Bosonization for Beginners --- Refermionization for Experts

This tutorial gives an elementary and self-contained review of abelian bosonization in 1 dimension in a system of finite size $L$, following and simplifying Haldane's constructive approach. As a non-trivial application, we rigorously resolve (following Furusaki) a recent controversy regarding the tunneling density of states, $\rho_{dos} (\omega)$, at the site of an impurity in a Tomonaga-Luttinger liquid: we use finite-size refermionization to show exactly that for g=1/2 its asymptotic low-energy behavior is $\rho_{dos}(\omega) \sim \omega$. This agrees with the results of Fabrizio & Gogolin and of Furusaki, but not with those of Oreg and Finkel'stein (probably because we capture effects not included in their mean-field treatment of the Coulomb gas that they obtained by an exact mapping; their treatment of anti-commutation relations in this mapping is correct, however, contrary to recent suggestions in the literature). --- The tutorial is addressed to readers unfamiliar with bosonization, or for those interested in seeing ``all the details'' explicitly; it requires knowledge of second quantization only, not of field theory. At the same time, we hope that experts too might find useful our explicit treatment of certain subtleties -- these include the proper treatment of the so-called Klein factors that act as fermion-number ladder operators (and also ensure the anti-commutation of different species of fermion fields), the retention of terms of order 1/L, and a novel, rigorous formulation of finite-size refermionization of both $e^{-i \Phi(x)}$ and the boson field $\Phi (x)$ itself.Comment: Revtex, 70 pages. Changes: Regarding the controversial tunneling density of states at an impurity in a g=1/2 Luttinger liquid, we (1) give a new, more explicit calculation, (2) show that contrary to recent suggestions (including our own), Oreg and Finkel'stein treat fermionic anticommutation relations CORRECTLY (see Appendix K), but (3) suggest that their MEAN-FIELD treatment of their Coulomb gas may not be sufficiently accurat

Quantum Algorithm Implementations for Beginners

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations

The CTL’s Research Support Newsletter (Summer 2019)

New Resources EndNote Nature Protocols Grants & Funding Open Access Publishing Fund Pivot Citation Tools EndNote F1000 RefWorks Statistical Tools NVivo SOSS Division of Biostatistics Support Library consultations Office for Writing, Publishing, and Communication Photographers, Graphic Designers, and Videographers Jefferson Digital Commons Events Lab Archives for Beginners: Professional Edition (Virtual) Lab Archives for Beginners: Classroom Edition (Virtual) Roadmap to Clinical Researc

Nine Quick Tips for Analyzing Network Data

These tips provide a quick and concentrated guide for beginners in the analysis of network data

Application for Beginners Guitar Basic Chord Using Macromedia Flah

Guitar Chord Making Applications Using Macromedia's Flash MX is a guitar chordapplication which contains information on how to search for basic chords usingMacromedia Flash MX, which is packed into an attractive and interactive form madeits appearance simple and easy. Expected that this application can help the beginnerwho wants to understand the basics of playing guitar and seek additional informationabout the search for the basic chord.By using Mcromedia Flash MX, this application is the combination of layers andelements of the picture frames, text and songs, which are summarized into a singleapplication into a form that is expected to easily be used by anyone and is made asattractive as possible while using this application.By simply clicking on one option from the menu then the user will immediatelyobtain information on the basic guitar chords