The Landau-Zener transition and the surface hopping method for the 2D Dirac equation for graphene

A Lagrangian surface hopping algorithm is implemented to study the two dimensional massless Dirac equation for Graphene with an electrostatic potential, in the semiclassical regime. In this problem, the crossing of the energy levels of the system at Dirac points requires a particular treatment in the algorithm in order to describe the quantum transition-- characterized by the Landau-Zener probability-- between different energy levels. We first derive the Landau-Zener probability for the underlying problem, then incorporate it into the surface hopping algorithm. We also show that different asymptotic models for this problem derived in [O. Morandi, F. Sch{\"u}rrer, J. Phys. A: Math. Theor. 44 (2011)] may give different transition probabilities. We conduct numerical experiments to compare the solutions to the Dirac equation, the surface hopping algorithm, and the asymptotic models of [O. Morandi, F. Sch{\"u}rrer, J. Phys. A: Math. Theor. 44 (2011)]

What are spin currents in Heisenberg magnets?

We discuss the proper definition of the spin current operator in Heisenberg magnets subject to inhomogeneous magnetic fields. We argue that only the component of the naive "current operator" J_ij S_i x S_j in the plane spanned by the local order parameters and is related to real transport of magnetization. Within a mean field approximation or in the classical ground state the spin current therefore vanishes. Thus, finite spin currents are a direct manifestation of quantum correlations in the system.Comment: 4 pages, 1 figure, published versio

Instability of rotating black holes: large D analysis

We study the stability of odd-dimensional rotating black holes with equal angular momenta by performing an expansion in the inverse of the number of dimensions D. Universality at large $D$ allows us to calculate analytically the complex frequency of quasinormal modes to next-to-leading order in the expansion. We identify the onset of non-axisymmetric, bar-mode instabilities at a specific finite rotation, and axisymmetric instabilities at larger rotation. The former occur at the threshold where the modes become superradiant, and before the ultraspinning regime is reached. Our results fully confirm the picture found in numerical studies, with very good quantitative agreement. We extend the analysis to the same class of black holes in Anti-deSitter space, and find the same qualitative features. We also discuss the appearance at high frequencies of the universal set of (stable) quasinormal modes.Comment: 38 pages, 14 figures. v3: NLO results included so the instability is shown to occur before the ultraspinning regime of rotation. Significant improvements in accuracy. Ancillary Mathematica notebook contains details of NLO result

Loss tolerant device-independent quantum key distribution: a proof of principle

We here present the rate analysis and a proof of principle realization of a device-independent quantum key distribution (QKD) protocol requiring the lowest detection efficiency necessary to achieve a secure key compared to device-independent protocols known so far. The protocol is based on non-maximally entangled state and its experimental realization has been performed by two-photon bipartite entangled states. The improvement with respect to protocols involving maximally entangled states has been estimated.Comment: 8 pages, 4 figure + appendi

Semantic Part Segmentation using Compositional Model combining Shape and Appearance

In this paper, we study the problem of semantic part segmentation for animals. This is more challenging than standard object detection, object segmentation and pose estimation tasks because semantic parts of animals often have similar appearance and highly varying shapes. To tackle these challenges, we build a mixture of compositional models to represent the object boundary and the boundaries of semantic parts. And we incorporate edge, appearance, and semantic part cues into the compositional model. Given part-level segmentation annotation, we develop a novel algorithm to learn a mixture of compositional models under various poses and viewpoints for certain animal classes. Furthermore, a linear complexity algorithm is offered for efficient inference of the compositional model using dynamic programming. We evaluate our method for horse and cow using a newly annotated dataset on Pascal VOC 2010 which has pixelwise part labels. Experimental results demonstrate the effectiveness of our method