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We synthesize and study single crystals of the layered honeycomb lattice Mott insulators Na2RuO3 and Li2RuO3 with magnetic Ru4+(4d4) ions. The newly found Na2RuO3 features a nearly ideal honeycomb lattice and orders antiferromagnetically at 30 K. Single-crystals of Li2RuO3 adopt a honeycomb lattice with either C2/m or more distorted P21/m below 300 K, depending on detailed synthesis conditions. We find that Li2RuO3 in both structures hosts a well-defined magnetic state, in contrast to the singlet ground state found in polycrystalline Li2RuO3. A phase diagram generated based on our results uncovers a new, direct correlation between the magnetic ground state and basal-plane distortions in the honeycomb ruthenates., Comment: 4 figures, accepted for publication in Phys. Rev. B

We synthesize and study single crystals of a new double-perovskite Sr2YIrO6. Despite two strongly unfavorable conditions for magnetic order, namely, pentavalent Ir5+(5d4) ions which are anticipated to have Jeff=0 singlet ground states in the strong spin-orbit coupling (SOC) limit, and geometric frustration in a face centered cubic structure formed by the Ir5+ ions, we observe this iridate to undergo a novel magnetic transition at temperatures below 1.3 K. We provide compelling experimental and theoretical evidence that the origin of magnetism is in an unusual interplay between strong non-cubic crystal fields and intermediate-strength SOC. Sr2YIrO6 provides a rare example of the failed dominance of SOC in the iridates., Comment: Four Figures

We report the successful synthesis of single-crystals of the layered iridate, (Na$_{1-x}$Li$_{x}$)$_2$IrO$_3$, $0\leq x \leq 0.9$, and a thorough study of its structural, magnetic, thermal and transport properties. The new compound allows a controlled interpolation between Na$_2$IrO$_3$ and Li$_2$IrO$_3$, while maintaing the novel quantum magnetism of the honeycomb Ir$^{4+}$ planes. The measured phase diagram demonstrates a dramatic suppression of the N\'eel temperature, $T_N$, at intermediate $x$ suggesting that the magnetic order in Na$_2$IrO$_3$ and Li$_2$IrO$_3$ are distinct, and that at $x\approx 0.7$, the compound is close to a magnetically disordered phase that has been sought after in Na$_2$IrO$_3$ and Li$_2$IrO$_3$. By analyzing our magnetic data with a simple theoretical model we also show that the trigonal splitting, on the Ir$^{4+}$ ions changes sign from Na$_2$IrO$_3$ and Li$_2$IrO$_3$, and the honeycomb iridates are in the strong spin-orbit coupling regime, controlled by $\jeff=1/2$ moments., Comment: updated version with more data

Sr2IrO4 is a magnetic insulator driven by spin-orbit interaction (SOI) whereas the isoelectronic and isostructural Sr2RhO4 is a paramagnetic metal. The contrasting ground states have been shown to result from the critical role of the strong SOI in the iridate. Our investigation of structural, transport, magnetic and thermal properties reveals that substituting 4d Rh4+ (4d5) ions for 5d Ir4+(5d5) ions in Sr2IrO4 directly reduces the SOI and rebalances the competing energies so profoundly that it generates a rich phase diagram for Sr2Ir1-xRhxO4 featuring two major effects: (1) Light Rh doping (0\leqx\leq0.16) prompts a simultaneous and precipitous drop in both the electrical resistivity and the magnetic ordering temperature TC, which is suppressed to zero at x = 0.16 from 240 K at x=0. (2) However, with heavier Rh doping (0.24< x<0.85 (\pm0.05)) disorder scattering leads to localized states and a return to an insulating state with spin frustration and exotic magnetic behavior that only disappears near x=1. The intricacy of Sr2Ir1-xRhxO4 is further highlighted by comparison with Sr2Ir1-xRuxO4 where Ru4+(4d4) drives a direct crossover from the insulating to metallic states., Comment: 5 figures

We consider an "impurity" with a spin degree of freedom coupled to a finite reservoir of non-interacting electrons, a system which may be realized by either a true impurity in a metallic nano-particle or a small quantum dot coupled to a large one. We show how the physics of such a spin impurity is revealed in the many-body spectrum of the entire finite-size system; in particular, the evolution of the spectrum with the strength of the impurity-reservoir coupling reflects the fundamental many-body correlations present. Explicit calculation in the strong and weak coupling limits shows that the spectrum and its evolution are sensitive to the nature of the impurity and the parity of electrons in the reservoir. The effect of the finite size spectrum on two experimental observables is considered. First, we propose an experimental setup in which the spectrum may be conveniently measured using tunneling spectroscopy. A rate equation calculation of the differential conductance suggests how the many-body spectral features may be observed. Second, the finite-temperature magnetic susceptibility is presented, both the impurity susceptibility and the local susceptibility. Extensive quantum Monte-Carlo calculations show that the local susceptibility deviates from its bulk scaling form. Nevertheless, for special assumptions about the reservoir -- the "clean Kondo box" model -- we demonstrate that finite-size scaling is recovered. Explicit numerical evaluations of these scaling functions are given, both for even and odd parity and for the canonical and grand-canonical ensembles., Comment: 16 pages; published version, corrections to figure and equation, clarifications

