Magnetic Properties and the Superatom Character of 13-Atom Platinum Nanoclusters
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Arxiv:Cond-Mat/0106646 29 Jun 2001 Landau Diamagnetism Revisited
Landau Diamagnetism Revisited Sushanta Dattagupta†,**, Arun M. Jayannavar‡ and Narendra Kumar# †S.N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700 098, India ‡Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India #Raman Research Institute, Bangalore 560 080, India The problem of diamagnetism, solved by Landau, continues to pose fascinating issues which have relevance even today. These issues relate to inherent quantum nature of the problem, the role of boundary and dissipation, the meaning of thermodynamic limits, and above all, the quantum–classical crossover occasioned by environment- induced decoherence. The Landau diamagnetism provides a unique paradigm for discussing these issues, the significance of which is far-reaching. Our central result connects the mean orbital magnetic moment, a thermodynamic property, with the electrical resistivity, which characterizes transport properties of material. In this communication, we wish to draw the attention of Peierls to term diamagnetism as one of the surprises in the reader to certain enigmatic issues concerning dia- theoretical physics4. Landau’s pathbreaking result also magnetism. Indeed, diamagnetism can be used as a demonstrated that the calculation of diamagnetic suscep- prototype phenomenon to illustrate the essential role of tibility did indeed require an explicit quantum treatment. quantum mechanics, surface–boundary, dissipation and Turning to the classical domain, two of the present nonequilibrium statistical mechanics itself. authors had worried, some years ago, about the issue: Diamagnetism is a material property that characterizes does the BV theorem survive dissipation5? This is a natu- the response of an ensemble of charged particles (more ral question to ask as dissipation is a ubiquitous property specifically, electrons) to an applied magnetic field. -
Magnetism, Magnetic Properties, Magnetochemistry
Magnetism, Magnetic Properties, Magnetochemistry 1 Magnetism All matter is electronic Positive/negative charges - bound by Coulombic forces Result of electric field E between charges, electric dipole Electric and magnetic fields = the electromagnetic interaction (Oersted, Maxwell) Electric field = electric +/ charges, electric dipole Magnetic field ??No source?? No magnetic charges, N-S No magnetic monopole Magnetic field = motion of electric charges (electric current, atomic motions) Magnetic dipole – magnetic moment = i A [A m2] 2 Electromagnetic Fields 3 Magnetism Magnetic field = motion of electric charges • Macro - electric current • Micro - spin + orbital momentum Ampère 1822 Poisson model Magnetic dipole – magnetic (dipole) moment [A m2] i A 4 Ampere model Magnetism Microscopic explanation of source of magnetism = Fundamental quantum magnets Unpaired electrons = spins (Bohr 1913) Atomic building blocks (protons, neutrons and electrons = fermions) possess an intrinsic magnetic moment Relativistic quantum theory (P. Dirac 1928) SPIN (quantum property ~ rotation of charged particles) Spin (½ for all fermions) gives rise to a magnetic moment 5 Atomic Motions of Electric Charges The origins for the magnetic moment of a free atom Motions of Electric Charges: 1) The spins of the electrons S. Unpaired spins give a paramagnetic contribution. Paired spins give a diamagnetic contribution. 2) The orbital angular momentum L of the electrons about the nucleus, degenerate orbitals, paramagnetic contribution. The change in the orbital moment -
DENDRAL Program E
