Joaquin M. Luttinger 1923–1997
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The Invention of the Transistor
The invention of the transistor Michael Riordan Department of Physics, University of California, Santa Cruz, California 95064 Lillian Hoddeson Department of History, University of Illinois, Urbana, Illinois 61801 Conyers Herring Department of Applied Physics, Stanford University, Stanford, California 94305 [S0034-6861(99)00302-5] Arguably the most important invention of the past standing of solid-state physics. We conclude with an century, the transistor is often cited as the exemplar of analysis of the impact of this breakthrough upon the how scientific research can lead to useful commercial discipline itself. products. Emerging in 1947 from a Bell Telephone Laboratories program of basic research on the physics I. PRELIMINARY INVESTIGATIONS of solids, it began to replace vacuum tubes in the 1950s and eventually spawned the integrated circuit and The quantum theory of solids was fairly well estab- microprocessor—the heart of a semiconductor industry lished by the mid-1930s, when semiconductors began to now generating annual sales of more than $150 billion. be of interest to industrial scientists seeking solid-state These solid-state electronic devices are what have put alternatives to vacuum-tube amplifiers and electrome- computers in our laps and on desktops and permitted chanical relays. Based on the work of Felix Bloch, Ru- them to communicate with each other over telephone dolf Peierls, and Alan Wilson, there was an established networks around the globe. The transistor has aptly understanding of the band structure of electron energies been called the ‘‘nerve cell’’ of the Information Age. in ideal crystals (Hoddeson, Baym, and Eckert, 1987; Actually the history of this invention is far more in- Hoddeson et al., 1992). -
Bosonization of 1-Dimensional Luttinger Liquid
Bosonization of 1-Dimensional Luttinger Liquid Di Zhou December 13, 2011 Abstract Due to the special dimensionality of one-dimensional Fermi system, Fermi Liquid Theory breaks down and we must find a new way to solve this problem. Here I will have a brief review of one-dimensional Luttinger Liquid, and introduce the process of Bosonization for 1- Dimensional Fermionic system. At the end of this paper, I will discuss the emergent state of charge density wave (CDW) and spin density wave (SDW) separation phenomena. 1 Introduction 3-Dimensional Fermi liquid theory is mostly related to a picture of quasi-particles when we adiabatically switch on interactions, to obtain particle-hole excitations. These quasi-particles are directly related to the original fermions. Of course they also obey the Fermi-Dirac Statis- tics. Based on the free Fermi gas picture, the interaction term: (i) it renormalizes the free Hamiltonians of the quasi-particles such as the effective mass, and the thermodynamic properties; (ii) it introduces new collective modes. The existence of quasi-particles results in a fi- nite jump of the momentum distribution function n(k) at the Fermi surface, corresponding to a finite residue of the quasi-particle pole in the electrons' Green function. 1-Dimensional Fermi liquids are very special because they keep a Fermi surface (by definition of the points where the momentum distribution or its derivatives have singularities) enclosing the same k-space vol- ume as that of free fermions, in agreement with Luttingers theorem. 1 1-Dimensional electrons spontaneously open a gap at the Fermi surface when they are coupled adiabatically to phonons with wave vector 2kF . -
The Physical Tourist Physics and New York City
Phys. perspect. 5 (2003) 87–121 © Birkha¨user Verlag, Basel, 2003 1422–6944/05/010087–35 The Physical Tourist Physics and New York City Benjamin Bederson* I discuss the contributions of physicists who have lived and worked in New York City within the context of the high schools, colleges, universities, and other institutions with which they were and are associated. I close with a walking tour of major sites of interest in Manhattan. Key words: Thomas A. Edison; Nikola Tesla; Michael I. Pupin; Hall of Fame for GreatAmericans;AlbertEinstein;OttoStern;HenryGoldman;J.RobertOppenheimer; Richard P. Feynman; Julian Schwinger; Isidor I. Rabi; Bronx High School of Science; StuyvesantHighSchool;TownsendHarrisHighSchool;NewYorkAcademyofSciences; Andrei Sakharov; Fordham University; Victor F. Hess; Cooper Union; Peter Cooper; City University of New York; City College; Brooklyn College; Melba Phillips; Hunter College; Rosalyn Yalow; Queens College; Lehman College; New York University; Courant Institute of Mathematical Sciences; Samuel F.B. Morse; John W. Draper; Columbia University; Polytechnic University; Manhattan Project; American Museum of Natural History; Rockefeller University; New York Public Library. Introduction When I was approached by the editors of Physics in Perspecti6e to prepare an article on New York City for The Physical Tourist section, I was happy to do so. I have been a New Yorker all my life, except for short-term stays elsewhere on sabbatical leaves and other visits. My professional life developed in New York, and I married and raised my family in New York and its environs. Accordingly, writing such an article seemed a natural thing to do. About halfway through its preparation, however, the attack on the World Trade Center took place. -
