1,508 research outputs found
Dbrane Phase Transitions and Monodromy in K-theory
Majumder and Sen have given an explicit construction of a first order phase
transition in a non-supersymmetric system of Dbranes that occurs when the B
field is varied. We show that the description of this transition in terms of
K-theory involves a bundle of K groups of non-commutative algebras over the
Kahler cone with nontrivial monodromy. Thus the study of monodromy in K groups
associated with quantized algebras can be used to predict the phase structure
of systems of (non-supersymmetric) Dbranes.Comment: 8 pages, RevTeX, 1 figur
On the quantization of Poisson brackets
In this paper we introduce two classes of Poisson brackets on algebras (or on
sheaves of algebras). We call them locally free and nonsingular Poisson
brackets. Using the Fedosov's method we prove that any locally free nonsingular
Poisson bracket can be quantized. In particular, it follows from this that all
Poisson brackets on an arbitrary field of characteristic zero can be quantized.
The well known theorem about the quantization of nondegenerate Poisson brackets
on smooth manifolds follows from the main result of this paper as well.Comment: Latex, 24 pp., essentially corrected versio
Universality of Fedosov's Construction for Star Products of Wick Type on Pseudo-K\"ahler Manilfolds
In this paper we construct star products on a pseudo-K\"ahler manifold
using a modification of the Fedosov method based on a different
fibrewise product similar to the Wick product on . In a first step
we show that this construction is rich enough to obtain star products of every
equivalence class by computing Deligne's characteristic class of these
products. Among these products we uniquely characterize the ones which have the
additional property to be of Wick type which means that the bidifferential
operators describing the star products only differentiate with respect to
holomorphic directions in the first argument and anti-holomorphic directions in
the second argument. These star products are in fact strongly related to star
products with separation of variables introduced and studied by Karabegov. This
characterization gives rise to special conditions on the data that enter the
Fedosov procedure. Moreover, we compare our results that are based on an
obviously coordinate independent construction to those of Karabegov that were
obtained by local considerations and give an independent proof of the fact that
star products of Wick type are in bijection to formal series of closed
two-forms of type on . Using this result we finally succeed in
showing that the given Fedosov construction is universal in the sense that it
yields all star products of Wick type on a pseudo-K\"ahler manifold.Comment: terminology corrected, typos removed, appendix adde
A heat trace anomaly on polygons
Let be a polygon in \RR^2, or more generally a compact surface
with piecewise smooth boundary and corners. Suppose that \Omega_\e is a
family of surfaces with \calC^\infty boundary which converges to
smoothly away from the corners, and in a precise way at the vertices to be
described in the paper. Fedosov \cite{Fe}, Kac \cite{K} and McKean-Singer
\cite{MS} recognized that certain heat trace coefficients, in particular the
coefficient of , are not continuous as \e \searrow 0. We describe this
anomaly using renormalized heat invariants of an auxiliary smooth domain
which models the corner formation. The result applies both for Dirichlet and
Neumann conditions. We also include a discussion of what one might expect in
higher dimensions.Comment: Revision includes treatment of the Neumann problem and a discussion
of the higher dimensional case; some new reference
Stability of heterogeneous parallel-bond adhesion clusters under static load
Adhesion interactions mediated by multiple bond types are relevant for many
biological and soft matter systems, including the adhesion of biological cells
and functionalized colloidal particles to various substrates. To elucidate
advantages and disadvantages of multiple bond populations for the stability of
heterogeneous adhesion clusters of receptor-ligand pairs, a theoretical model
for a homogeneous parallel adhesion bond cluster under constant loading is
extended to several bond types. The stability of the entire cluster can be
tuned by changing densities of different bond populations as well as their
extensional rigidity and binding properties. In particular, bond extensional
rigidities determine the distribution of total load to be shared between
different sub-populations. Under a gradual increase of the total load, the
rupture of a heterogeneous adhesion cluster can be thought of as a multistep
discrete process, in which one of the bond sub-populations ruptures first,
followed by similar rupture steps of other sub-populations or by immediate
detachment of the remaining cluster. This rupture behavior is qualitatively
independent of involved bond types, such as slip and catch bonds.
Interestingly, an optimal stability is generally achieved when the total
cluster load is shared such that loads on distinct bond populations are equal
to their individual critical rupture forces. We also show that cluster
heterogeneity can drastically affect cluster lifetime.Comment: 11 pages, 8 figure
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