Université Lille 1 Sciences et Technologies, Lille, France Lille Laboratoire de Physique des Lasers, Atomes et Molécules Équipe Chaos Quantique


 Francis Russell
 2 years ago
 Views:
Transcription
1 Université Lille 1 Sciences et Technologies, Lille, France Lille Laboratoire de Physique des Lasers, Atomes et Molécules Équipe Chaos Quantique FRISNO 11 Aussois 1/4/011 Quantum simulators: The Anderson transition and the quantum kicked rotor JeanClaude Garreau Aussois Matthias Lopez, Julien Chabé ( 8/008), PhDs Gabriel Lemarié, PhD ( 9/009) Hans Lignier ( 9/009) postdoc JeanFrançois Clément, Pascal Szriftgiser, J. C. G. Benoît Grémaud, Dominique Delande 1
2 Simulating condensed matter with cold atoms 198 R. P. Feynman Simulating Physics with computers, Int. J. Th. Phys (198) A. Hemmerich and T. W. Hänsch, Twodimensional atomic cristal bound by light, Phys. Rev. Lett. 70, (1993) G. Grynberg et al., Quantized motion of cold cesium atoms in two and threedimensional optical potentials, Phys. Rev. Lett. 70, 49 5 (1993) M. Ben Dahan et al., Bloch Oscillations of Atoms in an Optical Potential, Phys. Rev. Lett. 76, (1996) S. R. Wilkinson et al., Observation of atomic WannierStark ladders in an accelerating optical potential, PRL 76, (1996) M. Greiner et al., Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature 415, (00) J. Billy et al., Direct observation of Anderson localization of matterwaves in a controlled disorder, Nature 453, (008) 011 J. Chabé et al., Experimental Observation of the Anderson MetalInsulator Transition with Atomic Matter Waves, Phys. Rev. Lett. 101, 5570 (008) /6
3 The Anderson localization Tmum + Vr um + r = Eum Anderson crystal r W W Tm 1D: All eigenstates are localized whatever the disorder 3D: Mobility edge : For low enough disorder diffusion30restored P. W. Anderson, Absence of Diffusion in Certain Random Lattices, Phys. Rev. 109, 149 (1958) 3 /6
4 Anderson transition in 1D A pedestrians view of the Anderson transition L R L D. J. Thouless, Electrons in disordered systems and the theory of localization, Phys. Rep. 13, (1974) 4/6
5 The Anderson transition in 3D L L L Insulator Conductor 5 /6
6 The Anderson transition The Anderson transition in various dimensions Insulator Conductor α D D 3D 4D 5D ln r 6/6
7 Experiments in condensed matter Not easy to control decoherence No access to wavefunctions Strong interactions 7/6
8 Experiments in other wave systems Localization has been observed with sound waves, microwaves, light and with a BoseEinstein condensate, in 1D J. Billy et al., Direct observation of Anderson localization of matterwaves in a controlled disorder, Nature 453, 891 (008) Transition observed with light M. Störzer et al., Observation of the Critical Regime Near Anderson Localization of Light, PRL 96, (006) and sound waves H. Hu et al., Localization of ultrasound in a threedimensional elastic network, Nature Physics 4, 945 (008) experiments plagued by absorption: same signature as localization 8/6
9 Experiments with cold atoms Control of decoherence Direct access to wavefunctions Negligible particleparticle interactions How to implement disorder? Optical speckle (IOTA) Quasiperiodic spatial modulation (Florence) Temporal disorder: Quantum chaos (Lille) 9/6
10 The kicked rotor P H = + K cos x δ ( t n) n 10/6
11 The optical potential p after = p before + k L V ( x) I( x) sin( x) 11/6
12 The atomic kicked rotor (schematic) Acoustooptical modulator Coldatom cloud Mirror P H = + K cos x δ ( t n) n F. L. Moore et al., Atom optics realization of the quantum δkicked rotator, Phys. Rev. Lett. 75, 4598 (1995) 1/6
13 Dynamical localization Classical x quantum p p ~Dt p ~cte «Dynamical localization» t G. Casati et al., Stochastic behavior of a quantum pendulum under periodic perturbation, Lect. Notes Phys. 93, 334 (1979) 13/6
14 Anderson x dynamical localization T n n V n + r n = E n Anderson + r r n x = na Kicked rotor p0 p0 + n exp( ik sin x / ) n = ( i) J ( K / ) n + r r ( k) r r p = n k Random Eq. (1) tan( K cos x / ) = r V r e ikr T n ε n = tan n / (1) Floquet s quasienergy (deterministic!) Pseudo disorder Each Floquet state is a realization of the fixed disorder ~ W = cte K controls the tunneling ~ V Increasing K decreases W/V S. Fishman et al., Chaos, quantum recurrences, and Anderson localization, PRL 49, 509 (198) 14/6
