Chirality of Knots 9429_{42} and 107110_{71} and Chern-Simons Theory

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

Representations of Composite Braids and Invariants for Mutant Knots and Links in Chern-Simons Field Theories

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 reques

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

Black Hole Entropy from a Highly Excited Elementary String

Suggested correspondence between a black hole and a highly excited elementary string is explored. Black hole entropy is calculated by computing the density of states for an open excited string. We identify the square root of oscillator number of the excited string with Rindler energy of black hole to obtain an entropy formula which, not only agrees at the leading order with the Bekenstein-Hawking entropy, but also reproduces the logarithmic correction obtained for black hole entropy in the quantum geometry framework. This provides an additional supporting evidence for correspondence between black holes and strings.Comment: revtex, 4 page

Thermodynamics of horizons from a dual quantum system

It was shown recently that, in the case of Schwarschild black hole, one can obtain the correct thermodynamic relations by studying a model quantum system and using a particular duality transformation. We study this approach further for the case a general spherically symmetric horizon. We show that the idea works for a general case only if we define the entropy S as a congruence ("observer") dependent quantity and the energy E as the integral over the source of the gravitational acceleration for the congruence. In fact, in this case, one recovers the relation S=E/2T between entropy, energy and temperature previously proposed by one of us in gr-qc/0308070. This approach also enables us to calculate the quantum corrections of the Bekenstein-Hawking entropy formula for all spherically symmetric horizons.Comment: 5 pages; no figure

Proceedings of Bhutan: Biodemocracy & Resilience Conference 2020

The Second Bhutan Biodemocracy and Resilience Conference With a focus on pathways to resilience in the face of cross-sectoral and regional effects of the coronavirus pandemic)(held on December 21-22, 2020) brought together a range of people from politics, civil society, media, business, academia, education, industry, agriculture in multiple panels to discuss the key developmental challenges in the context of the pandemic. The conference was covered in the Bhutanese media and received an overwhelmingly positive feedback from various sectors of society and on social media. The aim of the project was to bring together key stakeholders in Bhutan to produce engaged deliberations and reports that can guide policymaking. The two-day conference had panel discussions on the effects of the coronavirus crisis in relation to economic vulnerability and climate change, volunteerism and public health, local governments, agriculture, employment, hydropower and tourism. A keynote address from Lyonpo Ugyen Dorji, Minister of Labour and Human Resources of the Royal Government of Bhutan, began the two days of panel discussions on the pandemic, public policy and development. The talks were livestreamed and watched by thousands of people and were covered nationally. The BBR 2020 conference built upon the first conference titled ‘Bhutan as Biodemocracy: Building Socioeconomic and Environmental Resilience’ which was held in July 2019

Hole dynamics in an antiferromagnet across a deconfined quantum critical point

We study the effects of a small density of holes, delta, on a square lattice antiferromagnet undergoing a continuous transition from a Neel state to a valence bond solid at a deconfined quantum critical point. We argue that at non-zero delta, it is likely that the critical point broadens into a non-Fermi liquid `holon metal' phase with fractionalized excitations. The holon metal phase is flanked on both sides by Fermi liquid states with Fermi surfaces enclosing the usual Luttinger area. However the electronic quasiparticles carry distinct quantum numbers in the two Fermi liquid phases, and consequently the limit of the ratio A_F/delta, as delta tends to zero (where A_F is the area of a hole pocket) has a factor of 2 discontinuity across the quantum critical point of the insulator. We demonstrate that the electronic spectrum at this transition is described by the `boundary' critical theory of an impurity coupled to a 2+1 dimensional conformal field theory. We compute the finite temperature quantum-critical electronic spectra and show that they resemble "Fermi arc" spectra seen in recent photoemission experiments on the pseudogap phase of the cuprates.Comment: 33 pages, 8 figures, Longer version of cond-mat/0611536, with additional results for electron spectrum at non-zero temperatur

In situ characterization of vertically oriented carbon nanofibers for three-dimensional nano-electro-mechanical device applications

We have performed mechanical and electrical characterization of individual as-grown, vertically oriented carbon nanofibers (CNFs) using in situ techniques, where such high-aspect-ratio, nanoscale structures are of interest for three-dimensional (3D) electronics, in particular 3D nano-electro-mechanical-systems (NEMS). Nanoindentation and uniaxial compression tests conducted in an in situ nanomechanical instrument, SEMentor, suggest that the CNFs undergo severe bending prior to fracture, which always occurs close to the bottom rather than at the substrate–tube interface, suggesting that the CNFs are well adhered to the substrate. This is also consistent with bending tests on individual tubes which indicated that bending angles as large as ~70° could be accommodated elastically. In situ electrical transport measurements revealed that the CNFs grown on refractory metallic nitride buffer layers were conducting via the sidewalls, whereas those synthesized directly on Si were electrically unsuitable for low-voltage dc NEMS applications. Electrostatic actuation was also demonstrated with a nanoprobe in close proximity to a single CNF and suggests that such structures are attractive for nonvolatile memory applications. Since the magnitude of the actuation voltage is intimately dictated by the physical characteristics of the CNFs, such as diameter and length, we also addressed the ability to tune these parameters, to some extent, by adjusting the plasma-enhanced chemical vapor deposition growth parameters with this bottom-up synthesis approach