Improving the Hough Transform gathering process for affine transformations

In this paper, we show that significant wrong evidence can be generated when the Hough Transform (HT) is used to extract arbitrary shapes under rigid transformations. In order to reduce the amount of wrong evidence, we consider two types of constraints. First, we define constraints by considering invariant features. Secondly, we consider constraints defined via gradient direction information. Our results show that these constraints can significantly improve the gathering strategy, leading to identification of the correct parameters. The presented formulation is valid for any rigid transformations represented by affine mappings

Explicit tensor network representation for the ground states of string-net models

The structure of string-net lattice models, relevant as examples of topological phases, leads to a remarkably simple way of expressing their ground states as a tensor network constructed from the basic data of the underlying tensor categories. The construction highlights the importance of the fat lattice to understand these models.Comment: 5 pages, pdf figure

DMRG Simulation of the SU(3) AFM Heisenberg Model

We analyze the antiferromagnetic $\text{SU}(3)$ Heisenberg chain by means of the Density Matrix Renormalization Group (DMRG). The results confirm that the model is critical and the computation of its central charge and the scaling dimensions of the first excited states show that the underlying low energy conformal field theory is the $\text{SU}(3)_1$ Wess-Zumino-Novikov-Witten model.Comment: corrections and improvements adde

Emergence of Bulk CsCl Structure in (CsCl)nCs+ Cluster Ions

The emergence of CsCl bulk structure in (CsCl)nCs+ cluster ions is investigated using a mixed quantum-mechanical/semiempirical theoretical approach. We find that rhombic dodecahedral fragments (with bulk CsCl symmetry) are more stable than rock-salt fragments after the completion of the fifth rhombic dodecahedral atomic shell. From this size (n=184) on, a new set of magic numbers should appear in the experimental mass spectra. We also propose another experimental test for this transition, which explicitely involves the electronic structure of the cluster. Finally, we perform more detailed calculations in the size range n=31--33, where recent experimental investigations have found indications of the presence of rhombic dodecahedral (CsCl)32Cs+ isomers in the cluster beams.Comment: LaTeX file. 6 pages and 4 pictures. Accepted for publication in Phys. Rev.

Structures and Stabilities of Doubly-charged (MgO)nMg2+ (n=1-29) Cluster Ions

Ab initio perturbed ion plus polarization calculations are reported for doubly-charged nonstoichiometric (MgO)nMg2+ (n=1-29) cluster ions. We consider a large number of isomers with full relaxations of the geometries, and add the correlation correction to the Hartree-Fock energies for all cluster sizes. The polarization contribution is included at a semiempirical level also for all cluster sizes. Comparison is made with theoretical results for neutral (MgO)n clusters and singly-charged alkali-halide cluster ions. Our method is also compared to phenomenological pair potential models in order to asses their reliability for calculations on small ionic systems. The large coordination-dependent polarizabilities of oxide anions favor the formation of surface sites, and thus bulklike structures begin to dominate only after n=24. The relative stabilities of the cluster ions against evaporation of a MgO molecule show variations that are in excellent agreement with the experimental abundance spectra.Comment: Final version accepted in Journal of Chemical Physics; 8 pages plus 8 figures (6 GIFs and 2 PSs). The main difference with respect to the original submission is the inclusion of coordination-dependent polarizabilities for oxide anions. That results in substantial changes in the result

Quantum versus classical counting in nonMarkovian master equations

We discuss the description of full counting statistics in quantum transport with a nonMarkovian master equation. We focus on differences arising from whether charge is considered as a classical or a quantum degree of freedom. These differences manifest themselves in the inhomogeneous term of the master equation which describes initial correlations. We describe the influence on current and in particular, the finite-frequency shotnoise. We illustrate these ideas by studying transport through a quantum dot and give results that include both sequential and cotunneling processes. Importantly, the noise spectra derived from the classical description are essentially frequency-independent and all quantum noise effects are absent. These effects are fully recovered when charge is considered as a quantum degree of freedom.Comment: 12 pages; 3 figure