Time Reversal I Operator
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Arxiv:1703.07468V1 [Cond-Mat.Str-El] 21 Mar 2017 Generating Spin Ice and Its Emergent Magnetic Monopoles Tion Metal fluoride Pyrochlores
Single-ion properties of the Seff = 1/2 XY antiferromagnetic pyrochlores, 0 0 2+ 2+ NaA Co2F7 (A = Ca , Sr ) K.A. Ross,1, 2 J.M. Brown,1 R.J. Cava,3 J.W. Krizan,3 S. E. Nagler,4 J.A. Rodriguez-Rivera,5, 6 and M. B. Stone4 1Colorado State University, Fort Collins, Colorado, 80523, USA 2Quantum Materials Program, Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada∗ 3Princeton University, Princeton, New Jersey 08544, USA 4Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 5NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA 6Materials Science and Engineering, University of Maryland, College Park, MD 20742, USA (Dated: March 23, 2017) The antiferromagnetic pyrochlore material NaCaCo2F7 is a thermal spin liquid over a broad 2+ temperature range (≈ 140 K down to TF = 2:4K), in which magnetic correlations between Co dipole moments explore a continuous manifold of antiferromagnetic XY states.1 The thermal spin liquid is interrupted by spin freezing at a temperature that is ∼ 2 % of the mean field interaction strength, leading to short range static XY clusters with distinctive relaxation dynamics. Here we report the low energy inelastic neutron scattering response from the related compound NaSrCo2F7, confirming that it hosts the same static and dynamic spin correlations as NaCaCo2F7. We then present the single-ion levels of Co2+ in these materials as measured by inelastic neutron scattering. An intermediate spin orbit coupling model applied to an ensemble of trigonally distorted octahedral crystal fields accounts for the observed transitions. -
Topological Insulators: Preliminaries1
PHYS598PTD A.J.Leggett 2013 Lecture 21 Topological insulators: preliminaries 1 Topological insulators: preliminaries1 At least as far as currently known, a good qualitative understanding of the properties of the class of materials now known as topological insulators (TI's) can be achieved on the basis of a picture of noninteracting electrons subject to a particular kind of band structure, which generally speaking involves nontrivial effects of the spin-orbit interaction (SOI). (As a result, the experimentally observed TI's generally contain heavy elements where the SOI is important). Thus, with the virtue of (considerable!) hindsight, the theory of TI's may be regarded as simply traditional undergraduate solid-state physics seen in a new light; the \new light" focuses particularly on states of the surface of the system, which have not traditionally received much attention. Let's start by reviewing some relevant elementary considerations. First, let's review some basic properties of a system which is confined to a 2-dimensional Hilbert space. Any such system is formally equivalent to a particle of spin 1=2 , and we will say that it is described by a \pseudospin" vector σ^, such that any pure state is an eigenstate of the operator n ·σ^ with eigenvalue ±1, where n is some unit vector: n · σ^j i = ±| i (1) We will usually choose to work in the basis of eigenstates ofσ ^z; depending on the context, these may be actual eigenstates of the true spin (intrinsic angular momentum) of the electron in question, but in the context of the theory of TI's are at least as as likely to correspond to different Bloch bands (cf. -
1 WKB Wavefunctions for Simple Harmonics Masatsugu
WKB wavefunctions for simple harmonics Masatsugu Sei Suzuki Department of Physics, SUNY at Binmghamton (Date: November 19, 2011) _________________________________________________________________________ Gregor Wentzel (February 17, 1898, in Düsseldorf, Germany – August 12, 1978, in Ascona, Switzerland) was a German physicist known for development of quantum mechanics. Wentzel, Hendrik Kramers, and Léon Brillouin developed the Wentzel– Kramers–Brillouin approximation in 1926. In his early years, he contributed to X-ray spectroscopy, but then broadened out to make contributions to quantum mechanics, quantum electrodynamics, and meson theory. http://en.wikipedia.org/wiki/Gregor_Wentzel _________________________________________________________________________ Hendrik Anthony "Hans" Kramers (Rotterdam, February 2, 1894 – Oegstgeest, April 24, 1952) was a Dutch physicist. http://en.wikipedia.org/wiki/Hendrik_Anthony_Kramers _________________________________________________________________________ Léon Nicolas Brillouin (August 7, 1889 – October 4, 1969) was a French physicist. He made contributions to quantum mechanics, radio wave propagation in the atmosphere, solid state physics, and information theory. http://en.wikipedia.org/wiki/L%C3%A9on_Brillouin _______________________________________________________________________ 1. Determination of wave functions using the WKB Approximation 1 In order to determine the eave function of the simple harmonics, we use the connection formula of the WKB approximation. V x E III II I x b O a The potential energy is expressed by 1 V (x) m 2 x 2 . 2 0 The x-coordinates a and b (the classical turning points) are obtained as 2 2 a 2 , b 2 , m0 m0 from the equation 1 V (x) m 2 x2 , 2 0 or 1 1 m 2a 2 m 2b2 , 2 0 2 0 where is the constant total energy. Here we apply the connection formula (I, upward) at x = a. -
Spontaneous Rotational Symmetry Breaking in a Kramers Two- Level System
Spontaneous Rotational Symmetry Breaking in a Kramers Two- Level System Mário G. Silveirinha* (1) University of Lisbon–Instituto Superior Técnico and Instituto de Telecomunicações, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal, [email protected] Abstract Here, I develop a model for a two-level system that respects the time-reversal symmetry of the atom Hamiltonian and the Kramers theorem. The two-level system is formed by two Kramers pairs of excited and ground states. It is shown that due to the spin-orbit interaction it is in general impossible to find a basis of atomic states for which the crossed transition dipole moment vanishes. The parametric electric polarizability of the Kramers two-level system for a definite ground-state is generically nonreciprocal. I apply the developed formalism to study Casimir-Polder forces and torques when the two-level system is placed nearby either a reciprocal or a nonreciprocal substrate. In particular, I investigate the stable equilibrium orientation of the two-level system when both the atom and the reciprocal substrate have symmetry of revolution about some axis. Surprisingly, it is found that when chiral-type dipole transitions are dominant the stable ground state is not the one in which the symmetry axes of the atom and substrate are aligned. The reason is that the rotational symmetry may be spontaneously broken by the quantum vacuum fluctuations, so that the ground state has less symmetry than the system itself. * To whom correspondence should be addressed: E-mail: [email protected] -1- I. Introduction At the microscopic level, physical systems are generically ruled by time-reversal invariant Hamiltonians [1]. -
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Memorial Tributes: Volume 12 Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 12 H E N D R I C K K R A M E R S 1917–2006 Elected in 1978 “For leadership in Dutch industry, education, and professional societies and research on chemical reactor design, separation processes, and process control.” BY R. BYRON BIRD AND BOUDEWIJN VAN NEDERVEEN HENDRIK KRAMERS (usually called Hans), formerly a member of the Governing Board of Koninklijke Zout Organon, later Akzo, and presently Akzo Nobel, passed away on September 17, 2006, at the age of 89. He became a foreign associate of the National Academy of Engineering in 1980. Hans was born on January 16, 1917, in Constantinople, Turkey, the son of a celebrated scholar of Islamic studies at the Univer- sity of Leiden (Prof. J.H. Kramers, 1891-1951) and nephew of the famous theoretical physicist at the same university (Prof. H.A. Kramers). He pursued the science preparatory curriculum at a Gymnasium (high-level high school) in Leiden from 1928 to 1934. Then, from 1934 to 1941, he was a student in engineering physics at the Technische Hogeschool in Delft (Netherlands), where he got his engineer’s degree (roughly equivalent to or slightly higher than an M.S. in the United States). From 1941 to 1944, Hans was employed as a research physi- cist in the Engineering Physics Section at TNO (Organization for Applied Scientific Research) associated with the Tech- nische Hogeschool in Delft. From 1944 to 1948, he worked at the Bataafsche Petroleum Maatschappij (BPM) (Royal Dutch Shell) in Amsterdam. -
