FQHE interferometers in strong tunneling regime. The role of compactness of edge fields

We consider multiple-point tunneling in the interferometers formed between edges of electron liquids with in general different filling factors in the regime of the Fractional Quantum Hall effect (FQHE). We derive an effective matrix Caldeira-Leggett models for the multiple tunneling contacts connected by the chiral single-mode FQHE edges. It is shown that the compactness of the Wen- Fr\"ohlich chiral boson fields describing the FQHE edge modes plays a crucial role in eliminating the spurious non-locality of the electron transport properties of the FQHE interferometers arising in the regime of strong tunneling.Comment: 5 page

Double Well Potential: Perturbation Theory, Tunneling, WKB (beyond instantons)

A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the potential, semi-classical approximation at large distances and a description of tunneling under the barrier. It provides 9-10 significant digits in energies and gives for wavefunctions the relative deviation in real $x$-space less than $\lesssim 10^{-3}$.Comment: 13 pages, invited talk at "Crossing the boundaries: Gauge dynamics at strong coupling (Shifmania)", Minneapolis, May 14-17, 200

Static Black Hole Solutions without Rotational Symmetry

We construct static black hole solutions that have no rotational symmetry. These arise in theories, including the standard electroweak model, that include charged vector mesons with mass $m\ne 0$. In such theories, a magnetically charged Reissner-Nordstrom black hole with horizon radius less than a critical value of the order of $m^{-1}$ is classically unstable against the development of a nonzero vector meson field just outside the horizon, indicating the existence of static black hole solutions with vector meson hair. For the case of unit magnetic charge, spherically symmetric solutions of this type have previously been studied. For other values of the magnetic charge, general arguments show that any new solution with hair cannot be spherically symmetric. In this paper we develop and apply a perturbative scheme (which may have applicability in other contexts) for constructing such solutions in the case where the Reissner-Nordstrom solution is just barely unstable. For a few low values of the magnetic charge the black holes retain a rotational symmetry about a single axis, but this axial symmetry disappears for higher charges. While the vector meson fields vanish exponentially fast at distances greater than $O(m^{-1})$, the magnetic field and the metric have higher multipole components that decrease only as powers of the distance from the black hole.Comment: 42 pages, phyzzx. 4 figures (PostScript, 1.7 MB when uncompressed) available by email from the Authors on reques

GENERALIZED TRUST AS A BASIS FOR DEMOCRATIZATION OF MODERN POLITICAL SPACE

The article considers generalized trust and sources of its origin, identifies the sources of social capital, as well as analyzes the institutions capable of generating social capital

Extended multiplet structure in Logarithmic Conformal Field Theories

We use the process of quantum hamiltonian reduction of SU(2)_k, at rational level k, to study explicitly the correlators of the h_{1,s} fields in the c_{p,q} models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may produce a rational extended c_{p,q} model. We also find a doublet of fields at h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic.Comment: 24 pages LATEX. Minor corrections and extra reference

Slow many-body delocalization beyond one dimension

We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and time scales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder $W_c(L, d)$ as a function of length $L$ and width $d$. In the quasi-1D case $W_c$ has a finite large-$L$ limit at fixed $d$, which increases strongly with $d$. In the 2D case $W_c(L,L)$ grows with $L$. The results are consistent with the avalanche picture of the many-body localization transition.Comment: 4+epsilon pages, 4 figures plus supplementary with 8 pages, 8 figures. Comments welcom

Instanton Corrections to Quark Form Factor at Large Momentum Transfer

Within the Wilson integral formalism, we discuss the structure of nonperturbative corrections to the quark form factor at large momentum transfer analyzing the infrared renormalon and instanton effects. We show that the nonperturbative effects determine the initial value for the perturbative evolution of the quark form factor and attribute their general structure to the renormalon ambiguities of the perturbative series. It is demonstrated that the instanton contributions result in the finite renormalization of the next-to-leading perturbative result and numerically are characterized by a small factor reflecting the diluteness of the QCD vacuum within the instanton liquid model.Comment: Version coincident with the journal publication, 9 pages; REVTe

Loop Representations

The loop representation plays an important role in canonical quantum gravity because loop variables allow a natural treatment of the constraints. In these lectures we give an elementary introduction to (i) the relevant history of loops in knot theory and gauge theory, (ii) the loop representation of Maxwell theory, and (iii) the loop representation of canonical quantum gravity. (Based on lectures given at the 117. Heraeus Seminar, Bad Honnef, Sept. 1993)Comment: 38 pages, MPI-Ph/93-9

Instanton Contribution to the Quark Form Factor

The nonperturbative effects in the quark form factor are considered in the Wilson loop formalism. The properties of the Wilson loops with cusp singularities are studied taking into account the perturbative and nonperturbative contributions, where the latter are considered within the framework of the instanton liquid model. For the integration path corresponding to this form factor -- the angle with infinite sides -- the explicit expression for the vacuum expectation value of the Wilson operator is found to leading order. The calculations are performed in the weak-field limit for the instanton vacuum contribution and compared with the one- and two-loop order results for the perturbative part. It is shown that the instantons produce the powerlike corrections to the perturbative result, which are comparable in magnitude with the perturbative part at the scale of order of the inverse average instanton size. It is demonstrated that the instanton contributions to the quark form factor are exponentiated to high orders in the small instanton density parameter.Comment: Version coincident with the journal publication. LaTeX, 15 pages, 1 figur