56,562 research outputs found
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 ). 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
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