15 pages, 2 eps figures, Revtex, submitted to Phys. Rev. B.
Sunj-class: superconductivit
Disorder Induced Transitions in Layered Coulomb Gases and Superconductors
A 3D layered system of charges with logarithmic interaction parallel to the
layers and random dipoles is studied via a novel variational method and an
energy rationale which reproduce the known phase diagram for a single layer.
Increasing interlayer coupling leads to successive transitions in which charge
rods correlated in N>1 neighboring layers are nucleated by weaker disorder. For
layered superconductors in the limit of only magnetic interlayer coupling, the
method predicts and locates a disorder-induced defect-unbinding transition in
the flux lattice. While N=1 charges dominate there, N>1 disorder induced defect
rods are predicted for multi-layer superconductors.Comment: 4 pages, 2 figures, RevTe
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