Rethinking Antiparticles. Hermann Weyl's Contribution to Neutrino Physics
Studies in History and Philosophy of Modern Physics 61 (2018) 68e79 Contents lists available at ScienceDirect Studies in History and Philosophy of Modern Physics journal homepage: www.elsevier.com/locate/shpsb Rethinking antiparticles. Hermann Weyl’s contribution to neutrino physics Silvia De Bianchi Department of Philosophy, Building B - Campus UAB, Universitat Autonoma de Barcelona 08193, Bellaterra Barcelona, Spain article info abstract Article history: This paper focuses on Hermann Weyl’s two-component theory and frames it within the early devel- Received 18 February 2016 opment of different theories of spinors and the history of the discovery of parity violation in weak in- Received in revised form teractions. In order to show the implications of Weyl’s theory, the paper discusses the case study of Ettore 29 March 2017 Majorana’s symmetric theory of electron and positron (1937), as well as its role in inspiring Case’s Accepted 31 March 2017 formulation of parity violation for massive neutrinos in 1957. In doing so, this paper clarifies the rele- Available online 9 May 2017 vance of Weyl’s and Majorana’s theories for the foundations of neutrino physics and emphasizes which conceptual aspects of Weyl’s approach led to Lee’s and Yang’s works on neutrino physics and to the Keywords: “ ” Weyl solution of the theta-tau puzzle in 1957. This contribution thus sheds a light on the alleged re-discovery ’ ’ Majorana of Weyl s and Majorana s theories in 1957, by showing that this did not happen all of a sudden. On the two-component theory contrary, the scientific community was well versed in applying these theories in the 1950s on the ground neutrino physics of previous studies that involved important actors in both Europe and United States. -
SELECTED PAPERS of J. M. BURGERS Selected Papers of J
SELECTED PAPERS OF J. M. BURGERS Selected Papers of J. M. Burgers Edited by F. T. M. Nieuwstadt Department of Mechanical Engineering and Maritime Technology, Delft University of Technology, The Netherlands and J. A. Steketee Department of Aero and Space Engineering, Delft University of Technology, The Netherlands SPRINGER SCIENCE+BUSINESS MEDIA, B.V. A CLP. Catalogue record for this book is available from the Library of Congress. ISBN 978-94-010-4088-4 ISBN 978-94-011-0195-0 (eBook) DOI 10.1007/978-94-011-0195-0 Printed on acid-free paper All Rights Reserved © 1995 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1995 Softcover reprint of the hardcover 1st edition 1995 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. Preface By the beginning of this century, the vital role of fluid mechanics in engineering science and technological progress was clearly recognised. In 1918, following an international trend, the University of Technology in Delft established a chair in fluid dynamics, and we can still admire the wisdom of the committee which appointed the young theoretical physicist, J.M. Burgers, at the age of 23, to this position within the department of Mechanical Engineering, Naval architecture and Electrical Engineering. The consequences of this appointment were to be far-reaching. J .M. Burgers went on to become one of the leading figures in the field of fluid mechanics: a giant on whose shoulders the Dutch fluid mechanics community still stands. -
C Copyright 2017 Joshua James Goings
