Abstract:
We review the recent theoretical developments towards understanding the Mott phases and quantum phase transition of extended Bose-Hubbard models on lattices in two spatial dimensions . We focuss on the description of these systems using the dual vortex picture and point out the crucial role played by the geometry of underlying lattices in determining the nature of both the Mott phases and the quantum phase transitions. We also briefly compare the results of dual vortex theory with quantum Monte Carlo results.

Abstract:
Indian Cancer Research Centre (ICRC) bacillus strain (C-44), a candidate vaccine against leprosy is cultured in vitro in Dubos medium enriched with amino acids and human serum. The study was conducted to find out whether ICRC bacilli obtained from these cultures are coated with anti mycobacterial antibody. Anti-ICRC antibody raised by intradermal inoculation of sonicated ICRC bacilli in rabbits reacted with both human immunoglobulin G (IgG) and antigens of ICRC. Further, ICRC bacilli could also be fluoresced directly with FITC labelled anti human IgG. Positive fluorescence of ICRC could be abolished by digestion of human IgG with trypsin and carbon tetrachloride (CCL4). It is concluded that ICRC bacilli present in the vaccine are coated with human IgG.

Abstract:
ABSTRACT: A 2 month old male infant born with a classical plaque of morphea over his abdomen is presented here for its unusual congenital occurrence.

Abstract:
We study Josephson effect in graphene superconductor- barrier- superconductor junctions with short and wide barriers of thickness $d$ and width $L$, which can be created by applying a gate voltage $V_0$ across the barrier region. We show that Josephson current in such graphene junctions, in complete contrast to their conventional counterparts, is an oscillatory function of both the barrier width $d$ and the applied gate voltage $V_0$. We also demonstrate that in the thin barrier limit, where $V_0 \to \infty$ and $d \to 0$ keeping $V_0 d$ finite, such an oscillatory behavior can be understood in terms of transmission resonance of Dirac-Bogoliubov-de Gennes quasiparticles in superconducting graphene. We discuss experimental relevance of our work.

Abstract:
We show theoretically that graphene, which exhibits a massless Dirac like spectrum for its electrons, can exhibit unconventional Kondo effect that can be tuned by an experimentally controllable applied gate voltage. We demonstrate the presence of a finite critical Kondo coupling strength in neutral graphene. We discuss the possibility of multichannel Kondo effect in this system which might lead to a non-Fermi liquid like ground state and provide a discussion of possible experimental realization of Kondo phenomenon in graphene.

Abstract:
We compute concurrence and negativity as measures of two-site entanglement generated by a power-law quench (characterized by a rate 1/tau and an exponent alpha) which takes an anisotropic XY chain in a transverse field through a quantum critical point (QCP). We show that only the even-neighbor pairs of sites get entangled in such a process. Moreover, there is a critical rate of quench, 1/tau_c, above which no two-site entanglement is generated; the entire entanglement is multipartite. The ratio of the two-site entanglements between consecutive even neighbors can be tuned by changing the quench rate. We also show that for large tau, the concurrence (negativity) scales as sqrt{alpha/tau} (alpha/tau), and we relate this scaling behavior to defect production by the quench through a QCP.

Abstract:
We study the Mott insulator-superfluid transition of ultracold bosonic atoms in a two-dimensional square optical lattice in the presence of a synthetic magnetic field with p/q (p and q being co-prime integers) flux quanta passing through each lattice plaquette. We show that on approach to the transition from the Mott side, the momentum distribution of the bosons exhibits q precursor peaks within the first magnetic Brillouin zone. We also provide an effective theory for the transition and show that it involves q interacting boson fields. We construct, from a mean-field analysis of this effective theory, the superfluid ground states near the transition and compute, for q=2,3, both the gapped and the gapless collective modes of these states. We suggest experiments to test our theory.

Abstract:
We study the magnetic-field-induced spin-density-wave (FISDW) phases in TMTSF organic conductors in the framework of the quantized nesting model. In agreement with recent suggestions, we find that the SDW wave-vector ${\bf Q}$ deviates from its quantized value near the transition temperature $T_c$ for all phases with quantum numbers $N>0$. Deviations from quantization are more pronounced at low pressure and higher $N$ and may lead to a suppression of the first-order transitions $N+1\to N$ for $N\ge 5$. Below a critical pressure, we find that the N=0 phase invades the entire phase diagram in accordance with earlier experiments. We also show that at T=0, the quantization of ${\bf Q}$ and hence the Hall conductance is always exact. Our results suggest a novel phase transition/crossover at intermediate temperatures between phases with quantized and non-quantized ${\bf Q}$.

Abstract:
We obtain the phase diagram of a Bose-Fermi mixture of hardcore spinless Bosons and spin-polarized Fermions with nearest neighbor intra-species interaction and on-site inter-species repulsion in an optical lattice at half-filling using a slave-boson mean-field theory. We show that such a system can have four possible phases which are a) supersolid Bosons coexisting with Fermions in the Mott state, b) Mott state of Bosons coexisting with Fermions in a metallic or charge-density wave state, c) a metallic Fermionic state coexisting with superfluid phase of Bosons, and d) Mott insulating state of Fermions and Bosons. We chart out the phase diagram of the system and provide analytical expressions for the phase boundaries within mean-field theory. We demonstrate that the transition between these phases are generically first order with the exception of that between the supersolid and the Mott states which is a continuous quantum phase transition. We also obtain the low-energy collective excitations of the system in these phases. Finally, we study the particle-hole excitations in the Mott insulating phase and use it to determine the dynamical critical exponent $z$ for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.

Abstract:
We review the superfluid to Mott-insulator transition of cold atoms in optical lattices. The experimental signatures of the transition are discussed and the RPA theory of the Bose-Hubbard model briefly described. We point out that the critical behavior at the transition, as well as the prediction by the RPA theory of a gapped mode (besides the Bogoliubov sound mode) in the superfluid phase, are difficult to understand from the Bogoliubov theory. On the other hand, these findings appear to be intimately connected to the non-trivial infrared behavior of the superfluid phase as recently studied within the non-perturbative renormalization group.