12 On Generality and Problem Solving: A Case Study Using the DENDRAL Program E. A. Feigenbaum, B. G. Buchanan and J. Lederberg Computer Science Department Stanford University In discussing the capability of a problem-solving system, ne should dis- tinguish between generality and expertness. Generality is being questioned when we ask: how broad a universe of problems is the problem solver prepared to work on? Expertness is being questioned when we ask: how good are the answers and were they arrived at with reasonable cost? Generality has great utility in some ways, but is not often associated with superior performance. The experts usually are specialists. In analytical chemistry, there is a domain of inductive inference problems involving the determination of molecular structure by analysis of certain physical spectra of the molecule. We have written a problem-solving program (Heuristic Dendral) that is prepared to attempt to solve any problem in this very large domain. By now, it has solved hundreds ofstructure-determina- tion problems in many different chemical families. For some families of molecules, it is an expert, even when compared with the best human perfor- mance. For the other families, i.e., most of chemistry, it performs as a novice, or worse. This paper will use the design of Heuristic Dendral and its performance on many different problems it has solved as raw material for a discussion of the following topics: 1. the design for generality; 2. the performance problems attendant upon too much generality; 3. the coupling of expertise to the general problem-solving processes; 4. the symbiotic relationship between generality and expertness, and the implications of this symbiosis for the study and design of problem-solving systems. -
Solid State Physics 2 Lecture 5: Electron Liquid
Physics 7450: Solid State Physics 2 Lecture 5: Electron liquid Leo Radzihovsky (Dated: 10 March, 2015) Abstract In these lectures, we will study itinerate electron liquid, namely metals. We will begin by re- viewing properties of noninteracting electron gas, developing its Greens functions, analyzing its thermodynamics, Pauli paramagnetism and Landau diamagnetism. We will recall how its thermo- dynamics is qualitatively distinct from that of a Boltzmann and Bose gases. As emphasized by Sommerfeld (1928), these qualitative di↵erence are due to the Pauli principle of electons’ fermionic statistics. We will then include e↵ects of Coulomb interaction, treating it in Hartree and Hartree- Fock approximation, computing the ground state energy and screening. We will then study itinerate Stoner ferromagnetism as well as various response functions, such as compressibility and conduc- tivity, and screening (Thomas-Fermi, Debye). We will then discuss Landau Fermi-liquid theory, which will allow us understand why despite strong electron-electron interactions, nevertheless much of the phenomenology of a Fermi gas extends to a Fermi liquid. We will conclude with discussion of electrons on the lattice, treated within the Hubbard and t-J models and will study transition to a Mott insulator and magnetism 1 I. INTRODUCTION A. Outline electron gas ground state and excitations • thermodynamics • Pauli paramagnetism • Landau diamagnetism • Hartree-Fock theory of interactions: ground state energy • Stoner ferromagnetic instability • response functions • Landau Fermi-liquid theory • electrons on the lattice: Hubbard and t-J models • Mott insulators and magnetism • B. Background In these lectures, we will study itinerate electron liquid, namely metals. In principle a fully quantum mechanical, strongly Coulomb-interacting description is required. -
Study of Spin Glass and Cluster Ferromagnetism in Rusr2eu1.4Ce0.6Cu2o10-Δ Magneto Superconductor Anuj Kumar, R
Study of spin glass and cluster ferromagnetism in RuSr2Eu1.4Ce0.6Cu2O10-δ magneto superconductor Anuj Kumar, R. P. Tandon, and V. P. S. Awana Citation: J. Appl. Phys. 110, 043926 (2011); doi: 10.1063/1.3626824 View online: http://dx.doi.org/10.1063/1.3626824 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v110/i4 Published by the American Institute of Physics. Related Articles Annealing effect on the excess conductivity of Cu0.5Tl0.25M0.25Ba2Ca2Cu3O10−δ (M=K, Na, Li, Tl) superconductors J. Appl. Phys. 111, 053914 (2012) Effect of columnar grain boundaries on flux pinning in MgB2 films J. Appl. Phys. 111, 053906 (2012) The scaling analysis on effective activation energy in HgBa2Ca2Cu3O8+δ J. Appl. Phys. 111, 07D709 (2012) Magnetism and superconductivity in the Heusler alloy Pd2YbPb J. Appl. Phys. 111, 07E111 (2012) Micromagnetic analysis of the magnetization dynamics driven by the Oersted field in permalloy nanorings J. Appl. Phys. 111, 07D103 (2012) Additional information on J. Appl. Phys. Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors Downloaded 12 Mar 2012 to 14.139.60.97. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions JOURNAL OF APPLIED PHYSICS 110, 043926 (2011) Study of spin glass and cluster ferromagnetism in RuSr2Eu1.4Ce0.6Cu2O10-d magneto superconductor Anuj Kumar,1,2 R. P. Tandon,2 and V. P. S. Awana1,a) 1Quantum Phenomena and Application Division, National Physical Laboratory (CSIR), Dr. -
