4,958 research outputs found
Conic degeneration and the determinant of the Laplacian
We investigate the behavior of various spectral invariants, particularly the
determinant of the Laplacian, on a family of smooth Riemannian manifolds which
undergo conic degeneration; that is, which converge in a particular way to a
manifold with a conical singularity. Our main result is an asymptotic formula
for the determinant up to terms which vanish as the degeneration parameter goes
to zero. The proof proceeds in two parts; we study the fine structure of the
heat trace on the degenerating manifolds via a parametrix construction, and
then use that fine structure to analyze the zeta function and determinant of
the Laplacian.Comment: 41 pages, 7 figures. Version 2: bug fixed in Theorem 2 statement,
other minor change
Experimentally Probing the Shape of Extra Dimensions
In brane world scenarios in which only gravity can propagate in the extra
dimensions, effects on the gravitational force may be experimentally testable
if there are two or three large extra dimensions. The strength of the force at
distances smaller than the compactification radius will be sensitive to the
volume of the extra dimensions, but the determination of the shape requires
knowing the gravitational potential at intermediate scales. We determine the
dependence of the potential vs. distance as a function of both the relative
size of the extra dimensions and the possible angle between the extra
dimensional unit vectors, and show that high precision measurements of the
gravitational force will allow the determination of the shape of the extra
dimensions.Comment: Much more pedagogical version. Version to be published in the
American Journal of Physic
SET based experiments for HTSC materials: II
The cuprates seem to exhibit statistics, dimensionality and phase transitions
in novel ways. The nature of excitations
[i.e. quasiparticle or collective], spin-charge separation, stripes [static
and dynamics], inhomogeneities, psuedogap, effect of impurity dopings [e.g. Zn,
Ni] and any other phenomenon in these materials must be consistently
understood. In this note we further discuss our original suggestion of using
Single Electron Tunneling Transistor
[SET] based experiments to understand the role of charge dynamics in these
systems. Assuming that SET operates as an efficient charge detection system we
can expect to understand the underlying physics of charge transport and charge
fluctuations in these materials for a range of doping. Experiments such as
these can be classed in a general sense as mesoscopic and nano characterization
of cuprates and related materials. In principle such experiments can show if
electron is fractionalized in cuprates as indicated by ARPES data. In contrast
to flux trapping experiments SET based experiments are more direct in providing
evidence about spin-charge separation. In addition a detailed picture of nano
charge dynamics in cuprates may be obtained.Comment: 10 pages revtex plus four figures; ICMAT 2001 Conference Symposium P:
P10-0
The heat kernel on curvilinear polygonal domains in surfaces
We construct the heat kernel on curvilinear polygonal domains in arbitrary
surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed
problems, including those of Zaremba type. We compute the short time asymptotic
expansion of the heat trace and apply this expansion to demonstrate a
collection of results showing that corners are spectral invariants
- …