Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States

Chiral conformal field theories are characterized by a ground-state current at finite temperature, that could be observed, e.g. in the edge excitations of the quantum Hall effect. We show that the corresponding thermal conductance is directly proportional to the gravitational anomaly of the conformal theory, upon extending the well-known relation between specific heat and conformal anomaly. The thermal current could signal the elusive neutral edge modes that are expected in the hierarchical Hall states. We then compute the thermal conductance for the Abelian multi-component theory and the W-infinity minimal model, two conformal theories that are good candidates for describing the hierarchical states. Their conductances agree to leading order but differ in the first, universal finite-size correction, that could be used as a selective experimental signature.Comment: Latex, 17 pages, 2 figure

Classification of Quantum Hall Universality Classes by $\ W_{1+\infty}\ $ symmetry

We show how two-dimensional incompressible quantum fluids and their excitations can be viewed as $\ W_{1+\infty}\$ edge conformal field theories, thereby providing an algebraic characterization of incompressibility. The Kac-Radul representation theory of the $\ W_{1+\infty}\$ algebra leads then to a purely algebraic complete classification of hierarchical quantum Hall states, which encompasses all measured fractions. Spin-polarized electrons in single-layer devices can only have Abelian anyon excitations.Comment: 11 pages, RevTeX 3.0, MPI-Ph/93-75 DFTT 65/9

On the c-theorem in more than two dimensions

Several pieces of evidence have been recently brought up in favour of the c-theorem in four and higher dimensions, but a solid proof is still lacking. We present two basic results which could be useful for this search: i) the values of the putative c-number for free field theories in any even dimension, which illustrate some properties of this number; ii) the general form of three-point function of the stress tensor in four dimensions, which shows some physical consequences of the c-number and of the other trace-anomaly numbers.Comment: Latex, 7 pages, 1 tabl

Modular Invariant Partition Functions in the Quantum Hall Effect

We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard form of rational conformal field theories. In particular, it is invariant under modular transformations of the toroidal geometry made by the angular variable and the compact Euclidean time. The Jain series of plateaus have been described by two types of edge theories: the minimal models of the W-infinity algebra of quantum area-preserving diffeomorphisms, and their non-minimal version, the theories with U(1)xSU(m) affine algebra. We find modular invariant partition functions for the latter models. Moreover, we relate the Wen topological order to the modular transformations and the Verlinde fusion algebra. We find new, non-diagonal modular invariants which describe edge theories with extended symmetry algebra; their Hall conductivities match the experimental values beyond the Jain series.Comment: Latex, 38 pages, 1 table (one minor error has been corrected

Coulomb Blockade in Hierarchical Quantum Hall Droplets

The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both Abelian and non-Abelian statistics, upon adapting known results for the annulus geometry. We analyze the Abelian states with hierarchical filling fractions, \nu=m/(mp \pm 1), and find a non trivial pattern of conductance peaks. In particular, each one of them occurs with a characteristic multiplicity, that is due to the extended symmetry of the m-folded edge. Experimental tests of the multiplicity can shed more light on the dynamics of this composite edge.Comment: 8 pages; v2: published version; effects of level multiplicities not well understood, see arXiv:0909.3588 for the correct analysi

The effects of soil acidity on the age structure and age at sexual maturity of eastern red-backed salamanders (Plethodon cinereus) in hardwood forests of New Hampshire and Vermont

Acidic deposition resulting from emissions of sulfur and nitrogen has negatively impacted the hardwood forests of the northeastern United States, causing depletion of key nutrients such as calcium and chronic acidification of forest soil habitats. Strongly acidic habitats (pH \u3c 3.5) have long been considered lethal to eastern red-backed salamanders (Plethodon cinereus), but recent studies found that P. cinereus were abundant in hardwood forests with soil pH as low as 2.7 – a condition resulting from anthropogenic acid inputs. Although abundance of P. cinereus does not appear to be constrained by soil pH, I hypothesized that very acidic habitats would negatively impact the demographics of P. cinereus populations, including age distribution, growth rates, and age at sexual maturity. I analyzed demographic parameters of extant P. cinereus populations that were sampled in 2012 at four hardwood forests in NH and VT (USA) that ranged in soil/forest floor pH from 2.7 – 3.7. I determined the age of each P. cinereus using skeletochronology techniques to estimate population age structure, estimated growth curves for each population using the von Bertalanffy equation and Chapman’s method, and evaluated mean age at sexual maturity for each population. Overall, soil pH did not appear to strongly affect P. cinereus populations. However, the most acidic site (pH 2.7) had a greater proportion of juveniles to adults, suggesting that fewer juveniles survive to adulthood at soil pH \u3c 3.0. The mean age of sexually mature individuals was significantly higher at the most acidic site compared to least acidic site, but was not significantly different from the sites with intermediate pH sites. My results suggest that it is possible that P. cinereus populations have locally adapted to very acidic soils, but that demographic differences may reveal sensitivity of populations to this stressor. Further study of habitat pH and P. cinereus is warranted because these salamanders comprise a large portion of forest faunal biomass and play an key ecological role in nutrient cyclin