Model anisotropic quantum Hall states

Model quantum Hall states including Laughlin, Moore-Read and Read-Rezayi states are generalized into appropriate anisotropic form. The generalized states are exact zero-energy eigenstates of corresponding anisotropic two- or multi-body Hamiltonians, and explicitly illustrate the existence of geometric degrees of in the fractional quantum Hall effect. These generalized model quantum Hall states can provide a good description of the quantum Hall system with anisotropic interactions. Some numeric results of these anisotropic quantum Hall states are also presented.Comment: 10 pages, 5 figure

First- and Second-Order Phase Transitions, Fulde-Ferrel Inhomogeneous State and Quantum Criticality in Ferromagnet/Superconductor Double Tunnel Junctions

First- and second-order phase transitions, Fulde-Ferrel (FF) inhomogeneous superconducting (SC) state and quantum criticality in ferromagnet/superconductor/ferromagnet double tunnel junctions are investigated. For the antiparallel alignment of magnetizations, it is shown that a first-order phase transition from the homogeneous BCS state to the inhomogeneous FF state occurs at a certain bias voltage $V^{\ast}$; while the transitions from the BCS state and the FF state to the normal state at $V_{c}$ are of the second-order. A phase diagram for the central superconductor is presented. In addition, a quantum critical point (QCP), $$, is identified. It is uncovered that near the QCP, the SC gap, the chemical potential shift induced by the spin accumulation, and the difference of free energies between the SC and normal states vanish as $$ with the quantum critical exponents $z\nu =1/2$, 1 and 2, respectively. The tunnel conductance and magnetoresistance are also discussed.Comment: 5 pages, 4 figures, Phys. Rev. B 71, 144514 (2005

Reconnoitering the effect of shallow groundwater on land surface temperature and surface energy balance using MODIS and SEBS

The possibility of observing shallow groundwater depth and areal extent using satellite measurements can support groundwater models and vast irrigation systems management. Moreover, these measurements can help to include the effect of shallow groundwater on surface energy balance within land surface models and climate studies, which broadens the methods that yield more reliable and informative results. To examine the capacity of MODIS in detecting the effect of shallow groundwater on land surface temperature and the surface energy balance in an area within Al-Balikh River basin in northern Syria, we studied the interrelationship between in-situ measured water table depths and land surface temperatures measured by MODIS. We, also, used the Surface Energy Balance System (SEBS) to calculate surface energy fluxes, evaporative fraction and daily evaporation, and inspected their relationships with water table depths. We found out that the daytime temperature increased while the nighttime temperature decreased when the depth of the water table increased. And, when the water table depth increased, net radiation, latent and ground heat fluxes, evaporative fraction and daily evaporation decreased, while sensible heat flux increased. This concords with the findings of a companion paper (Alkhaier et al., 2012). The observed clear relationships were the result of meeting both conditions that were concluded in the companion paper, i.e. high potential evaporation and big contrast in day-night temperature. Moreover, the prevailing conditions in this study area helped SEBS to yield accurate estimates. Under bare soil conditions and under the prevailing weather conditions, we conclude that MODIS is suitable for detecting the effect of shallow groundwater because it has proper imaging times and adequate sensor accuracy; nevertheless, its coarse spatial resolution is disadvantageous

Exploiting Cognitive Structure for Adaptive Learning

Adaptive learning, also known as adaptive teaching, relies on learning path recommendation, which sequentially recommends personalized learning items (e.g., lectures, exercises) to satisfy the unique needs of each learner. Although it is well known that modeling the cognitive structure including knowledge level of learners and knowledge structure (e.g., the prerequisite relations) of learning items is important for learning path recommendation, existing methods for adaptive learning often separately focus on either knowledge levels of learners or knowledge structure of learning items. To fully exploit the multifaceted cognitive structure for learning path recommendation, we propose a Cognitive Structure Enhanced framework for Adaptive Learning, named CSEAL. By viewing path recommendation as a Markov Decision Process and applying an actor-critic algorithm, CSEAL can sequentially identify the right learning items to different learners. Specifically, we first utilize a recurrent neural network to trace the evolving knowledge levels of learners at each learning step. Then, we design a navigation algorithm on the knowledge structure to ensure the logicality of learning paths, which reduces the search space in the decision process. Finally, the actor-critic algorithm is used to determine what to learn next and whose parameters are dynamically updated along the learning path. Extensive experiments on real-world data demonstrate the effectiveness and robustness of CSEAL.Comment: Accepted by KDD 2019 Research Track. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD'19

Theory for Gossamer and Resonating Valence Bond Superconductivity

We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed gossamer superconductivity. We formulate a renormalized mean field theory to approximately take into account the strong correlation effect in the partially projected Gutzwiller wavefucntions. At the half filled, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion U from a gossamer superconductor at small U. Away from the half filled,the Mott insulator is evolved into an resonating valence bond state, which is adiabatically connected to the gossamer superconductor.Comment: 10 pages, 13 figure

Inherited Twistor-Space Structure of Gravity Loop Amplitudes

At tree-level, gravity amplitudes are obtainable directly from gauge theory amplitudes via the Kawai, Lewellen and Tye closed-open string relations. We explain how the unitarity method allows us to use these relations to obtain coefficients of box integrals appearing in one-loop N=8 supergravity amplitudes from the recent computation of the coefficients for N=4 super-Yang-Mills non-maximally-helicity-violating amplitudes. We argue from factorisation that these box coefficients determine the one-loop N=8 supergravity amplitudes, although this remains to be proven. We also show that twistor-space properties of the N=8 supergravity amplitudes are inherited from the corresponding properties of N=4 super-Yang-Mills theory. We give a number of examples illustrating these ideas.Comment: 32 pages, minor typos correcte

Universality class of the restricted solid-on-solid model with hopping

We study the restricted solid-on-solid (RSOS) model with finite hopping distance $l_{0}$, using both analytical and numerical methods. Analytically, we use the hard-core bosonic field theory developed by the authors [Phys. Rev. E {\bf 62}, 7642 (2000)] and derive the Villain-Lai-Das Sarma (VLD) equation for the $l_{0}=\infty$ case which corresponds to the conserved RSOS (CRSOS) model and the Kardar-Parisi-Zhang (KPZ) equation for all finite values of $l_{0}$. Consequently, we find that the CRSOS model belongs to the VLD universality class and the RSOS models with any finite hopping distance belong to the KPZ universality class. There is no phase transition at a certain finite hopping distance contrary to the previous result. We confirm the analytic results using the Monte Carlo simulations for several values of the finite hopping distance.Comment: 13 pages, 3 figure

Scalar diagrammatic rules for Born amplitudes in QCD

We show that all Born amplitudes in QCD can be calculated from scalar propagators and a set of three- and four-valent vertices. In particular, our approach includes amplitudes with any number of quark pairs. The quarks may be massless or massive. The proof of the formalism is given entirely within quantum field theory.Comment: 20 pages, references adde