Majorana Fermions, Exact Mappings between Classical and Topological Orders

Motivated by the duality between site-centered spin and bond-centered spin in one-dimensional system, which connects two different constructions of fermions from the same set of Majorana fermions, we show that two-dimensional models with topological orders can be constructed from certain well-known models with classical orders characterized by symmetry-breaking. Topology-dependent ground state degeneracy, vanishing two-point correlation functions, and unpaired Majorana fermions on boundaries emerge naturally from such construction. The approach opens a new way to construct and characterize topological orders.Comment: 5 pages, 4 figure

Observability of Higgs Mode in a system without Lorentz invariance

We study the observability of the Higgs mode in BEC-BCS crossover. The observability of Higgs mode is investigated by calculating the spectral weight functions of the amplitude fluctuation below the critical transition temperature. At zero temperature, we find that there are two sharp peaks on the spectral function of the amplitude fluctuation attributed to Goldstone and Higgs modes respectively. As the system goes from BCS to BEC side, there is strong enhancement of spectral weight transfer from the Higgs to Goldstone mode. However, even at the unitary regime where the Lorentz invariance is lost, the sharp feature of Higgs mode still exists. We specifically calculate the finite temperature spectral function of amplitude fluctuation at the unitary regime and show that the Higgs mode is observable at the temperature that present experiments can reach.Comment: 5 pages, 2 figure

Emergence of Topological and Strongly Correlated Ground States in trapped Rashba Spin-Orbit Coupled Bose Gases

We theoretically study an interacting few-body system of Rashba spin-orbit coupled two-component Bose gases confined in a harmonic trapping potential. We solve the interacting Hamiltonian at large Rashba coupling strengths using Exact Diagonalization scheme, and obtain the ground state phase diagram for a range of interatomic interactions and particle numbers. At small particle numbers, we observe that the bosons condense to an array of topological states with n+1/2 quantum angular momentum vortex configurations, where n = 0, 1, 2, 3... At large particle numbers, we observe two distinct regimes: at weaker interaction strengths, we obtain ground states with topological and symmetry properties that are consistent with mean-field theory computations; at stronger interaction strengths, we report the emergence of strongly correlated ground states.Comment: 14 pages, 9 figure

A Robust Quasi-dense Matching Approach for Underwater Images

While different techniques for finding dense correspondences in images taken in air have achieved significant success, application of these techniques to underwater imagery still presents a serious challenge, especially in the case of “monocular stereo” when images constituting a stereo pair are acquired asynchronously. This is generally because of the poor image quality which is inherent to imaging in aquatic environments (blurriness, range-dependent brightness and color variations, time-varying water column disturbances, etc.). The goal of this research is to develop a technique resulting in maximal number of successful matches (conjugate points) in two overlapping images. We propose a quasi-dense matching approach which works reliably for underwater imagery. The proposed approach starts with a sparse set of highly robust matches (seeds) and expands pair-wise matches into their neighborhoods. The Adaptive Least Square Matching (ALSM) is used during the search process to establish new matches to increase the robustness of the solution and avoid mismatches. Experiments on a typical underwater image dataset demonstrate promising results

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter $H>1/2$). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motion and the corresponding underlying standard Brownian motion. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need to develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motion while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.Comment: 44 page