A Glimpse of a Luttinger Liquid IGOR A. ZALIZNYAK Physics Department
1 A glimpse of a Luttinger liquid IGOR A. ZALIZNYAK Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA email: [email protected] The concept of a Luttinger liquid has recently been established as a fundamental paradigm vital to our understanding of the properties of one-dimensional quantum systems, leading to a number of theoretical breakthroughs. Now theoretical predictions have been put to test by the comprehensive experimental study. Our everyday life experience is that of living in a three-dimensional world. Phenomena in a world with only one spatial dimension may appear an esoteric subject, and for a long time it was perceived as such. This has now changed as our knowledge of matter’s inner atomic structure has evolved. It appears that in many real-life materials a chain-like pattern of overlapping atomic orbitals leaves electrons belonging on these orbitals with only one dimension where they can freely travel. The same is obviously true for polymers and long biological macro-molecules such as proteins or RNA. Finally, with the nano-patterned microchips and nano-wires heading into consumer electronics, the question “how do electrons behave in one dimension?” is no longer a theoretical playground but something that a curious mind might ask when thinking of how his or her computer works. One-dimensional problems being mathematically simpler, a number of exact solutions describing “model” one-dimensional systems were known to theorists for years. Outstanding progress, however, has only recently been achieved with the advent of conformal field theory 1,2. It unifies the bits and pieces of existing knowledge like the pieces of a jigsaw puzzle and predicts remarkable universal critical behaviour for one-dimensional systems 3,4. -
Chapter 1 LUTTINGER LIQUIDS: the BASIC CONCEPTS
Chapter 1 LUTTINGER LIQUIDS: THE BASIC CONCEPTS K.Schonhammer¨ Institut fur¨ Theoretische Physik, Universitat¨ Gottingen,¨ Bunsenstr. 9, D-37073 Gottingen,¨ Germany Abstract This chapter reviews the theoretical description of interacting fermions in one dimension. The Luttinger liquid concept is elucidated using the Tomonaga- Luttinger model as well as integrable lattice models. Weakly coupled chains and the attempts to experimentally verify the theoretical predictions are dis- cussed. Keywords Luttinger liquids, Tomonaga model, bosonization, anomalous power laws, break- down of Fermi liquid theory, spin-charge separation, spectral functions, coupled chains, quasi-one-dimensional conductors 1. Introduction In this chapter we attempt a simple selfcontained introduction to the main ideas and important computational tools for the description of interacting fermi- ons in one spatial dimension. The reader is expected to have some knowledge of the method of second quantization. As in section 3 we describe a constructive approach to the important concept of bosonization, no quantum field-theoretical background is required. After mainly focusing on the Tomonaga-Luttinger 1 2 model in sections 2 and 3 we present results for integrable lattice models in section 4. In order to make contact to more realistic systems the coupling of strictly ¢¡ systems as well as to the surrounding is addressed in section 5. The attempts to experimentally verify typical Luttinger liquid features like anoma- lous power laws in various correlation functions are only shortly discussed as this is treated in other chapters of this book. 2. Luttinger liquids - a short history of the ideas As an introduction the basic steps towards the general concept of Luttinger liquids are presented in historical order. -
Pairing in Luttinger Liquids and Quantum Hall States
PHYSICAL REVIEW X 7, 031009 (2017) Pairing in Luttinger Liquids and Quantum Hall States Charles L. Kane,1 Ady Stern,2 and Bertrand I. Halperin3 1Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 2Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel 3Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA (Received 8 February 2017; published 18 July 2017) We study spinless electrons in a single-channel quantum wire interacting through attractive interaction, and the quantum Hall states that may be constructed by an array of such wires. For a single wire, the electrons may form two phases, the Luttinger liquid and the strongly paired phase. The Luttinger liquid is gapless to one- and two-electron excitations, while the strongly paired state is gapped to the former and gapless to the latter. In contrast to the case in which the wire is proximity coupled to an external superconductor, for an isolated wire there is no separate phase of a topological, weakly paired superconductor. Rather, this phase is adiabatically connected to the Luttinger liquid phase. The properties of the one-dimensional topological superconductor emerge when the number of channels in the wire becomes large. The quantum Hall states that may be formed by an array of single-channel wires depend on the Landau-level filling factors. For odd- denominator fillings ν ¼ 1=ð2n þ 1Þ, wires at the Luttinger phase form Laughlin states, while wires in the strongly paired phase form a bosonic fractional quantum Hall state of strongly bound pairs at a filling of 1=ð8n þ 4Þ. -
