985 research outputs found
Classical Structures Based on Unitaries
Starting from the observation that distinct notions of copying have arisen in
different categorical fields (logic and computation, contrasted with quantum
mechanics) this paper addresses the question of when, or whether, they may
coincide. Provided all definitions are strict in the categorical sense, we show
that this can never be the case. However, allowing for the defining axioms to
be taken up to canonical isomorphism, a close connection between the classical
structures of categorical quantum mechanics, and the categorical property of
self-similarity familiar from logical and computational models becomes
apparent.
The required canonical isomorphisms are non-trivial, and mix both typed
(multi-object) and untyped (single-object) tensors and structural isomorphisms;
we give coherence results that justify this approach.
We then give a class of examples where distinct self-similar structures at an
object determine distinct matrix representations of arrows, in the same way as
classical structures determine matrix representations in Hilbert space. We also
give analogues of familiar notions from linear algebra in this setting such as
changes of basis, and diagonalisation.Comment: 24 pages,7 diagram
Semigroup Closures of Finite Rank Symmetric Inverse Semigroups
We introduce the notion of semigroup with a tight ideal series and
investigate their closures in semitopological semigroups, particularly inverse
semigroups with continuous inversion. As a corollary we show that the symmetric
inverse semigroup of finite transformations of the rank
is algebraically closed in the class of (semi)topological inverse
semigroups with continuous inversion. We also derive related results about the
nonexistence of (partial) compactifications of classes of semigroups that we
consider.Comment: With the participation of the new coauthor - Jimmie Lawson - the
manuscript has been substantially revised and expanded. Accordingly, we have
also changed the manuscript titl
Normal State Resistivity of Underdoped YBa2Cu3Ox Thin Films and La2-xSrxCuO4 Ultra-Thin Films under Epitaxial Strain
The normal state resistivity of high temperature superconductors can be
probed in the region below Tc by suppressing the superconducting state in high
magnetic fields. Here we present the normal state properties of YBa2Cu3Ox thin
films in the underdoped regime and the normal state resistance of La2-xSrxCuO4
thin films under epitaxial strain, measured below Tc by applying pulsed fields
up to 60 T. A universal rho(T) behaviour is reported. We interpret these data
in terms of the recently proposed 1D quantum transport model with the 1D paths
corresponding to the charge stripes.Comment: 5 pages, PDF and PS, including figures, presented at MOS99 and
accepted for publication in J. of Low Temp. Phy
Low-frequency measurement of the tunneling amplitude in a flux qubit
We have observed signatures of resonant tunneling in an Al three-junction
qubit, inductively coupled to a Nb LC tank circuit. The resonant properties of
the tank oscillator are sensitive to the effective susceptibility (or
inductance) of the qubit, which changes drastically as its flux states pass
through degeneracy. The tunneling amplitude is estimated from the data. We find
good agreement with the theoretical predictions in the regime of their
validity.Comment: REVTeX4, 3pp., 3 EPS figures. v2: new sample, textual clarifications.
v3: minor polishing; final, to appear in PRB Rapid
Critical point network for drainage between rough surfaces
In this paper, we present a network method for computing two-phase flows between two rough surfaces with significant contact areas. Low-capillary number drainage is investigated here since one-phase flows have been previously investigated in other contributions. An invasion percolation algorithm is presented for modeling slow displacement of a wetting fluid by a non wetting one between two rough surfaces. Short-correlated Gaussian process is used to model random rough surfaces.The algorithm is based on a network description of the fracture aperture field. The network is constructed from the identification of critical points (saddles and maxima) of the aperture field. The invasion potential is determined from examining drainage process in a flat mini-channel. A direct comparison between numerical prediction and experimental visualizations on an identical geometry has been performed for one realization of an artificial fracture with a moderate fractional contact area of about 0.3. A good agreement is found between predictions and observations
Carrier relaxation, pseudogap, and superconducting gap in high-Tc cuprates: A Raman scattering study
We describe results of electronic Raman-scattering experiments in differently
doped single crystals of Y-123 and Bi-2212. The comparison of AF insulating and
metallic samples suggests that at least the low-energy part of the spectra
originates predominantly from excitations of free carriers. We therefore
propose an analysis of the data in terms of a memory function approach.
