20,615 research outputs found
Entanglement properties of quantum spin chains
We investigate the entanglement properties of a finite size 1+1 dimensional
Ising spin chain, and show how these properties scale and can be utilized to
reconstruct the ground state wave function. Even at the critical point, few
terms in a Schmidt decomposition contribute to the exact ground state, and to
physical properties such as the entropy. Nevertheless the entanglement here is
prominent due to the lower-lying states in the Schmidt decomposition.Comment: 5 pages, 6 figure
Quantitative Photo-acoustic Tomography with Partial Data
Photo-acoustic tomography is a newly developed hybrid imaging modality that
combines a high-resolution modality with a high-contrast modality. We analyze
the reconstruction of diffusion and absorption parameters in an elliptic
equation and improve an earlier result of Bal and Uhlmann to the partial date
case. We show that the reconstruction can be uniquely determined by the
knowledge of 4 internal data based on well-chosen partial boundary conditions.
Stability of this reconstruction is ensured if a convexity condition is
satisfied. Similar stability result is obtained without this geometric
constraint if 4n well-chosen partial boundary conditions are available, where
is the spatial dimension. The set of well-chosen boundary measurements is
characterized by some complex geometric optics (CGO) solutions vanishing on a
part of the boundary.Comment: arXiv admin note: text overlap with arXiv:0910.250
The chameleon groups of Richard J. Thompson: automorphisms and dynamics
The automorphism groups of several of Thompson's countable groups of
piecewise linear homeomorphisms of the line and circle are computed and it is
shown that the outer automorphism groups of these groups are relatively small.
These results can be interpreted as stability results for certain structures of
PL functions on the circle. Machinery is developed to relate the structures on
the circle to corresponding structures on the line
Replica equivalence in the Edwards-Anderson model
After introducing and discussing the "link-overlap" between spin
configurations we show that the Edwards-Anderson model has a
"replica-equivalent" quenched equilibrium state, a property introduced by
Parisi in the description of the mean-field spin-glass phase which generalizes
ultrametricity. Our argument is based on the control of fluctuations through
the property of stochastic stability and works for all the finite-dimensional
spin-glass models.Comment: 12 pages, few remarks added. To appear in Journal of Physics A:
Mathematical and Genera
The Dynamics of Poor Systems of Galaxies
We assemble and observe a sample of poor galaxy systems that is suitable for
testing N-body simulations of hierarchical clustering (Navarro, Frenk, & White
1997; NFW) and other dynamical halo models (e.g., Hernquist 1990). We (1)
determine the parameters of the density profile rho(r) and the velocity
dispersion profile sigma(R), (2) separate emission-line galaxies from
absorption-line galaxies, examining the model parameters and as a function of
spectroscopic type, and (3) for the best-behaved subsample, constrain the
velocity anisotropy parameter, beta, which determines the shapes of the galaxy
orbits.
The NFW universal profile and the Hernquist (1990) model both provide good
descriptions of the spatial data. In most cases an isothermal sphere is ruled
out. Systems with declining sigma(R) are well-matched by theoretical profiles
in which the star-forming galaxies have predominantly radial orbits (beta > 0);
many of these galaxies are probably falling in for the first time. There is
significant evidence for spatial segregation of the spectroscopic classes
regardless of sigma(R).Comment: 36 pages, 20 figures, and 5 tables. To appear in the Astrophysical
Journa
Shearlets and Optimally Sparse Approximations
Multivariate functions are typically governed by anisotropic features such as
edges in images or shock fronts in solutions of transport-dominated equations.
One major goal both for the purpose of compression as well as for an efficient
analysis is the provision of optimally sparse approximations of such functions.
Recently, cartoon-like images were introduced in 2D and 3D as a suitable model
class, and approximation properties were measured by considering the decay rate
of the error of the best -term approximation. Shearlet systems are to
date the only representation system, which provide optimally sparse
approximations of this model class in 2D as well as 3D. Even more, in contrast
to all other directional representation systems, a theory for compactly
supported shearlet frames was derived which moreover also satisfy this
optimality benchmark. This chapter shall serve as an introduction to and a
survey about sparse approximations of cartoon-like images by band-limited and
also compactly supported shearlet frames as well as a reference for the
state-of-the-art of this research field.Comment: in "Shearlets: Multiscale Analysis for Multivariate Data",
Birkh\"auser-Springe
Research review: young people leaving care
This paper reviews the international research on young people leaving care. Set in the context of a social exclusion framework, it explores young people's accelerated and compressed transitions to adulthood, and discusses the development and classification of leaving care services in responding to their needs. It then considers the evidence from outcome studies and argues that adopting a resilience framework suggests that young people leaving care may fall into three groups: young people 'moving on', 'survivors' and 'victims'. In concluding, it argues that these three pathways are associated with the quality of care young people receive, their transitions from care and the support they receive after care
Inverse Diffusion Theory of Photoacoustics
This paper analyzes the reconstruction of diffusion and absorption parameters
in an elliptic equation from knowledge of internal data. In the application of
photo-acoustics, the internal data are the amount of thermal energy deposited
by high frequency radiation propagating inside a domain of interest. These data
are obtained by solving an inverse wave equation, which is well-studied in the
literature. We show that knowledge of two internal data based on well-chosen
boundary conditions uniquely determines two constitutive parameters in
diffusion and Schroedinger equations. Stability of the reconstruction is
guaranteed under additional geometric constraints of strict convexity. No
geometric constraints are necessary when internal data for well-chosen
boundary conditions are available, where is spatial dimension. The set of
well-chosen boundary conditions is characterized in terms of appropriate
complex geometrical optics (CGO) solutions.Comment: 24 page
The Structure of Operators in Effective Particle-Conserving Models
For many-particle systems defined on lattices we investigate the global
structure of effective Hamiltonians and observables obtained by means of a
suitable basis transformation. We study transformations which lead to effective
Hamiltonians conserving the number of excitations. The same transformation must
be used to obtain effective observables. The analysis of the structure shows
that effective operators give rise to a simple and intuitive perspective on the
initial problem. The systematic calculation of n-particle irreducible
quantities becomes possible constituting a significant progress. Details how to
implement the approach perturbatively for a large class of systems are
presented.Comment: 12 pages, 1 figure, accepted by J. Phys. A: Math. Ge
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