c Copyright 2017 Joshua James Goings Breaking symmetry in time-dependent electronic structure theory to describe spectroscopic properties of non-collinear and chiral molecules. Joshua James Goings A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2017 Reading Committee: Xiaosong Li, Chair David Masiello Stefan Stoll Program Authorized to Offer Degree: Chemistry University of Washington Abstract Breaking symmetry in time-dependent electronic structure theory to describe spectroscopic properties of non-collinear and chiral molecules. Joshua James Goings Chair of the Supervisory Committee: Professor Xiaosong Li Department of Chemistry Time-dependent electronic structure theory has the power to predict and probe the ways electron dynamics leads to useful phenomena and spectroscopic data. Here we report several advances and extensions of broken-symmetry time-dependent electronic structure theory in order to capture the flexibility required to describe non-equilibrium spin dynamics, as well as electron dynamics for chiroptical properties and vibrational effects. In the first half, we begin by discussing the generalization of self-consistent field methods to the so-called two-component structure in order to capture non-collinear spin states. This means that individual electrons are allowed to take a superposition of spin-1=2 projection states, instead of being constrained to either spin-up or spin-down. The system is no longer a spin eigenfunction, and is known a a spin-symmetry broken wave function. This flexibility to break spin symmetry may lead to variational instabilities in the approximate wave function, and we discuss how these may be overcome. -
De Tweede Gouden Eeuw
De tweede Gouden Eeuw Nederland en de Nobelprijzen voor natuurwetenschappen 1870-1940 Bastiaan Willink bron Bastiaan Willink, De tweede Gouden Eeuw. Bert Bakker, Amsterdam 1998 Zie voor verantwoording: http://www.dbnl.org/tekst/will078twee01_01/colofon.php © 2007 dbnl / Bastiaan Willink 9 Dankwoord In juni 1996 wandelde ik over de begraafplaats van Montparnasse in Parijs, op zoek naar het graf van Henri Poincaré. Na enige omzwervingen vond ik het, verscholen achter graven van onbekenden, tegen de grote muur. Opluchting over de vondst mengde zich met verontwaardiging. Dit is geen passende plaats voor de grootste Franse wiskundige van de Belle Epoque. Hij hoort in het Pantheon! Meteen zag ik in dat zo'n reactie bij een Nederlander geen pas geeft. In ons land is er geen erebegraafplaats voor personen die grote prestaties leverden. Het is al een wonder, gelukkig minder zeldzaam dan vroeger, als er een biografie verschijnt van een Nederlandse wetenschappelijke coryfee. Dat motiveerde me om het plan voor dit boek definitief door te zetten. Het zou geen biografie worden, maar een mini-Pantheon van de Nederlandse wetenschap rond 1900. Er zijn eerder vergelijkbare boeken verschenen, maar een recent overzicht dat bovendien speciale aandacht schenkt aan oorzaken en gevolgen van bloei is er niet. Toen de tekst vorm begon te krijgen, sloeg de onzekerheid toe. Wie ben ik om al die verschillende specialisten te karakteriseren? Veel deskundige vrienden en vriendelijke deskundigen hebben me geholpen om de ergste omissies en fouten weg te werken. Ik ben de volgende hoog- en zeergeleerden erkentelijk voor literatuursuggesties en soms zeer indringend commentaar: A. Blaauw, H.B.G. -
Statistical Mechanics of Branched Polymers Physical Virology ICTP Trieste, July 20, 2017
Statistical Mechanics of Branched Polymers Physical Virology ICTP Trieste, July 20, 2017 Alexander Grosberg Center for Soft Matter Research Department of Physics, New York University My question to an anonymous referee: why do you think this is a perpetual motion machine? First part based on this image never published… From RNA to branched polymer Drawing by Joshua Kelly and Robijn Bruinsma To view RNA as a branched polymer is an imperfect approximation, with limited applicability … but let us explore it. Drawing by Angelo Rosa What is known about branched polymers? Classics 1: Main result: gyration radius 1/4 Rg ~ N Excluded volume becomes very important, because Bruno Zimm N/R 3~N1/4 grows with N Walter Stockmayer 1920-2005 g 1914-2004 “Chemical diameter” other people call it MLD Zimm-Stockmayer result: “typical” chemical diameter ~N1/2 Then its size in space is (N1/2)1/2=N1/4 Interesting: similar measures used to characterize dendritic arbors as well as vasculature in a human body or in a plant leave… Two ways to swell Always May or may not possible be possible Quenched Annealed Flory theory: old work and recent review Flory theory Highly Even less nontrivial trivial Quenched Annealed Kramers matrix comment Already a prediction J.Kelly developed algorithm to compute the right L Kramers theorem J.Kelly developed algorithm to compute the right L Quenched Qkm = ±K(k)M(m) 2 Trace(Qkm) = Rg (see Ben Shaul lecture yesterday) Maximal eigenvalue of Qkm gives the right L Hendrik (Hans) Kramers (1894-1952) Prediction works reasonably well Other predictions are also OK Green – single macromolecule in a good solvent; Magenta – single macromolecule in Q-solvent; Blue – one macromolecule among similar ones in a melt. -