Dynamical scattering rates and mass-enhancement factors for the carriers are
obtained. In B2g symmetry the Raman data compare well to the results obtained
from ordinary and optical transport. For underdoped materials the dc scattering
rates in B1g symmetry become temperature independent and considerably larger
than in B2g symmetry. This increasing anisotropy is accompanied by a loss of
spectral weight in B2g symmetry in the range between the superconducting
transition at Tc and a characteristic temperature T* of order room temperature
which compares well with the pseudogap temperature found in other experiments.
The energy range affected by the pseudogap is doping and temperature
independent. The integrated spectral loss is approximately 25% in underdoped
samples and becomes much weaker towards higher carrier concentration. In
underdoped samples, superconductivity related features in the spectra can be
observed only in B2g symmetry. The peak frequencies scale with Tc. We do not
find a direct relation between the pseudogap and the superconducting gap.Comment: RevTeX, 21 pages, 24 gif figures. For PostScript with embedded eps
figures, see http://www.wmi.badw-muenchen.de/~opel/k2.htm
Fragmentation Function and Hadronic Production of the Heavy Supersymmetric Hadrons
The light top-squark \sto may be the lightest squark and its lifetime may
be `long enough' in a kind of SUSY models which have not been ruled out yet
experimentally, so colorless `supersymmetric hadrons (superhadrons)' (\sto
\bar{q}) ( is a quark except -quark) may be formed as long as the light
top-squark \sto can be produced. Fragmentation function of \sto to heavy
`supersymmetric hadrons (superhadrons)' (\sto \bar{Q}) ( or
) and the hadronic production of the superhadrons are investigated
quantitatively. The fragmentation function is calculated precisely. Due to the
difference in spin of the SUSY component, the asymptotic behavior of the
fragmentation function is different from those of the existent ones. The
fragmentation function is also applied to compute the production of heavy
superhadrons at hadronic colliders Tevatron and LHC under the so-called
fragmentation approach. The resultant cross-section for the heavy superhadrons
is too small to observe at Tevatron, but great enough at LHC, even when all the
relevant parameters in the SUSY models are taken within the favored region for
the heavy superhadrons. The production of `light superhadrons' (\sto \bar{q})
() is also roughly estimated. It is pointed out that the production
cross-sections of the light superhadrons (\sto \bar{q}) may be much greater
than those of the heavy superhadrons, so that even at Tevatron the light
superhadrons may be produced in great quantities.Comment: 20 pages, 9 figure
Interplay between edge states and simple bulk defects in graphene nanoribbons
We study the interplay between the edge states and a single impurity in a
zigzag graphene nanoribbon. We use tight-binding exact diagonalization
techniques, as well as density functional theory calculations to obtain the
eigenvalue spectrum, the eigenfunctions, as well the dependence of the local
density of states (LDOS) on energy and position. We note that roughly half of
the unperturbed eigenstates in the spectrum of the finite-size ribbon hybridize
with the impurity state, and the corresponding eigenvalues are shifted with
respect to their unperturbed values. The maximum shift and hybridization occur
for a state whose energy is inverse proportional to the impurity potential;
this energy is that of the impurity peak in the DOS spectrum. We find that the
interference between the impurity and the edge gives rise to peculiar
modifications of the LDOS of the nanoribbon, in particular to oscillations of
the edge LDOS. These effects depend on the size of the system, and decay with
the distance between the edge and the impurity.Comment: 10 pages, 15 figures, revtex
Quasi-Monte Carlo rules for numerical integration over the unit sphere
We study numerical integration on the unit sphere using equal weight quadrature rules, where the weights are such
that constant functions are integrated exactly.
The quadrature points are constructed by lifting a -net given in the
unit square to the sphere by means of an area
preserving map. A similar approach has previously been suggested by Cui and
Freeden [SIAM J. Sci. Comput. 18 (1997), no. 2].
We prove three results. The first one is that the construction is (almost)
optimal with respect to discrepancies based on spherical rectangles. Further we
prove that the point set is asymptotically uniformly distributed on
. And finally, we prove an upper bound on the spherical cap
-discrepancy of order (where denotes the
number of points). This slightly improves upon the bound on the spherical cap
-discrepancy of the construction by Lubotzky, Phillips and Sarnak [Comm.
Pure Appl. Math. 39 (1986), 149--186]. Numerical results suggest that the
-nets lifted to the sphere have spherical cap
-discrepancy converging with the optimal order of
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