RVB gauge theory and the Topological degeneracy in the Honeycomb Kitaev model

We relate the Z$_2$ gauge theory formalism of the Kitaev model to the SU(2) gauge theory of the resonating valence bond (RVB) physics. Further, we reformulate a known Jordan-Wigner transformation of Kitaev model on a torus in a general way that shows that it can be thought of as a Z$_2$ gauge fixing procedure. The conserved quantities simplify in terms of the gauge invariant Jordan-Wigner fermions, enabling us to construct exact eigen states and calculate physical quantities. We calculate the fermionic spectrum for flux free sector for different gauge field configurations and show that the ground state is four-fold degenerate on a torus in thermodynamic limit. Further on a torus we construct four mutually anti-commuting operators which enable us to prove that all eigenstates of this model are four fold degenerate in thermodynamic limit.Comment: 12 pages, 3 figures. Added affiliation and a new section, 'Acknowledgements'.Typos correcte

Exactly solvable Kitaev model in three dimensions

We introduce a spin-1/2 model in three dimensions which is a generalization of the well-known Kitaev model on a honeycomb lattice. Following Kitaev, we solve the model exactly by mapping it to a theory of non-interacting fermions in the background of a static Z_2 gauge field. The phase diagram consists of a gapped phase and a gapless one, similar to the two-dimensional case. Interestingly, unlike in the two-dimensional model, in the gapless phase the gap vanishes on a contour in the k space. Furthermore, we show that the flux excitations of the gauge field, due to some local constraints, form loop like structures; such loops exist on a lattice formed by the plaquettes in the original lattice and is topologically equivalent to the pyrochlore lattice. Finally, we derive a low-energy effective Hamiltonian that can be used to study the properties of the excitations in the gapped phase.Comment: 9 pages, 7 figures; published version; a new section and more references adde

Development of sustainable aquaculture project (DSAP): mid-term review report

Aquaculture, Fish culture, Pond Culture, Rice field aquaculture, Farmers, Bangladesh,

Estimating treatment effectiveness with sample selection

We consider a situation where treatment outcome is observed after two stages of selection; first of participation into the treatment, then in completion of the treatment. Estimates were obtained using two methods. First, three different binary response selection models were estimated sequentially in multiple steps. Second, all three equations were estimated jointly. All methods produce similar parameter estimates. We find evidence of selection effects from completion to outcome that could bias parameter estimates of the outcome equation, but not from participation to outcome, indicating that correcting only for participation may be insufficient to avoid biased estimates in the outcome equation.selection bias, trivariate probit, bivariate probit, treatment effects

Rolling tachyon solution of two-dimensional string theory

We consider a classical (string) field theory of $c=1$ matrix model which was developed earlier in hep-th/9207011 and subsequent papers. This is a noncommutative field theory where the noncommutativity parameter is the string coupling $g_s$. We construct a classical solution of this field theory and show that it describes the complete time history of the recently found rolling tachyon on an unstable D0 brane.Comment: 19 pages, 2 figures, minor changes in text and additional references, correction of decay time (version to appear in JHEP.

Riemann-Langevin Particle Filtering in Track-Before-Detect

Track-before-detect (TBD) is a powerful approach that consists in providing the tracker with sensor measurements directly without pre-detection. Due to the measurement model non-linearities, online state estimation in TBD is most commonly solved via particle filtering. Existing particle filters for TBD do not incorporate measurement information in their proposal distribution. The Langevin Monte Carlo (LMC) is a sampling method whose proposal is able to exploit all available knowledge of the posterior (that is, both prior and measurement information). This letter synthesizes recent advances in LMC-based filtering to describe the Riemann-Langevin particle filter and introduces its novel application to TBD. The benefits of our approach are illustrated in a challenging low-noise scenario.Comment: Minor grammatical update

Characterizing steam penetration through thermal protective fabric materials

This study performs an analysis of steam penetration through thermal protective fabric materials. Different, multilayered thermal protective fabrics were selected and tested in a laboratory-simulated steam exposure, and their steam protective performance (SPP) was measured in terms of the time required to generate second-degree burns on the bodies of wearers. Additionally, the total transmitted thermal energy (TTTE) through the fabrics during testing was measured. Through statistical analysis, it was established that fabric properties, namely air permeability and thickness, are the key factors that affect the SPP and TTTE; the relationship among the fabric properties, SPP, and TTTE is also summarized. Theoretically, it has been found that heat and mass (steam) transfer occur through fabrics in the course of steam exposure, which mainly affect the SPP and TTTE. This study could help textile/materials engineers to develop high performance thermal protective fabrics for the increased occupational health and safety of firefighters and industrial workers.Dept of Design and Merchandisin