Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law

This work explores the use of a tree tensor network ansatz to simulate the ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting the entropic area law, the tree tensor network ansatz seems to produce quasi-exact results in systems with sizes well beyond the reach of exact diagonalisation techniques. We describe an algorithm to approximate the ground state of a local Hamiltonian on a L times L lattice with the topology of a torus. Accurate results are obtained for L={4,6,8}, whereas approximate results are obtained for larger lattices. As an application of the approach, we analyse the scaling of the ground state entanglement entropy at the quantum critical point of the model. We confirm the presence of a positive additive constant to the area law for half a torus. We also find a logarithmic additive correction to the entropic area law for a square block. The single copy entanglement for half a torus reveals similar corrections to the area law with a further term proportional to 1/L.Comment: Major rewrite, new version published in Phys. Rev. B with highly improved numerical results for the scaling of the entropies and several new sections. The manuscript has now 19 pages and 30 Figure

Beam-size effect and particle losses at SuperBB factory (Italy)

In the colliders, the macroscopically large impact parameters give a substantial contribution to the standard cross section of the $e^+ e^- \to e^+ e^- \gamma$ process. These impact parameters may be much larger than the transverse sizes of the colliding bunches. It means that the standard cross section of this process has to be substantially modified. In the present paper such a beam-size effect is calculated for bremsstrahlung at Super$B$ factory developed in Italy. We find out that this effect reduces beam losses due to bremsstrahlung by about 40%.Comment: 11 pages, 4 figure

Eddy Current measurement of Fiber Volume Fraction in Metal Matrix Composite Extrusions

The objective of this work was to develop an eddy current method for measuring fiber volume fraction in continuous-fiber metal matrix composites. Because an eddy current measurement can be affected by the spatial distribution of fibers as well as the overall fiber density, the measurement method had to be tolerant of possible variations in spatial distribution that might be encountered in practice. For this reason, the work began with the development of models of the effective resistivity tensor for a composite with an arbitrary fiber distribution and the resulting eddy current probe response [1,2]. The intent was to use these models to help design a measurement method and to test the method for ordered and disordered arrangements of fibers

Conformal off-diagonal boundary density profiles on a semi-infinite strip

The off-diagonal profile phi(v) associated with a local operator (order parameter or energy density) close to the boundary of a semi-infinite strip with width L is obtained at criticality using conformal methods. It involves the surface exponent x_phi^s and displays a simple universal behaviour which crosses over from surface finite-size scaling when v/L is held constant to corner finite-size scaling when v/L -> 0.Comment: 5 pages, 1 figure, IOP macros and eps

Casimir Forces between Spherical Particles in a Critical Fluid and Conformal Invariance

Mesoscopic particles immersed in a critical fluid experience long-range Casimir forces due to critical fluctuations. Using field theoretical methods, we investigate the Casimir interaction between two spherical particles and between a single particle and a planar boundary of the fluid. We exploit the conformal symmetry at the critical point to map both cases onto a highly symmetric geometry where the fluid is bounded by two concentric spheres with radii R_- and R_+. In this geometry the singular part of the free energy F only depends upon the ratio R_-/R_+, and the stress tensor, which we use to calculate F, has a particularly simple form. Different boundary conditions (surface universality classes) are considered, which either break or preserve the order-parameter symmetry. We also consider profiles of thermodynamic densities in the presence of two spheres. Explicit results are presented for an ordinary critical point to leading order in epsilon=4-d and, in the case of preserved symmetry, for the Gaussian model in arbitrary spatial dimension d. Fundamental short-distance properties, such as profile behavior near a surface or the behavior if a sphere has a `small' radius, are discussed and verified. The relevance for colloidal solutions is pointed out.Comment: 37 pages, 2 postscript figures, REVTEX 3.0, published in Phys. Rev. B 51, 13717 (1995

Eddy current probe design for second-layer cracks under installed fasteners

The United States Air Force has an operational need to reliably detect second-layer cracks around fastener holes in two-layer airframe structures with the fasteners in place. Because access to the second layer is usually not available, the inspection must be performed by placing a probe on the outer surface of the structure and detecting cracks through the first layer. Eddy current methods have been applied to this inspection problem [1–6], and have met with some success; however, much improvement is still needed to achieve the desired sensitivity to cracks and rejection of signals caused by the geometry of the structure under inspection

Surface Critical Behavior of Binary Alloys and Antiferromagnets: Dependence of the Universality Class on Surface Orientation

The surface critical behavior of semi-infinite (a) binary alloys with a continuous order-disorder transition and (b) Ising antiferromagnets in the presence of a magnetic field is considered. In contrast to ferromagnets, the surface universality class of these systems depends on the orientation of the surface with respect to the crystal axes. There is ordinary and extraordinary surface critical behavior for orientations that preserve and break the two-sublattice symmetry, respectively. This is confirmed by transfer-matrix calculations for the two-dimensional antiferromagnet and other evidence.Comment: Final version that appeared in PRL, some minor stylistic changes and one corrected formula; 4 pp., twocolumn, REVTeX, 3 eps fig

Average trajectory of returning walks

We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For uncorrelated random walks the average shape is semicircular, independently from the single increments distribution, as long as it is symmetric. Such universality extends to biased random walks and Levy flights, with the exception of a particular class of biased Levy flights. Adding a linear damping term destroys scaling and leads asymptotically to flat excursions. The introduction of short and long ranged noise correlations induces non trivial asymmetric shapes, which are studied numerically.Comment: 16 pages, 16 figures; accepted for publication in Phys. Rev.

Eddy Current Detection of Subsurface Cracks in Engine Disk Boltholes

The development of a reliable eddy current inspection system to detect second layer cracks in sleeved engine disk bolt holes poses serious difficulties. This paper discusses some initial results obtained in two separate investigations that are aimed at advancing the state-of-the-art in eddy current detection of subsurface cracks. Both finite element design optimization results of a horseshoe shaped ferrite core probe, and the results of preliminary evaluation of the applicability of electric current perturbation (ECP) technique to the current problem are presented in this paper

Entropic Elasticity of Double-Strand DNA Subject to Simple Spatial Constraints

The aim of the present paper is the study of the entropic elasticity of the dsDNA molecule, having a cristallographic length L of the order of 10 to 30 persistence lengths A, when it is subject to spatial obstructions. We have not tried to obtain the single molecule partition function by solving a Schodringer-like equation. We prefer to stay within a discretized version of the WLC model with an added one-monomer potential, simulating the spatial constraints. We derived directly from the discretized Boltzmann formula the transfer matrix connecting the partition functions relative to adjacent "effective monomers". We have plugged adequate Dirac delta-functions in the functional integral to ensure that the monomer coordinate and the tangent vector are independent variables. The partition function is, then, given by an iterative process which is both numerically efficient and physically transparent. As a test of our discretized approach, we have studied two configurations involving a dsDNA molecule confined between a pair of parallel plates.Comment: The most formal developments of Section I have been moved into an appendix and replaced by a direct derivation of the transfer matrix used in the applications. of Section II. Two paragraphs and two figures have been added to clarify the physical interpretation of the result