SHELDON LEE GLASHOW Lyman Laboratory of Physics Harvard University Cambridge, Mass., USA
TOWARDS A UNIFIED THEORY - THREADS IN A TAPESTRY Nobel Lecture, 8 December, 1979 by SHELDON LEE GLASHOW Lyman Laboratory of Physics Harvard University Cambridge, Mass., USA INTRODUCTION In 1956, when I began doing theoretical physics, the study of elementary particles was like a patchwork quilt. Electrodynamics, weak interactions, and strong interactions were clearly separate disciplines, separately taught and separately studied. There was no coherent theory that described them all. Developments such as the observation of parity violation, the successes of quantum electrodynamics, the discovery of hadron resonances and the appearance of strangeness were well-defined parts of the picture, but they could not be easily fitted together. Things have changed. Today we have what has been called a “standard theory” of elementary particle physics in which strong, weak, and electro- magnetic interactions all arise from a local symmetry principle. It is, in a sense, a complete and apparently correct theory, offering a qualitative description of all particle phenomena and precise quantitative predictions in many instances. There is no experimental data that contradicts the theory. In principle, if not yet in practice, all experimental data can be expressed in terms of a small number of “fundamental” masses and cou- pling constants. The theory we now have is an integral work of art: the patchwork quilt has become a tapestry. Tapestries are made by many artisans working together. The contribu- tions of separate workers cannot be discerned in the completed work, and the loose and false threads have been covered over. So it is in our picture of particle physics. Part of the picture is the unification of weak and electromagnetic interactions and the prediction of neutral currents, now being celebrated by the award of the Nobel Prize. -
Tunneling Conductance of Long-Range Coulomb Interacting Luttinger Liquid
Tunneling conductance of long-range Coulomb interacting Luttinger liquid DinhDuy Vu,1 An´ıbal Iucci,1, 2, 3 and S. Das Sarma1 1Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA 2Instituto de F´ısica La Plata - CONICET, Diag 113 y 64 (1900) La Plata, Argentina 3Departamento de F´ısica, Universidad Nacional de La Plata, cc 67, 1900 La Plata, Argentina. The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long- range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one- dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynamic range of temperature and bias voltage, the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale- dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid. I. INTRODUCTION This power-law tunneling behavior is considered a signa- ture of the Luttinger liquid since in Fermi liquids, G is simply a constant for small values of T and V (as long Luttinger liquids emerge from interacting one- 0 as k T; eV E , where E is the Fermi energy). -
Scientific and Related Works of Chen Ning Yang
Scientific and Related Works of Chen Ning Yang [42a] C. N. Yang. Group Theory and the Vibration of Polyatomic Molecules. B.Sc. thesis, National Southwest Associated University (1942). [44a] C. N. Yang. On the Uniqueness of Young's Differentials. Bull. Amer. Math. Soc. 50, 373 (1944). [44b] C. N. Yang. Variation of Interaction Energy with Change of Lattice Constants and Change of Degree of Order. Chinese J. of Phys. 5, 138 (1944). [44c] C. N. Yang. Investigations in the Statistical Theory of Superlattices. M.Sc. thesis, National Tsing Hua University (1944). [45a] C. N. Yang. A Generalization of the Quasi-Chemical Method in the Statistical Theory of Superlattices. J. Chem. Phys. 13, 66 (1945). [45b] C. N. Yang. The Critical Temperature and Discontinuity of Specific Heat of a Superlattice. Chinese J. Phys. 6, 59 (1945). [46a] James Alexander, Geoffrey Chew, Walter Salove, Chen Yang. Translation of the 1933 Pauli article in Handbuch der Physik, volume 14, Part II; Chapter 2, Section B. [47a] C. N. Yang. On Quantized Space-Time. Phys. Rev. 72, 874 (1947). [47b] C. N. Yang and Y. Y. Li. General Theory of the Quasi-Chemical Method in the Statistical Theory of Superlattices. Chinese J. Phys. 7, 59 (1947). [48a] C. N. Yang. On the Angular Distribution in Nuclear Reactions and Coincidence Measurements. Phys. Rev. 74, 764 (1948). 2 [48b] S. K. Allison, H. V. Argo, W. R. Arnold, L. del Rosario, H. A. Wilcox and C. N. Yang. Measurement of Short Range Nuclear Recoils from Disintegrations of the Light Elements. Phys. Rev. 74, 1233 (1948). [48c] C. -