Quantization Conditions, 1900–1927
Quantization Conditions, 1900–1927 Anthony Duncan and Michel Janssen March 9, 2020 1 Overview We trace the evolution of quantization conditions from Max Planck’s intro- duction of a new fundamental constant (h) in his treatment of blackbody radiation in 1900 to Werner Heisenberg’s interpretation of the commutation relations of modern quantum mechanics in terms of his uncertainty principle in 1927. In the most general sense, quantum conditions are relations between classical theory and quantum theory that enable us to construct a quantum theory from a classical theory. We can distinguish two stages in the use of such conditions. In the first stage, the idea was to take classical mechanics and modify it with an additional quantum structure. This was done by cut- ting up classical phase space. This idea first arose in the period 1900–1910 in the context of new theories for black-body radiation and specific heats that involved the statistics of large collections of simple harmonic oscillators. In this context, the structure added to classical phase space was used to select equiprobable states in phase space. With the arrival of Bohr’s model of the atom in 1913, the main focus in the development of quantum theory shifted from the statistics of large numbers of oscillators or modes of the electro- magnetic field to the detailed structure of individual atoms and molecules and the spectra they produce. In that context, the additional structure of phase space was used to select a discrete subset of classically possible motions. In the second stage, after the transition to modern quantum quan- tum mechanics in 1925–1926, quantum theory was completely divorced from its classical substratum and quantum conditions became a means of con- trolling the symbolic translation of classical relations into relations between quantum-theoretical quantities, represented by matrices or operators and no longer referring to orbits in classical phase space.1 More specifically, the development we trace in this essay can be summa- rized as follows. -
Levensbericht N.G. Van Kampen
Nicolaas Godfried van Kampen 22 juni 1921 – 6 oktober 2013 levensberichten en herdenkingen 2014 22 L&H_2014.indd 22 10/22/2014 3:20:10 PM Levensbericht door G. ’t Hooft Na een kort ziekbed, overleed op 6 oktober 2013 Nicolaas Godfried van Kampen, lid van de Koninklijke Nederlandse Akademie van Wetenschappen sinds 1973. Nico was 92 jaar, en tot nog onlangs bleef hij een trouw bezoeker van de vergaderingen van de Afdeling Natuurkunde, waar zijn aanwezigheid zelden onopgemerkt bleef. Nico’s vader, Pieter Nicolaas van Kampen, was hoogleraar zoölogie in Leiden en zijn moeder, Lize, was van de familie Zernike, die opmerkelijke personages telde, zoals haar broer, Frits Zernike, die in 1953 de Nobelprijs voor Natuurkunde kreeg toegekend voor de uitvinding van de fasecontrast- microscoop, een voor die tijd revolutionaire techniek die het mogelijk maakte om bijvoorbeeld het celdelingsproces in levende cellen waar te nemen. Een andere broer, Johannes Zernike, was hoogleraar in de scheikunde en schrijver van een boek over ‘Entropie’. Een zuster, Elisabeth Zernike, werd een bekend schrijfster, en een andere zuster, Nico’s tante Annie, werd de eerste Neder- landse vrouwelijke predikante, in Bovenknijpe. Zij huwde met de schilder Jan Mankes. Nico deed in 1939 eindexamen als beste van zijn klas in het gymnasium te Leiden. Hij was nog maar net begonnen met de natuurkundestudie in Leiden, toen de universiteit daar door de bezetters werd gesloten. Nico vertrok in 1941 naar Groningen waar zijn oom Frits Zernike hoogleraar theoretische natuurkunde was en waar hij in 1947 zijn doctoraal behaalde. Met Zernike werkte hij aan diffractie van licht.