In this paper we report on the Markarian 501 results obtained during our TeV $\gamma$-ray observations from March 11 to May 12, 2005 and February 28 to May 7, 2006 for 112.5 hours with the TACTIC $\gamma$-ray telescope. During 2005 observations for 45.7 hours, the source was found to be in a low state and we have placed an upper limit of 4.62 $\times$ 10$^{-12}$ photons cm$^{-2}$ s$^{-1}$ at 3$\sigma$ level on the integrated TeV $\gamma$-ray flux above 1 TeV from the source direction. However, during the 2006 observations for 66.8h, detailed data analysis revealed the presence of a TeV $\gamma$-ray signal from the source with a statistical significance of 7.5$\sigma$ above $E_{\gamma}\geq$ 1 TeV. The time averaged differential energy spectrum of the source in the energy range 1-11 TeV is found to match well with the power law function of the form ($d\Phi/dE=f_0 E^{-\Gamma}$) with $f_0=(1.66\pm0.52)\times 10^{-11}cm^{-2}s^{-1}TeV^{-1}$ and $\Gamma=2.80\pm0.27$., Comment: 16 pages and 8 Figures Accepted for publication in the Journal of Physics G

The TACTIC $\gamma$-ray telescope, equipped with a light collector of area $\sim$9.5m$^2$ and a medium resolution imaging camera of 349-pixels, has been in operation at Mt.Abu, India since 2001. This paper describes the main features of its various subsystems and its overall performance with regard to (a) tracking accuracy of its 2-axes drive system, (b) spot size of the light collector, (c) back-end signal processing electronics and topological trigger generation scheme, (d) data acquisition and control system and (e) relative and absolute gain calibration methodology. Using a trigger field of view of 11$\times$11 pixels ($\sim$ 3.4$^\circ$$\times3.4^\circ$), the telescope records a cosmic ray event rate of $\sim$2.5 Hz at a typical zenith angle of 15$^\circ$. Monte Carlo simulation results are also presented in the paper for comparing the expected performance of the telescope with actual observational results. The consistent detection of a steady signal from the Crab Nebula above $\sim$1.2 TeV energy, at a sensitivity level of $\sim5.0\sigma$ in $\sim$25 h, alongwith excellent matching of its energy spectrum with that obtained by other groups, reassures that the performance of the TACTIC telescope is quite stable and reliable. Furthermore, encouraged by the detection of strong $\gamma$-ray signals from Mrk 501 (during 1997 and 2006 observations) and Mrk 421 (during 2001 and 2005-2006 observations), we believe that there is considerable scope for the TACTIC telescope to monitor similar TeV $\gamma$-ray emission activity from other active galactic nuclei on a long term basis., Comment: 27 pages, 13 figures, accepted for publication in NIM A

We have observed the BL Lac object 1ES2344+514 (z = 0.044) in Very High Energy (VHE) gamma-ray and near-infrared wavelength bands with TACTIC and MIRO telescopes respectively. The observations were made from 18th October to 9th December 2004 and 27th October 2005 to 1st January 2006. Detailed analysis of the TACTIC data indicates absence of a statistically significant gamma-ray signal both in overall data and on a nightly basis from the source direction. We estimate an upper limit of I($\geq$1.5 TeV)$\leq 3.84 \times 10^{-12}$ photons cm$^{-2}$ s$^{-1}$ at a 3$\sigma$ confidence level on the integrated $\gamma$-ray flux. In addition, we have also compared TACTIC TeV light curves with those of the RXTE ASM (2-12keV) for the contemporary period and find that there are no statistically significant increases in the signal strengths from the source in both these energy regions. During 2004 IR observations, 1ES2344+514 shows low level (~0.06 magnitude) day-to-day variation in both, J & H bands. However, during 2005 observation epoch, the source brightens up by about 0.41 magnitude from its October 2005 level J magnitude= 12.64 to J = 12.23 on December 6, 2005. It then fades by about 0.2 magnitude during 6 to 10 December, 2005. The variation is seen in both, J & H, bands simultaneously. The light travel time arguments suggest that the emission region size is of the order of $10^{17}$ cms., Comment: 15 pages, 6 figures, 4 tables, accepted for publication in Journal of Physics G