PHILIP W. ANDERSON Bell Telephone Laboratories, Inc, Murray Hill, New Jersey, and Princeton University, Princeton, New Jersey, USA
LOCAL MOMENTS AND LOCALIZED STATES Nobel Lecture, 8 December, 1977 by PHILIP W. ANDERSON Bell Telephone Laboratories, Inc, Murray Hill, New Jersey, and Princeton University, Princeton, New Jersey, USA I was cited for work both. in the field of magnetism and in that of disordered systems, and I would like to describe here one development in each held which was specifically mentioned in that citation. The two theories I will discuss differed sharply in some ways. The theory of local moments in metals was, in a sense, easy: it was the condensation into a simple mathematical model of ideas which. were very much in the air at the time, and it had rapid and permanent acceptance because of its timeliness and its relative simplicity. What mathematical difficulty it contained has been almost fully- cleared up within the past few years. Localization was a different matter: very few believed it at the time, and even fewer saw its importance; among those who failed to fully understand it at first was certainly its author. It has yet to receive adequate mathematical treatment, and one has to resort to the indignity of numerical simulations to settle even the simplest questions about it. Only now, and through primarily Sir Nevill Mott’s efforts, is it beginning to gain general acceptance. Yet these two finally successful brainchildren have also much in common: first, they flew in the face of the overwhelming ascendancy. at the time of the band theory of solids, in emphasizing locality : how a magnetic moment, or an eigenstate, could be permanently pinned down in a given region. -
Julian Seymour Schwinger Papers, 1920-1994
http://oac.cdlib.org/findaid/ark:/13030/tf5870062x No online items Finding Aid for the Julian Seymour Schwinger Papers, 1920-1994 Processed by Russell Johnson and Charlotte B. Brown; machine-readable finding aid created by Caroline Cubé UCLA Library, Department of Special Collections Manuscripts Division Room A1713, Charles E. Young Research Library Box 951575 Los Angeles, CA 90095-1575 Email: [email protected] URL: http://www.library.ucla.edu/libraries/special/scweb/ © 1999 The Regents of the University of California. All rights reserved. Finding Aid for the Julian 371 1 Seymour Schwinger Papers, 1920-1994 Finding Aid for the Julian Seymour Schwinger Papers, 1920-1994 Collection number: 371 UCLA Library, Department of Special Collections Manuscripts Division Los Angeles, CA Contact Information Manuscripts Division UCLA Library, Department of Special Collections Room A1713, Charles E. Young Research Library Box 951575 Los Angeles, CA 90095-1575 Telephone: 310/825-4988 (10:00 a.m. - 4:45 p.m., Pacific Time) Email: [email protected] URL: http://www.library.ucla.edu/libraries/special/scweb/ Processed by: Charlotte B. Brown, 13 October 1995 and Russell A. Johnson, 12 February 1997 Encoded by: Caroline Cubé Online finding aid edited by: Josh Fiala, November 2002 © 1999 The Regents of the University of California. All rights reserved. Descriptive Summary Title: Julian Seymour Schwinger Papers, Date (inclusive): 1920-1994 Collection number: 371 Creator: Schwinger, Julian Seymour, 1918- Extent: 28 cartons (28 linear ft.) 1 oversize box Repository: University of California, Los Angeles. Library. Department of Special Collections. Los Angeles, California 90095-1575 Abstract: Julian Seymour Schwinger (1918-1994) worked with J. -
Arxiv:Cond-Mat/0106256 V1 13 Jun 2001
Quantum Phenomena in Low-Dimensional Systems Michael R. Geller Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602-2451 (June 18, 2001) A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible. I. INTRODUCTION transverse eigenfunction and only the plane wave factor changes. This means that motion in those transverse di- A low-dimensional system is one where the motion rections is \frozen out," leaving only motion along the of microscopic degrees-of-freedom, such as electrons, wire. phonons, or photons, is restricted from exploring the full This article will provide a very brief introduction to three dimensions of our world. There has been tremen- the physics of low-dimensional quantum systems. The dous interest in low-dimensional quantum systems dur- material should be accessible to advanced physics under- ing the past twenty years, fueled by a constant stream graduate students. References to recent review articles of striking discoveries and also by the potential for, and and books are provided when possible. The fabrication of realization of, new state-of-the-art electronic device ar- low-dimensional structures is introduced in Section II. In chitectures. Section III some general features of quantum phenomena The paradigm and workhorse of low-dimensional sys- in low dimensions are discussed. The remainder of the tems is the nanometer-scale semiconductor structure, or article is devoted to particular low-dimensional quantum semiconductor \nanostructure," which consists of a com- systems, organized by their \dimension." positionally varying semiconductor alloy engineered at the atomic scale [1].