Comments on the quantum field theory of the Coulomb gas formalism

The holomorphic Coulomb gas formalism, as developed by Feigin-Fuchs, Dotsenko-Fateev and Felder, is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of quantum field theory. We begin with a careful examination of the timelike linear dilaton. Although the background charge of the model breaks the scalar field’s continuous shift symmetry, the exponential of the action remains invariant under a discrete shift because the background charge is imaginary. Gauging this symmetry makes the dilaton compact and introduces winding modes into the spectrum. One of these winding operators corresponds to the anti-holomorphic completion of the BRST current first introduced by Felder, and the full left/right cohomology of this BRST charge isolates the irreducible representations of the Virasoro algebra within the degenerate Fock space of the linear dilaton. The “supertrace” in the BRST complex reproduces the minimal model partition function and exhibits delicate cancellations between states with both momentum and winding. The model at the radius $$ R=\sqrt{pp^{\prime }} $$ R = pp ′ has two marginal operators corresponding to the Dotsenko-Fateev “screening charges”. Deforming by them, we obtain a model that might be called a “BRST quotiented compact timelike Liouville theory”. The Hamiltonian of the zero-mode quantum mechanics of this model is not Hermitian, but it is PT-symmetric and exactly solvable. Its eigenfunctions have support on an infinite number of plane waves, suggesting an infinite reduction in the number of independent states in the full quantum field theory. Applying conformal perturbation theory to the exponential interactions reproduces the Coulomb gas calculations of minimal model correlation functions. In contrast to spacelike Liouville, these “resonance correlators” are finite because the zero mode is compact. We comment on subtleties regarding the reflection operator identification, as well as naive violations of truncation in correlators with multiple reflection operators inserted. This work is part of an attempt to understand the relationship between the JT model of two dimen- sional gravity and the worldsheet description of the (2, p) minimal string as suggested by Seiberg and Stanford.

Charge transport in organic semiconductors

In this chapter, the basic principles of the origins of transport levels and bands, charge conduction in disordered materials, and injection from contacts are introduced. Charge transport in organics is fundamentally different than in inorganic semiconductors due to narrow transport bands that, in general, lead to charge transport via hopping, resulting in carrier mobilities that are at most only a few cm2/V s. Processes of charge injection leading to space charge limited transport that defines the current vs. voltage characteristics of the materials are discussed. Methods of measuring mobility, background charge densities, and quantifying charge recombination are described. Doping of organics using both molecular and atomic species to modify their conductivity is also considered. The theory of transport in energetically and structurally disordered films is developed. The chapter closes by describing, from first principles, the theory of conduction over organic and organic/inorganic semiconductor heterojunctions that are used in almost all organic photonic devices.

CHARGE Syndrome: An Indonesian Case Report

Background: CHARGE syndrome is an autosomal dominant congenital and rare genetic disease.The prevalence of CHARGE syndrome approximately 1:12,000 births.In the previous study, the CHD7 gene mutation is responsible in about 2/3 cases of CHARGE syndrome. The syn­drome associations consist of C-coloboma of the eyes, H-heart disease, A-atresia of the choanae, R-retarded growth and development, G-genital hypoplasia/genitourinary anomalies and E-ear anomalies and/or hearing loss. All defects are not seen in every case and a different spectrum of associations is seen in most of the cases.Method: Case was undergone physical examination by experience pediatricians, pedigree construction, and other diagnostic procedure (X-ray, echo­cardiography, and multi slice computer tomography (MSCT) scan).Results: A boy aged 2 years 9 months with clinical features with match major and minor criterias of CHARGE syndrome.

BULK AND EDGE QUASIHOLE TUNNELING AMPLITUDES IN THE LAUGHLIN STATE

The tunneling between the Laughlin state and its quasihole excitations are studied by using the Jack polynomial. We find a universal analytical formula for the tunneling amplitude, which can describe both bulk and edge quasihole excitations. The asymptotic behavior of the tunneling amplitude reveals the difference and the crossover between bulk and edge states. The effects of the realistic coulomb interaction with a background-charge confinement potential and disorder are also discussed. The stability of the tunneling amplitude manifests the topological nature of fractional quantum Hall liquids.

QUASINEUTRAL LIMIT OF THE MULTI-DIMENSIONAL DRIFT-DIFFUSION-POISSON MODELS FOR SEMICONDUCTORS WITH PN-JUNCTIONS

In this paper the vanishing Debye length limit (space charge neutral limit) of bipolar time-dependent drift-diffusion models for semiconductors with p-n-junctions (i.e. with a fixed bipolar background charge) is studied in the multi-dimensional case. For generally smooth sign-changing doping profiles with good boundary conditions, the quasineutral limit (zero-Debye-length limit) is justified rigorously in the Sobolev's norm uniformly in time. The proof is based on the elaborate energy method and the relative entropy functional method which yields the uniform estimates with respect to the scaled Debye length.