The TACTIC $\gamma$-ray telescope has observed Mrk 421 on 66 clear nights from Dec. 07, 2005 to Apr. 30, 2006, totalling $\sim$ 202 hours of on-source observations. Here, we report the detection of flaring activity from the source at $\geq$ 1 TeV energy and the time-averaged differential $\gamma$-ray spectrum in the energy range 1-11 TeV for the data taken between Dec. 27, 2005 to Feb. 07, 2006 when the source was in a relatively higher state as compared to the rest of the observation period. Analysis of this data spell, comprising about $\sim$97h reveals the presence of a $\sim 12.0 \sigma$ $\gamma$-ray signal with daily flux of $>$ 1 Crab unit on several days. A pure power law spectrum with exponent $-3.11\pm0.11$ as well as a power law spectrum with an exponential cutoff $(\Gamma = -2.51\pm0.26$ and $E_0=(4.7\pm2.1) TeV)$ are found to provide reasonable fits to the inferred differential spectrum within statistical uncertainties. We believe that the TeV light curve presented here, for nearly 5 months of extensive coverage, as well as the spectral information at $\gamma$-ray energies of $>$ 5 TeV provide a useful input for other groups working in the field of $\gamma$-ray astronomy., Comment: 13pages,4figures; Accepted for publication in Astroparticle Physics

Topological quantum field theories can be used to probe topological properties of low dimensional manifolds. A class of these theories known as Schwarz type theories, comprise of Chern-Simons theories and BF theories. In three dimensions both capture the properties of knots and links leading to invariants characterising them. These can also be used to construct three-manifold invariants. Three dimensional gravity is described by these field theories. BF theories exist also in higher dimensions. In four dimensions, these describe two-dimensional generalization of knots as well as Donaldson invariants., Comment: 20 pages, Prepared for Encyclopedia of Mathematical Physics, paragraph added minor corrections and few references added

Properties of the Kondo effect in quantum dots depend sensitively on the coupling parameters and so on the realization of the quantum dot -- the Kondo temperature itself becomes a mesoscopic quantity. Assuming chaotic dynamics in the dot, we use random matrix theory to calculate the distribution of both the Kondo temperature and the conductance in the Coulomb blockade regime. We study two experimentally relevant cases: leads with single channels and leads with many channels. In the single-channel case, the distribution of the conductance is very wide as $T_K$ fluctuates on a logarithmic scale. As the number of channels increases, there is a slow crossover to a self-averaging regime., Comment: 4 pages, 3 figures

We study quantum gravity on $dS_{3}$ using the Chern-Simons formulation of three -dimensional gravity. We derive an exact expression for the partition function for quantum gravity on $dS_{3}$ in a Euclidean path integral approach. We show that the topology of the space relevant for studying de Sitter entropy is a solid torus. The quantum fluctuations of de Sitter space are sectors of configurations of point masses taking a {\em discrete} set of values. The partition function gives the correct semi-classical entropy. The sub-leading correction to the entropy is logarithmic in horizon area, with a coefficient -1. We discuss this correction in detail, and show that the sub-leading correction to the entropy from the dS/CFT correspondence agrees with our result. A comparison with the corresponding results for the $AdS_{3}$ BTZ black hole is also presented., Comment: 10 pages, revtex4, 1 eps figure, published version

We derive an exact expression for the partition function of the Euclidean BTZ black hole. Using this, we show that for a black hole with large horizon area, the correction to the Bekenstein-Hawking entropy is $-3/2 log(Area)$, in agreement with that for the Schwarzschild black hole obtained in the canonical gravity formalism and also in a Lorentzian computation of BTZ black hole entropy. We find that the right expression for the logarithmic correction in the context of the BTZ black hole comes from the modular invariance associated with the toral boundary of the black hole., Comment: LaTeX, 10 pages, typos corrected, clarifications added

Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. Chern-Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots and links in three dimensions. These are rare examples of quantum field theories which can be exactly (non-perturbatively) and explicitly solved. Abelian Chern-Simons theory provides a field theoretic interpretation of the linking and self-linking numbers of a link. In non-Abelian theories, vacuum expectation values of Wilson link operators yield a class of polynomial link invariants; the simplest of them is the famous Jones polynomial. Other invariants obtained are more powerful than that of Jones. Powerful methods for completely analytical and non-perturbative computation of these knot and link invariants have been developed. In the process answers to some of the open problems in knot theory are obtained. From these invariants for unoriented and framed links in $S^3$, an invariant for any three-manifold can be easily constructed by exploiting the Lickorish-Wallace surgery presentation of three-manifolds. This invariant up to a normalization is the partition function of the Chern-Simons field theory. Even perturbative analysis of the Chern-Simons theories are rich in their mathematical structure; these provide a field theoretic interpretation of Vassiliev knot invariants. Not only in mathematics, Chern-Simons theories find important applications in three and four dimensional quantum gravity also., Comment: Latex, 27 eps figures