(2020) Observation of Collective Decay Dynamics of a Single Rydberg
PHYSICAL REVIEW RESEARCH 2, 043339 (2020) Observation of collective decay dynamics of a single Rydberg superatom Nina Stiesdal ,1 Hannes Busche ,1 Jan Kumlin ,2 Kevin Kleinbeck,2 Hans Peter Büchler ,2 and Sebastian Hofferberth 1,* 1Department of Physics, Chemistry and Pharmacy, Physics@SDU, University of Southern Denmark, 5320 Odense, Denmark 2Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, University of Stuttgart, 70550 Stuttgart, Germany (Received 11 May 2020; accepted 11 November 2020; published 8 December 2020) We experimentally investigate the collective decay of a single Rydberg superatom, formed by an ensemble of thousands of individual atoms supporting only a single excitation due to the Rydberg blockade. Instead of observing a constant decay rate determined by the collective coupling strength to the driving field, we show that the enhanced emission of the single stored photon into the forward direction of the coupled optical mode depends on the dynamics of the superatom before the decay. We find that the observed decay rates are reproduced by an expanded model of the superatom which includes coherent coupling between the collective bright state and subradiant states. DOI: 10.1103/PhysRevResearch.2.043339 I. INTRODUCTION been used to study the propagation of quantized light in one- dimensional waveguides, while the semiclassical approach The collective interaction between an ensemble of emitters enables investigation of large, weakly driven ensembles in two and photons is a fundamental topic of quantum optics, which or three dimensions. In the single-excitation sector and as long has been extensively studied for over 60 years [1]. Collective as saturation of the medium can be neglected, the two ap- enhancement of the emission, known as superradiance, has proaches lead to equivalent results [34,35]. -
Condensation of Bosons with Several Degrees of Freedom Condensación De Bosones Con Varios Grados De Libertad
Condensation of bosons with several degrees of freedom Condensación de bosones con varios grados de libertad Trabajo presentado por Rafael Delgado López1 para optar al título de Máster en Física Fundamental bajo la dirección del Dr. Pedro Bargueño de Retes2 y del Prof. Fernando Sols Lucia3 Universidad Complutense de Madrid Junio de 2013 Calificación obtenida: 10 (MH) 1 [email protected], Dep. Física Teórica I, Universidad Complutense de Madrid 2 [email protected], Dep. Física de Materiales, Universidad Complutense de Madrid 3 [email protected], Dep. Física de Materiales, Universidad Complutense de Madrid Abstract The condensation of the spinless ideal charged Bose gas in the presence of a magnetic field is revisited as a first step to tackle the more complex case of a molecular condensate, where several degrees of freedom have to be taken into account. In the charged bose gas, the conventional approach is extended to include the macroscopic occupation of excited kinetic states lying in the lowest Landau level, which plays an essential role in the case of large magnetic fields. In that limit, signatures of two diffuse phase transitions (crossovers) appear in the specific heat. In particular, at temperatures lower than the cyclotron frequency, the system behaves as an effectively one-dimensional free boson system, with the specific heat equal to (1/2) NkB and a gradual condensation at lower temperatures. In the molecular case, which is currently in progress, we have studied the condensation of rotational levels in a two–dimensional trap within the Bogoliubov approximation, showing that multi–step condensation also occurs. -
