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 $n$ 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

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 $L^2$ error of the best $N$-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

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

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 $2n$ internal data for well-chosen boundary conditions are available, where $n$ 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