Probing Non-Abelian Statistics in nu=12/5 Quantum Hall State

The tunneling current and shot noise of the current between two Fractional Quantum Hall (FQH) edges in the $\nu=12/5$ FQH state in electronic Mach-Zehnder interferometer are studied. It is shown that the tunneling current and shot noise can be used to probe the existence of $k=3$ parafermion statistics in the $\nu=12/5$ FQH state. More specifically, the dependence of the current on the Aharonov-Bohm flux in the Read-Rezayi state is asymmetric under the change of the sign of the applied voltage. This property is absent in the Abelian Laughlin states. Moreover the Fano factor can exceed 12.7 electron charges in the $\nu=12/5$ FQH state . This number well exceeds the maximum possible Fano factor in all Laughlin states and the $\nu=5/2$ Moore-Read state which was shown previously to be $e$ and $3.2 e$ respectively.Comment: 10 pages, 6 figure

Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules

The recursion relations of 2D quantum gravity coupled to the Ising model discussed by the author previously are reexamined. We study the case in which the matter sector satisfies the fusion rules and only the primary operators inside the Kac table contribute. The theory involves unregularized divergences in some of correlators. We obtain the recursion relations which form a closed set among well-defined correlators on sphere, but they do not have a beautiful structure that the bosonized theory has and also give an inconsistent result when they include an ill-defined correlator with the divergence. We solve them and compute the several normalization independent ratios of the well-defined correlators, which agree with the matrix model results.Comment: Latex, 22 page

Boundary states for a free boson defined on finite geometries

Langlands recently constructed a map that factorizes the partition function of a free boson on a cylinder with boundary condition given by two arbitrary functions in the form of a scalar product of boundary states. We rewrite these boundary states in a compact form, getting rid of technical assumptions necessary in his construction. This simpler form allows us to show explicitly that the map between boundary conditions and states commutes with conformal transformations preserving the boundary and the reality condition on the scalar field.Comment: 16 pages, LaTeX (uses AMS components). Revised version; an analogy with string theory computations is discussed and references adde

The Number of Incipient Spanning Clusters in Two-Dimensional Percolation

Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.Comment: 9 pages, LaTeX, 1 eps figure. Additional references and comparison with existing numerical results include

Toda Fields on Riemann Surfaces: remarks on the Miura transformation

We point out that the Miura transformation is related to a holomorphic foliation in a relative flag manifold over a Riemann Surface. Certain differential operators corresponding to a free field description of $W$--algebras are thus interpreted as partial connections associated to the foliation.Comment: AmsLatex 1.1, 10 page

SU(m) non-Abelian anyons in the Jain hierarchy of quantum Hall states

We show that different classes of topological order can be distinguished by the dynamical symmetry algebra of edge excitations. Fundamental topological order is realized when this algebra is the largest possible, the algebra of quantum area-preserving diffeomorphisms, called $W_{1+\infty}$. We argue that this order is realized in the Jain hierarchy of fractional quantum Hall states and show that it is more robust than the standard Abelian Chern-Simons order since it has a lower entanglement entropy due to the non-Abelian character of the quasi-particle anyon excitations. These behave as SU($m$) quarks, where $m$ is the number of components in the hierarchy. We propose the topological entanglement entropy as the experimental measure to detect the existence of these quantum Hall quarks. Non-Abelian anyons in the $\nu = 2/5$ fractional quantum Hall states could be the primary candidates to realize qbits for topological quantum computation.Comment: 5 pages, no figures, a few typos corrected, a reference adde

Perturbation Theory in Two Dimensional Open String Field Theory

In this paper we develop the covariant string field theory approach to open 2d strings. Upon constructing the vertices, we apply the formalism to calculate the lowest order contributions to the 4- and 5- point tachyon--tachyon tree amplitudes. Our results are shown to match the `bulk' amplitude calculations of Bershadsky and Kutasov. In the present approach the pole structure of the amplitudes becomes manifest and their origin as coming from the higher string modes transparent.Comment: 26 page

Cyclic dinucleotides bind the C-linker of HCN4 to control channel cAMP responsiveness

cAMP mediates autonomic regulation of heart rate by means of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which underlie the pacemaker current If. cAMP binding to the C-terminal cyclic nucleotide binding domain enhances HCN open probability through a conformational change that reaches the pore via the C-linker. Using structural and functional analysis, we identified a binding pocket in the C-linker of HCN4. Cyclic dinucleotides, an emerging class of second messengers in mammals, bind the C-linker pocket (CLP) and antagonize cAMP regulation of the channel. Accordingly, cyclic dinucleotides prevent cAMP regulation of If in sinoatrial node myocytes, reducing heart rate by 30%. Occupancy of the CLP hence constitutes an efficient mechanism to hinder β-adrenergic stimulation on If. Our results highlight the regulative role of the C-linker and identify a potential drug target in HCN4. Furthermore, these data extend the signaling scope of cyclic dinucleotides in mammals beyond their first reported role in innate immune system

Entropy flow in near-critical quantum circuits

Near-critical quantum circuits are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective excitations evolve reversibly, effectively isolated from the environment. The design of reversible computers is constrained by the laws governing entropy flow within the computer. In near-critical quantum circuits, entropy flows as a locally conserved quantum current, obeying circuit laws analogous to the electric circuit laws. The quantum entropy current is just the energy current divided by the temperature. A quantum circuit made from a near-critical system (of conventional type) is described by a relativistic 1+1 dimensional relativistic quantum field theory on the circuit. The universal properties of the energy-momentum tensor constrain the entropy flow characteristics of the circuit components: the entropic conductivity of the quantum wires and the entropic admittance of the quantum circuit junctions. For example, near-critical quantum wires are always resistanceless inductors for entropy. A universal formula is derived for the entropic conductivity: \sigma_S(\omega)=iv^{2}S/\omega T, where \omega is the frequency, T the temperature, S the equilibrium entropy density and v the velocity of `light'. The thermal conductivity is Real(T\sigma_S(\omega))=\pi v^{2}S\delta(\omega). The thermal Drude weight is, universally, v^{2}S. This gives a way to measure the entropy density directly.Comment: 2005 paper published 2017 in Kadanoff memorial issue of J Stat Phys with revisions for clarity following referee's suggestions, arguments and results unchanged, cross-posting now to quant-ph, 27 page

Full quantum distribution of contrast in interference experiments between interacting one dimensional Bose liquids

We analyze interference experiments for a pair of independent one dimensional condensates of interacting bosonic atoms at zero temperature. We show that the distribution function of fringe amplitudes contains non-trivial information about non-local correlations within individual condensates and can be calculated explicitly using methods of conformal field theory. We point out interesting relations between these distribution functions, the partition function for a quantum impurity in a one-dimensional Luttinger liquid, and transfer matrices of conformal field theories. We demonstrate the connection between interference experiments in cold atoms and a variety of statistical models ranging from stochastic growth models to two dimensional quantum gravity. Such connection can be used to design a quantum simulator of unusual two-dimensional models described by nonunitary conformal field theories with negative central charges.Comment: 9 pages, 5 figures; Accepted for publication in Nature Physic