1,599 research outputs found
Shape Space Methods for Quantum Cosmological Triangleland
With toy modelling of conceptual aspects of quantum cosmology and the problem
of time in quantum gravity in mind, I study the classical and quantum dynamics
of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do
so by importing techniques to the triangle model from the corresponding 4
particles in 1-d model, using the fact that both have 2-spheres for shape
spaces, though the latter has a trivial realization whilst the former has a
more involved Hopf (or Dragt) type realization. I furthermore interpret the
ensuing Dragt-type coordinates as shape quantities: a measure of
anisoscelesness, the ellipticity of the base and apex's moments of inertia, and
a quantity proportional to the area of the triangle. I promote these quantities
at the quantum level to operators whose expectation and spread are then useful
in understanding the quantum states of the system. Additionally, I tessellate
the 2-sphere by its physical interpretation as the shape space of triangles,
and then use this as a back-cloth from which to read off the interpretation of
dynamical trajectories, potentials and wavefunctions. I include applications to
timeless approaches to the problem of time and to the role of uniform states in
quantum cosmological modelling.Comment: A shorter version, as per the first stage in the refereeing process,
and containing some new reference
A random matrix decimation procedure relating to
Classical random matrix ensembles with orthogonal symmetry have the property
that the joint distribution of every second eigenvalue is equal to that of a
classical random matrix ensemble with symplectic symmetry. These results are
shown to be the case of a family of inter-relations between eigenvalue
probability density functions for generalizations of the classical random
matrix ensembles referred to as -ensembles. The inter-relations give
that the joint distribution of every -st eigenvalue in certain
-ensembles with is equal to that of another
-ensemble with . The proof requires generalizing a
conditional probability density function due to Dixon and Anderson.Comment: 19 pages, 1 figur
Matroids over a ring
We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a field, we recover matroids. When R D Z, and when R is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, i.e. tropical linear spaces, respectively. More generally, whenever R is a Dedekind domain, we extend all the usual properties and operations holding for matroids (e.g., duality), and we explicitly describe the structure of the matroids over R. Furthermore, we compute the Tutte-Grothendieck ring of matroids over R. We also show that the Tutte quasi-polynomial of a matroid over Z can be obtained as an evaluation of the class of the matroid in the Tutte-Grothendieck ring
The effect of pore-former morphology on the electrochemical performance of solid oxide fuel cells under combined fuel cell and electrolysis modes
The effect of the pore-former used in the Ni-YSZ fuel electrode on the electrochemical performance of solid oxide cells is studied. Three cells with the configuration of Ni-YSZ/YSZ/Nd2NiO4+d-YSZ were fabricated with different pore-formers, such as graphite, PMMA (polymethyl methacrylate) or an equal mixture of both, which were added to the Ni-YSZ support during the fabrication process. The results show that the Ni-YSZ support containing graphite leads to a more porous support and formation of coarser pores in the vicinity of the electrolyte. This leads to a reduction in the triple phase boundary (TPB) length with a corresponding increase of activation polarization and, as a consequence, the overall cell performance decreases in both fuel cell and electrolysis modes. The cell having PMMA delivered the highest performance under both operation modes (818 and -713 mAcm-2 were obtained in SOFC and SOEC modes at 800 °C), due to finer pores next to the electrolyte. The cell having the mixture of both pore-formers delivered intermediate results. All the cells show similar concentration polarization values meaning that even the least porous cell (PMMA) provided sufficient porosity for gas flow. In addition, long term reversible experiments were performed, showing no degradation for a period above 400 h
Superconductors are topologically ordered
We revisit a venerable question: what is the nature of the ordering in a
superconductor? We find that the answer is properly that the superconducting
state exhibits topological order in the sense of Wen, i.e. that while it lacks
a local order parameter, it is sensitive to the global topology of the
underlying manifold and exhibits an associated fractionalization of quantum
numbers. We show that this perspective unifies a number of previous
observations on superconductors and their low lying excitations and that this
complex can be elegantly summarized in a purely topological action of the
``'' type and its elementary quantization. On manifolds with boundaries,
the action correctly predicts non-chiral edge states, gapped in general,
but crucial for fractionalization and establishing the ground state degeneracy.
In all of this the role of the physical electromagnetic fields is central. We
also observe that the action describes the topological order in several
other physically distinct systems thus providing an example of topological
universality
Surface Instability in Windblown Sand
We investigate the formation of ripples on the surface of windblown sand
based on the one-dimensional model of Nishimori and Ouchi [Phys. Rev. Lett. 71,
197 (1993)], which contains the processes of saltation and grain relaxation. We
carry out a nonlinear analysis to determine the propagation speed of the
restabilized ripple patterns, and the amplitudes and phases of their first,
second, and third harmonics. The agreement between the theory and our numerical
simulations is excellent near the onset of instability. We also determine the
Eckhaus boundary, outside which the steady ripple patterns are unstable.Comment: 23 pages, 8 figure
Statistical Theory for Incoherent Light Propagation in Nonlinear Media
A novel statistical approach based on the Wigner transform is proposed for
the description of partially incoherent optical wave dynamics in nonlinear
media. An evolution equation for the Wigner transform is derived from a
nonlinear Schrodinger equation with arbitrary nonlinearity. It is shown that
random phase fluctuations of an incoherent plane wave lead to a Landau-like
damping effect, which can stabilize the modulational instability. In the limit
of the geometrical optics approximation, incoherent, localized, and stationary
wave-fields are shown to exist for a wide class of nonlinear media.Comment: 4 pages, REVTeX4. Submitted to Physical Review E. Revised manuscrip
Photoproduction of mesons in nuclei at GeV energies
In a transport model that combines initial state interactions of the photon
with final state interactions of the produced particles we present a
calculation of inclusive photoproduction of mesons in nuclei in the energy
range from 1 to 7 GeV. We give predictions for the photoproduction cross
sections of pions, etas, kaons, antikaons, and invariant mass
spectra in ^{12}C and ^{208}Pb. The effects of nuclear shadowing and final
state interaction of the produced particles are discussed in detail.Comment: Text added in summary in general reliability of the method,
references updated. Phys. Rev. C (2000) in pres
Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures
We derive and discuss the equations of motion for the condensate and its
fluctuations for a dilute, weakly interacting Bose gas in an external potential
within the self--consistent Hartree--Fock--Bogoliubov (HFB) approximation.
Account is taken of the depletion of the condensate and the anomalous Bose
correlations, which are important at finite temperatures. We give a critical
analysis of the self-consistent HFB approximation in terms of the
Hohenberg--Martin classification of approximations (conserving vs gapless) and
point out that the Popov approximation to the full HFB gives a gapless
single-particle spectrum at all temperatures. The Beliaev second-order
approximation is discussed as the spectrum generated by functional
differentiation of the HFB single--particle Green's function. We emphasize that
the problem of determining the excitation spectrum of a Bose-condensed gas
(homogeneous or inhomogeneous) is difficult because of the need to satisfy
several different constraints.Comment: plain tex, 19 page
Hadron formation in high energy photonuclear reactions
We present a new method to account for coherence length effects in a
semi-classical transport model. This allows us to describe photo- and
electroproduction at large nuclei (A>12) and high energies using a realistic
coupled channel description of the final state interactions that goes beyond
simple Glauber theory. We show that the purely absorptive treatment of the
final state interactions can lead to wrong estimates of color transparency and
formation time effects in particle production. As an example, we discuss
exclusive rho^0 photoproduction on Pb at a photon energy of 7 GeV as well as
K^+ production in the photon energy range 1-7 GeV.Comment: 14 pages, 6 figures, version published in Phys. Rev.
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