1,156 research outputs found
Continuum Theory of Edge States of Topological Insulators: Variational Principle and Boundary Conditions
We develop a continuum theory to model low energy excitations of a generic
four-band time reversal invariant electronic system with boundaries. We propose
a variational energy functional for the wavefunctions which allows us derive
natural boundary conditions valid for such systems. Our formulation is
particularly suited to develop a continuum theory of the protected edge/surface
excitations of topological insulators both in two and three dimensions. By a
detailed comparison of our analytical formulation with tight binding
calculations of ribbons of topological insulators modeled by the
Bernevig-Hughes-Zhang (BHZ) hamiltonian, we show that the continuum theory with
the natural boundary condition provides an appropriate description of the low
energy physics. As a spin-off, we find that in a certain parameter regime, the
gap that arises in topological insulator ribbons of finite width due to the
hybridization of edges states from opposite edges, depends non-monotonically on
the ribbon width and can nearly vanish at certain "magic widths".Comment: 8 pages, 5 figure
Fermionic Superfluid from a Bilayer Band Insulator in an Optical Lattice
We propose a model to realize a fermionic superfluid state in an optical
lattice circumventing the cooling problem. Our proposal exploits the idea of
tuning the interaction in a characteristically low entropy state, a
band-insulator in an optical bilayer system, to obtain a superfluid. By
performing a detailed analysis of the model including fluctuations and
augmented by a variational quantum Monte Carlo calculations of the ground
state, we show that the superfluid state obtained has high transition
temperature of the order of the hopping energy. Our system is designed to
suppress other competing orders such as a charge density wave. We suggest a
laboratory realization of this model via an orthogonally shaken optical lattice
bilayer.Comment: 5 pages, 7 figures, typos fixed, figures modifie
The Lov\'asz-Softmax loss: A tractable surrogate for the optimization of the intersection-over-union measure in neural networks
The Jaccard index, also referred to as the intersection-over-union score, is
commonly employed in the evaluation of image segmentation results given its
perceptual qualities, scale invariance - which lends appropriate relevance to
small objects, and appropriate counting of false negatives, in comparison to
per-pixel losses. We present a method for direct optimization of the mean
intersection-over-union loss in neural networks, in the context of semantic
image segmentation, based on the convex Lov\'asz extension of submodular
losses. The loss is shown to perform better with respect to the Jaccard index
measure than the traditionally used cross-entropy loss. We show quantitative
and qualitative differences between optimizing the Jaccard index per image
versus optimizing the Jaccard index taken over an entire dataset. We evaluate
the impact of our method in a semantic segmentation pipeline and show
substantially improved intersection-over-union segmentation scores on the
Pascal VOC and Cityscapes datasets using state-of-the-art deep learning
segmentation architectures.Comment: Accepted as a conference paper at CVPR 201
Synchronous and Asynchronous Mott Transitions in Topological Insulator Ribbons
We address how the nature of linearly dispersing edge states of two
dimensional (2D) topological insulators evolves with increasing
electron-electron correlation engendered by a Hubbard like on-site repulsion
in finite ribbons of two models of topological band insulators. Using an
inhomogeneous cluster slave rotor mean-field method developed here, we show
that electronic correlations drive the topologically nontrivial phase into a
Mott insulating phase via two different routes. In a synchronous transition,
the entire ribbon attains a Mott insulating state at one critical that
depends weakly on the width of the ribbon. In the second, asynchronous route,
Mott localization first occurs on the edge layers at a smaller critical value
of electronic interaction which then propagates into the bulk as is further
increased until all layers of the ribbon become Mott localized. We show that
the kind of Mott transition that takes place is determined by certain
properties of the linearly dispersing edge states which characterize the
topological resilience to Mott localization.Comment: 4+ pages, 5 figure
Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists
This book introduces the concept of fuzzy super matrices and operations on
them. This book will be highly useful to social scientists who wish to work
with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy
Relational Maps, Bidirectional Associative Memories and Fuzzy Associative
Memories are defined here. The authors introduce 13 multi-expert models using
the notion of fuzzy supermatrices. These models are described with illustrative
examples. This book has three chapters. In the first chaper, the basic concepts
about super matrices and fuzzy super matrices are recalled. Chapter two
introduces the notion of fuzzy super matrices adn their properties. The final
chapter introduces many super fuzzy multi expert models.Comment: 280 page
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