Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole

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 adde

BTZ Black Hole Entropy from Ponzano-Regge Gravity

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 unchange

Artificial Neural Network-based error compensation procedure for low-cost encoders

An Artificial Neural Network-based error compensation method is proposed for improving the accuracy of resolver-based 16-bit encoders by compensating for their respective systematic error profiles. The error compensation procedure, for a particular encoder, involves obtaining its error profile by calibrating it on a precision rotary table, training the neural network by using a part of this data and then determining the corrected encoder angle by subtracting the ANN-predicted error from the measured value of the encoder angle. Since it is not guaranteed that all the resolvers will have exactly similar error profiles because of the inherent differences in their construction on a micro scale, the ANN has been trained on one error profile at a time and the corresponding weight file is then used only for compensating the systematic error of this particular encoder. The systematic nature of the error profile for each of the encoders has also been validated by repeated calibration of the encoders over a period of time and it was found that the error profiles of a particular encoder recorded at different epochs show near reproducible behavior. The ANN-based error compensation procedure has been implemented for 4 encoders by training the ANN with their respective error profiles and the results indicate that the accuracy of encoders can be improved by nearly an order of magnitude from quoted values of ~6 arc-min to ~0.65 arc-min when their corresponding ANN-generated weight files are used for determining the corrected encoder angle.Comment: 16 pages, 4 figures. Accepted for Publication in Measurement Science and Technology (MST

A new alkylated benzoquinone from rhizomes of Iris kumaonensis

A novel alkylated unsaturated p-benzoquinone designated as 3-[(z)-120-heptadecenyl]- 2-hydroxy-5-methoxy-1,4-benzoquinone was isolated from hexane extract of the rhizomes of Iris kumaonensis and it’s structure was confirmed by extensive spectroscopic analysis, IR, MS, HREIMS, 1D, 2D NMR and comparison with the literature data of known compounds

Spin-orbit tuned metal-insulator transitions in single-crystal Sr2Ir1-xRhxO4 (0\leqx\leq1)

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 figure

Exotic Gapless Mott Insulators of Bosons on Multi-Leg Ladders

We present evidence for an exotic gapless insulating phase of hard-core bosons on multi-leg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at $\nu=1/3$ filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other $N$-leg systems and to $N$-layer two-dimensional structures.Comment: 5 pages, 4 figures; v3 is the print version; supplemental material attache

Evolution of Magnetism in Single-Crystal Honeycomb Iridates

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 dat