Pauli Paramagnetism of an Ideal Fermi Gas
Pauli paramagnetism of an ideal Fermi gas The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Lee, Ye-Ryoung, Tout T. Wang, Timur M. Rvachov, Jae-Hoon Choi, Wolfgang Ketterle, and Myoung-Sun Heo. "Pauli paramagnetism of an ideal Fermi gas." Phys. Rev. A 87, 043629 (April 2013). © 2013 American Physical Society As Published http://dx.doi.org/10.1103/PhysRevA.87.043629 Publisher American Physical Society Version Final published version Citable link http://hdl.handle.net/1721.1/88740 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. PHYSICAL REVIEW A 87, 043629 (2013) Pauli paramagnetism of an ideal Fermi gas Ye-Ryoung Lee,1 Tout T. Wang,1,2 Timur M. Rvachov,1 Jae-Hoon Choi,1 Wolfgang Ketterle,1 and Myoung-Sun Heo1,* 1MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA (Received 7 January 2013; published 24 April 2013) We show how to use trapped ultracold atoms to measure the magnetic susceptibility of a two-component Fermi gas. The method is illustrated for a noninteracting gas of 6Li, using the tunability of interactions around a wide Feshbach resonance. The susceptibility versus effective magnetic field is directly obtained from the inhomogeneous density profile of the trapped atomic cloud. The wings of the cloud realize the high-field limit where the polarization approaches 100%, which is not accessible for an electron gas. -
Faculty of Science Internal Bylaw of Graduate Studies "Program Curricula and Course Contents" 2016
. Faculty of Science Internal Bylaw of Graduate Studies "Program Curricula and Course Contents" 2016 Table of Contents Page 1-Mathematics Department Mathematics Programs 1 Diplomas Professional Diploma in Applied Statistics 2 Professional Diploma in Bioinformatics 3 M.Sc. Degree M.Sc. Degree in Pure Mathematics 4 M.Sc. Degree in Applied Mathematics 5 M.Sc. Degree in Mathematical Statistics 6 M.Sc. Degree in Computer Science 7 M.Sc. Degree in Scientific Computing 8 Ph.D. Degree Ph. D. Degree in Pure Mathematics 9 Ph. D Degree in Applied Mathematics 10 Ph. D. Degree in Mathematical Statistics 11 Ph. D Degree in Computer Science 12 Ph. D Degree in Scientific Computing 13 2- Physics Department Physics Programs 14 Diplomas Diploma in Medical Physics 15 M.Sc. Degree M.Sc. Degree in Solid State Physics 16 M.Sc. Degree in Nanomaterials 17 M.Sc. Degree in Nuclear Physics 18 M.Sc. Degree in Radiation Physics 19 M.Sc. Degree in Plasma Physics 20 M.Sc. Degree in Laser Physics 21 M.Sc. Degree in Theoretical Physics 22 M.Sc. Degree in Medical Physics 23 Ph.D. Degree Ph.D. Degree in Solid State Physics 24 Ph.D. Degree in Nanomaterials 25 Ph.D. Degree in Nuclear Physics 26 Ph.D. Degree in Radiation Physics 27 Ph.D. Degree in Plasma Physics 28 Ph.D. Degree in Laser Physics 29 Ph.D. Degree in Theoretical Physics 30 3- Chemistry Department Chemistry Programs 31 Diplomas Professional Diploma in Biochemistry 32 Professional Diploma in Quality Control 33 Professional Diploma in Applied Forensic Chemistry 34 Professional Diploma in Applied Organic Chemistry 35 Environmental Analytical Chemistry Diploma 36 M.Sc. -
Energy and Charge Transfer in Open Plasmonic Systems
Energy and Charge Transfer in Open Plasmonic Systems Niket Thakkar A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2017 Reading Committee: David J. Masiello Randall J. LeVeque Mathew J. Lorig Daniel R. Gamelin Program Authorized to Offer Degree: Applied Mathematics ©Copyright 2017 Niket Thakkar University of Washington Abstract Energy and Charge Transfer in Open Plasmonic Systems Niket Thakkar Chair of the Supervisory Committee: Associate Professor David J. Masiello Chemistry Coherent and collective charge oscillations in metal nanoparticles (MNPs), known as localized surface plasmons, offer unprecedented control and enhancement of optical processes on the nanoscale. Since their discovery in the 1950's, plasmons have played an important role in understanding fundamental properties of solid state matter and have been used for a variety of applications, from single molecule spectroscopy to directed radiation therapy for cancer treatment. More recently, experiments have demonstrated quantum interference between optically excited plasmonic materials, opening the door for plasmonic applications in quantum information and making the study of the basic quantum mechanical properties of plasmonic structures an important research topic. This text describes a quantitatively accurate, versatile model of MNP optics that incorporates MNP geometry, local environment, and effects due to the quantum properties of conduction electrons and radiation. We build the theory from -