The results of our observational campaigns on the two extragalactic sources Mkn 501 and Mkn 421, carried out with the Imaging Element of the TACTIC array, during March-May, 1998 and April-May, 1999, are presented. The results indicate that the two BL Lac objects (Mkn 501 and Mkn 421) were in a `low' gamma-ray emission state during both epochs of our observations., Comment: 3 pages, 1 Figure, to be presented in the 26th ICRC1999: OG 2.4.20

The entropy of the BTZ black hole is computed in the Ponzano-Regge formulation of three-dimensional lattice gravity. It is seen that the correct semi-classical behaviour of entropy is reproduced by states that correspond to all possible triangulations of the Euclidean black hole., Comment: 11 pages LaTeX, 3 eps figures, some minor clarifications added, result unchanged

We show that any of the new knot invariants obtained from Chern-Simons theory based on an arbitrary non-abelian gauge group do not distinguish isotopically inequivalent mutant knots and links. In an attempt to distinguish these knots and links, we study Murakami (symmetrized version) $r$-strand composite braids. Salient features of the theory of such composite braids are presented. Representations of generators for these braids are obtained by exploiting properties of Hilbert spaces associated with the correlators of Wess-Zumino conformal field theories. The $r$-composite invariants for the knots are given by the sum of elementary Chern-Simons invariants associated with the irreducible representations in the product of $r$ representations (allowed by the fusion rules of the corresponding Wess-Zumino conformal field theory) placed on the $r$ individual strands of the composite braid. On the other hand, composite invariants for links are given by a weighted sum of elementary multicoloured Chern-Simons invariants. Some mutant links can be distinguished through the composite invariants, but mutant knots do not share this property. The results, though developed in detail within the framework of $SU(2)$ Chern-Simons theory are valid for any other non-abelian gauge group., Comment: Latex, 25pages + 16 diagrams available on request

Upto ten crossing number, there are two knots, $9_{42}$ and $10_{71}$ whose chirality is not detected by any of the known polynomials, namely, Jones invariants and their two variable generalisations, HOMFLY and Kauffman invariants. We show that the generalised knot invariants, obtained through $SU(2)$ Chern-Simons topological field theory, which give the known polynomials as special cases, are indeed sensitive to the chirality of these knots., Comment: 15 pages + 7 diagrams (available on request)

A framework for studying knot and link invariants from any rational conformal field theory is developed. In particular, minimal models, superconformal models and $W_N$ models are studied. The invariants are related to the invariants obtained from the Wess-Zumino models associated with the coset representations of these models. Possible Chern-Simons representation of these models is also indicated. This generalises the earlier work on knot and link invariants from Chern-Simons theories., Comment: 18pages+6 figures (available on request through email)

Representations of braid group obtained from rational conformal field theories can be used to obtain explicit representations of Temperley-Lieb-Jones algebras. The method is described in detail for SU(2)$_k$ Wess - Zumino conformal field theories and its generalization to an arbitrary rational conformal field theory outlined. Explicit definition of an associated linear trace operation in terms of a certain matrix element in the space of conformal blocks of such a conformal theory is presented. Further for every primary field of a rational conformal field theory, there is a subfactor of hyperfinite II$_1$ factor with trivial relative commutant. The index of the subfactor is given in terms of identity - identity element of certain duality matrix for conformal blocks of four-point correlators. Jones formula for index ( $<$ 4 ) for subfactors corresponds to spin ${\frac{1}{2}}$ representation of SU(2)$_k$ Wess-Zumino conformal field theory. Definition of the trace operation also provides a method of obtaining link invariants explicitly., Comment: 24 pages

A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for the correlators of $SU(2)_k$ Wess-Zumino conformal field theory are presented. A large class of representations of the generators of the groupoid of coloured-oriented braids are obtained. These provide a whole lot of new link invariants of which Jones polynomials are the simplest examples. These new invariants are explicitly calculated as illustrations for knots upto eight crossings and two-component multicoloured links upto seven crossings., Comment: 48 pages + 20 diagrams

Explicit and complete topological solution of SU(2) Chern-Simons theory on S^3 is presented., Comment: Plain TeX, 11 pages, (4 Figures not included) Preprint IMSc--92/56

Chern-Simons field theory based on a compact non-abelian gauge group is studied as a theory of knots and links in three dimensions. A method to obtain the invariants for links made from braids of upto four strands is developed. This generalizes our earlier work on $SU(2)$ Chern-Simons theory., Comment: 20 pages + diagrams

Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants within this field theoretic framework. The monodromy properties of the correlators of the associated Wess-Zumino SU(2)$_k$ conformal field theory on a two-dimensional sphere prove to be useful tools. The method is simple enough to yield a whole variety of new knot invariants of which the Jones polynomials are the simplest example., Comment: 45 pages (without figures)