16,668 research outputs found
Persistence for Circle Valued Maps
We study circle valued maps and consider the persistence of the homology of
their fibers. The outcome is a finite collection of computable invariants which
answer the basic questions on persistence and in addition encode the topology
of the source space and its relevant subspaces. Unlike persistence of real
valued maps, circle valued maps enjoy a different class of invariants called
Jordan cells in addition to bar codes. We establish a relation between the
homology of the source space and of its relevant subspaces with these
invariants and provide a new algorithm to compute these invariants from an
input matrix that encodes a circle valued map on an input simplicial complex.Comment: A complete algorithm to compute barcodes and Jordan cells is provided
in this version. The paper is accepted in in the journal Discrete &
Computational Geometry. arXiv admin note: text overlap with arXiv:1210.3092
by other author
Theory of THz Conductivity in the Pseudogap Phase of the Cuprates: A Pre-Formed Pair Perspective
In this paper we deduce transport properties in the presence of a pseudogap
associated with precursor superconductivity. Our theoretical analysis is based
on the widely adopted self energy expression reflecting this normal state gap,
which has appeared in interpretations of photoemission and in other
experiments. Thus, it should be generally applicable. Here we address THz
conductivity
measurements in the underdoped high temperature superconductors and arrive at
reasonable agreement between theory and recent experiment for both
and above and below .Comment: 8 pages, 2 figure
Contrasting Nodal and Anti-Nodal Behavior in the Cuprates Via Multiple Gap Spectroscopies
Using a precursor superconductivity scenario for the cuprates we present a
theory for the temperature dependent behavior of the spectral gaps associated
with four distinct spectroscopies: angle resolved photoemission (ARPES),
differential conductance , quasi-particle interference spectroscopy, and
the autocorrelated ARPES pattern. We find good agreement for a range of
existing experiments and make predictions for others. Our theory, which
incorporates the necessary (observed) contrast between the nodal and anti-nodal
response, shows how different nodal gap shapes are associated with these
alternative spectroscopies.Comment: 4 pages, 3 figure
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