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

Photoinduced Floquet topological magnons in Kitaev magnets

We study periodically driven pure Kitaev model and ferromagnetic phase of the Kitaev-Heisenberg model on the honeycomb lattice by off-resonant linearly and circularly-polarized lights at zero magnetic field. Using a combination of linear spin wave and Floquet theories, we show that the effective time-independent Hamiltonians in the off-resonant regime map onto the corresponding anisotropic static spin model, plus a tunable photoinduced magnetic field along the $[111]$ direction, which precipitates Floquet topological magnons and chiral magnon edge modes. They are tunable by the light amplitude and polarization. Similarly, we show that the thermal Hall effect induced by the Berry curvature of the Floquet topological magnons can also be tuned by the laser field. Our results pave the way for ultrafast manipulation of topological magnons in irradiated Kitaev magnets, and could play a pivotal role in the investigation of ultrafast magnon spin current generation in Kitaev materials.Comment: 7 pages, 5 figures + Supplemental Materia

Structure and Dynamics of a Phase-Separating Active Colloidal Fluid

We examine a minimal model for an active colloidal fluid in the form of self-propelled Brownian hard spheres that interact purely through excluded volume. Despite the absence of an aligning interaction, this system shows the signature behaviors of an active fluid, including anomalous number fluctuations and phase separation behavior. Using simulations and analytic modeling, we quantify the phase diagram and separation kinetics. The dense phase is a unique material that we call an active hexatic, which exhibits the structural signatures of a crystalline solid near the crystal-hexatic transition point, but the rheological and transport properties associated with a viscoelastic fluid.Comment: 5 pages, 5 figure

Propagation of waves in elliptic ducts. A theoretical study

The cut-off frequencies for high order circumferential modes were calculated for various eccentricities of an elliptic duct section. The problem was studied with a view to the reduction of jet engine compressor noise by elliptic ducts, instead of circular ducts. The cut-off frequencies for even functions decrease with increasing eccentricity. The third order eigen frequencies are oscillatory as the eccentricity increases for odd functions. The eigen frequencies decrease for higher order odd functions inasmuch as, for higher orders, they assume the same values as those for even functions. Deformation of a circular pipe into an elliptic one of sufficiently large eccentricity produces only a small reduction in the cut-off frequency, provided the area of the pipe section is kept invariable

Hardware-software co-design of AES on FPGA

This paper presents a compact hardware-software co-design of Advanced Encryption Standard (AES) on the field programmable gate arrays (FPGA) designed for low-cost embedded systems. The design uses MicroBlaze, a soft-core processor from Xilinx. The computationally intensive operations of the AES are implemented in hardware for better speed. The sub-byte calculation is designed with the help of the processor carrying out the calculations using hardware blocks implemented using FPGA. By incorporating the processor in the AES design, the total number of slices required to implement the AES algorithm on FPGA is proved to be reduced. The entire AES system design is validated using 460 slices in Spartan-3E XC3S500E, which is one of the low-cost FPGA