Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex

The asymptotics of some spin foam amplitudes for a quantum 4-simplex is known to display rapid oscillations whose frequency is the Regge action. In this note, we reformulate this result through a difference equation, asymptotically satisfied by these models, and whose semi-classical solutions are precisely the sine and the cosine of the Regge action. This equation is then interpreted as coming from the canonical quantization of a simple constraint in Regge calculus. This suggests to lift and generalize this constraint to the phase space of loop quantum gravity parametrized by twisted geometries. The result is a reformulation of the flat model for topological BF theory from the Hamiltonian perspective. The Wheeler-de-Witt equation in the spin network basis gives difference equations which are exactly recursion relations on the 15j-symbol. Moreover, the semi-classical limit is investigated using coherent states, and produces the expected results. It mimics the classical constraint with quantized areas, and for Regge geometries it reduces to the semi-classical equation which has been introduced in the beginning.Comment: 16 pages, the new title is that of the published version (initial title: A taste of Hamiltonian constraint in spin foam models

Summing the Instanton Series in N=2 Superconformal Large-N QCD

We consider the multi-instanton collective coordinate integration measure in N=2 supersymmetric SU(N) gauge theory with N_F fundamental hypermultiplets. In the large-N limit, at the superconformal point where N_F=2N and all VEVs are turned off, the k-instanton moduli space collapses to a single copy of AdS_5*S^1. The resulting k-instanton effective measure is proportional to N^{1/2} g^4 Z_k^(6), where Z_k^(6) is the partition function of N=(1,0) SYM theory in six dimensions reduced to zero dimensions. The multi-instanton can in fact be summed in closed form. As a hint of an AdS/CFT duality, with the usual relation between the gauge theory and string theory parameters, this precisely matches the normalization of the charge-k D-instanton measure in type IIB string theory compactified to six dimensions on K3 with a vanishing two-cycle.Comment: 12 pages, amslate

Gauge symmetries in spinfoam gravity: the case for "cellular quantization"

The spinfoam approach to quantum gravity rests on a "quantization" of BF theory using 2-complexes and group representations. We explain why, in dimension three and higher, this "spinfoam quantization" must be amended to be made consistent with the gauge symmetries of discrete BF theory. We discuss a suitable generalization, called "cellular quantization", which (1) is finite, (2) produces a topological invariant, (3) matches with the properties of the continuum BF theory, (4) corresponds to its loop quantization. These results significantly clarify the foundations - and limitations - of the spinfoam formalism, and open the path to understanding, in a discrete setting, the symmetry-breaking which reduces BF theory to gravity.Comment: 6 page

Adiabatic Preparation of a Heisenberg Antiferromagnet Using an Optical Superlattice

We analyze the possibility to prepare a Heisenberg antiferromagnet with cold fermions in optical lattices, starting from a band insulator and adiabatically changing the lattice potential. The numerical simulation of the dynamics in 1D allows us to identify the conditions for success, and to study the influence that the presence of holes in the initial state may have on the protocol. We also extend our results to two-dimensional systems.Comment: 5 pages, 4 figures + Supplementary Material (5 pages, 6 figures), published versio

Exploiting Points and Lines in Regression Forests for RGB-D Camera Relocalization

Camera relocalization plays a vital role in many robotics and computer vision tasks, such as global localization, recovery from tracking failure and loop closure detection. Recent random forests based methods exploit randomly sampled pixel comparison features to predict 3D world locations for 2D image locations to guide the camera pose optimization. However, these image features are only sampled randomly in the images, without considering the spatial structures or geometric information, leading to large errors or failure cases with the existence of poorly textured areas or in motion blur. Line segment features are more robust in these environments. In this work, we propose to jointly exploit points and lines within the framework of uncertainty driven regression forests. The proposed approach is thoroughly evaluated on three publicly available datasets against several strong state-of-the-art baselines in terms of several different error metrics. Experimental results prove the efficacy of our method, showing superior or on-par state-of-the-art performance.Comment: published as a conference paper at 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS

Micromagnetic Simulation of Nanoscale Films with Perpendicular Anisotropy

A model is studied for the theoretical description of nanoscale magnetic films with high perpendicular anisotropy. In the model the magnetic film is described in terms of single domain magnetic grains with Ising-like behavior, interacting via exchange as well as via dipolar forces. Additionally, the model contains an energy barrier and a coupling to an external magnetic field. Disorder is taken into account in order to describe realistic domain and domain wall structures. The influence of a finite temperature as well as the dynamics can be modeled by a Monte Carlo simulation. Many of the experimental findings can be investigated and at least partly understood by the model introduced above. For thin films the magnetisation reversal is driven by domain wall motion. The results for the field and temperature dependence of the domain wall velocity suggest that for thin films hysteresis can be described as a depinning transition of the domain walls rounded by thermal activation for finite temperatures.Comment: Revtex, Postscript Figures, to be published in J. Appl.Phy

Heavy-Quark Potentials and AdS/QCD

We give an example of modeling phenomenological heavy-quark potentials in a five-dimensional framework nowadays known as AdS/QCD. In particular we emphasize the absence of infrared renormalons.Comment: 10 pages, 3 figures; v3: some corrections, to appear in PR