Mesoscopic Rydberg-Blockaded Ensembles in the Superatom Regime and Beyond
LETTERS PUBLISHED ONLINE: 12 JANUARY 2015 | DOI: 10.1038/NPHYS3214 Mesoscopic Rydberg-blockaded ensembles in the superatom regime and beyond T. M. Weber, M. Höning, T. Niederprüm, T. Manthey, O. Thomas, V. Guarrera†, M. Fleischhauer, G. Barontini† and H. Ott* The control of strongly interacting many-body systems of a Bose–Einstein condensate of 87Rb atoms. We first load the enables the creation of tailored quantum matter with complex condensate into a one-dimensional optical lattice with a spacing of properties. Atomic ensembles that are optically driven to a 532 nm, to suppress the axial movement of the atoms. We subse- Rydberg state provide many examples for this: atom–atom quently compress the atomic sample in the radial direction to reduce entanglement1,2, many-body Rabi oscillations3, strong its size below the blockade radius and empty all but three (or more) photon–photon interaction4 and spatial pair correlations5. lattice sites using a focused electron beam8–10 (Fig. 1a and Methods). In its most basic form Rydberg quantum matter consists of The atom number within the ensemble (N) can be adjusted between an isolated ensemble of strongly interacting atoms spatially 100 and 500 at a temperature of T D .3.5 0.5/ µK and the typical confined to the blockade volume—a superatom. Here we size of the sample is ≤3 µm in diameter (Fig. 1b). Our preparation demonstrate the controlled creation and characterization scheme is readily scalable to arrays of superatoms (Fig. 1d). of an isolated mesoscopic superatom by means of accurate After preparation we excite the atomic ensemble with a density engineering and excitation to Rydberg p-states. -
CHEMISTRY MODULE No.31 : Magnetic Properties of Transition
Web links http://en.wikipedia.org/wiki/Magnetism http://wwwchem.uwimona.edu.jm/courses/magnetism.html https://www.boundless.com/chemistry/textbooks/boundless-chemistry-textbook/transition- metals-22/bonding-in-coordination-compounds-crystal-field-theory-160/magnetic-properties- 616-6882/ http://en.wikipedia.org/wiki/Transition_metal http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Crystal_Field_Theory/Crystal_Field_Theo ry/Magnetic_Properties_of_Coordination_Complexes Suggested Readings Miessler, G. L.; Tarr, D. A. (2003). Inorganic Chemistry (3rd ed.). Pearson Prentice Hall. ISBN 0-13-035471-6 Drago, R. S.Physical Methods In Chemistry. W.B. Saunders Company. ISBN 0721631843 (ISBN13: 9780721631844) Huheey, J. E.; Keiter, E.A. ; Keiter, R. L. ; Medhi O. K. Inorganic Chemistry: Principles of Structure and Reactivity.Pearson Education India, 2006 - Chemistry, Inorganic CHEMISTRY PAPER No.: 7; Inorganic Chemistry-II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) MODULE No.31 : Magnetic properties of transition metal ions Carlin, R. L. Magnetochemistry. SPRINGER VERLAG GMBH. ISBN 10: 3642707351 / ISBN 13: 9783642707353 SELWOOD, P. W. MAGNETOCHEMISIRY. Swinburne Press. ISBN 1443724890. Earnshaw, A. Introduction to Magnetochemistry Academic Press. ISBN 10: 1483255239 / ISBN 13: 9781483255231 Lacheisserie É, D. T. De; Gignoux, D., Schlenker, M. Magnetism Time-Lines Timeline Image Description s 1600 Dr. William Gilbert published the first systematic experiments on magnetism in "De Magnete". Source: http://en.wikipedia.org/wiki/William_Gilbert_(astronomer) CHEMISTRY PAPER No.: 7; Inorganic Chemistry-II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) MODULE No.31 : Magnetic properties of transition metal ions 1777 Charles-Augustin de Coulomb showed that the magnetic repulsion or attraction between magnetic poles varies inversely with the square of the http://en.wikipedia.org/wiki/Charles-Augustin_de_Coulomb distance r.