15 The 3D kicked rotor How to realize a 3D kicked rotor? H = P + K cos x ( 1+ ε cos( ω t)cos( ω t) ) δ ( t 3 n n) substantially equivalent to an anisotropic 3D Anderson model The underlying unit of nature : different systems described by the same equations (The Feynman Lectures in Physics, vol. ch. 1) 15/6 G. Casati et al., Anderson transition in a onedimensional system with three incommensurate frequencies, PRL 6, 345 (1989)
16 The (real) experiment 16/6
17 Sweeping the Anderson transition H = P + K cos x ( 1+ ε cos( ω t)cos( ω t) ) δ ( t 3 n n) Diffusive 0.8 Metal ε Critical Localized Insulator K 9 17/6
18 Experimental momentum distributions Linear scale 150 kicks Log scale ψ ( p) ψ ( p) K = 5.0 Π 0 K = 5.0 K = 9.0 K = 9.0 p p G. Lemarié et al. Observation of the Anderson metalinsulator transition with atomic matter waves: Theory and experiment 18/6 PRA 80, (009)
19 Determination of the critical point Theory: at criticality Recipe: make a loglog plot of and measure its slope 19/6
20 Observing the transition experimentally Localized log(t 1/3 Π 0 ) Critical Diffusive log(t) 0/6
21 Finite size/time effects Small samples : no singular behavior Example: BoseEinstein condensation N N 0 /N N = N = T/T c 1/6
22 Extracting a critical exponent ξ K Kc ν Numerical Experimental KR (num.) K c = 6.9 v =1.59 ± 0.01 K c v = 6.7 ± =1.5 ± J. Chabé et al., PRL 101, 5570 (008) G. Lemarié et al., PRA 80, (009) Anderson (num) v =1.6 ± 0.01 /6
23 Scaling of the critical wavefunction Localized Critical Diffusive G. Lemarié et al. Critical state of the Anderson transition: Between a metal and an insulator, PRL 105, (010) 3/6
24 Form of the critical wavefunction Airy fit ρ fit ρ th P(p,t)t 1/3 Airy Exponential χ =1.1 χ = 4.5 Gaussian χ = 8.8 PRL Editor s reading suggestion and Synopsis 4/6
25 Conclusion Prospects for future work Is the critical exponent really universal? How decoherence affects the transition? Other dimensions: D, 4D, 5D? ε More generally What is the effect of interactions on the transition? Use a BoseEinstein condensate and Feshbach resonances Still more generally Simulation of condensed matter systems by dynamical, cold atom systems For example: Harper model : J. Wang and J. Gong, Proposal of a coldatom realization of quantum maps with Hofstadter's butterfly spectrum, PRA 77, (R) (008) 5/6
26 The end 6
Université Lille 1 Sciences et Technologies, Lille, France Laboratoire de Physique des Lasers, Atomes et Molécules Équipe Chaos Quantique
Université Lille 1 Sciences et Technologies, Lille, France Laboratoire de Physique des Lasers, Atomes et Molécules Équipe Chaos Quantique 16 years of experiments on the atomic kicked rotor! Chaos, disorder
More informationInstability, dispersion management, and pattern formation in the superfluid flow of a BEC in a cylindrical waveguide
Instability, dispersion management, and pattern formation in the superfluid flow of a BEC in a cylindrical waveguide Michele Modugno LENS & Dipartimento di Fisica, Università di Firenze, Italy Workshop
More informationarxiv:condmat/0308498v1 [condmat.soft] 25 Aug 2003
1 arxiv:condmat/38498v1 [condmat.soft] 2 Aug 23 Matterwave interference, Josephson oscillation and its disruption in a BoseEinstein condensate on an optical lattice Sadhan K. Adhikari Instituto de
More information particle with kinetic energy E strikes a barrier with height U 0 > E and width L.  classically the particle cannot overcome the barrier
Tunnel Effect:  particle with kinetic energy E strikes a barrier with height U 0 > E and width L  classically the particle cannot overcome the barrier  quantum mechanically the particle can penetrated
More informationStrong correlations in fewatom systems. Selim Jochim, Universität Heidelberg
Strong correlations in fewatom systems Selim Jochim, Universität Heidelberg Control over few atoms IBM, 1989: Control over individual atoms Our vision: Control also all correlations between atoms 1 2
More informationUltracold fewfermion systems with tunable interactions Selim Jochim Physikalisches Institut Universität Heidelberg
Ultracold fewfermion systems with tunable interactions Selim Jochim Physikalisches Institut Universität Heidelberg The matter we deal with T=40nK 1µK Density n=10 9 10 14 cm 3 Pressures as low as 1017
More informationContents XIII. Preface XVII. List of Contributors. PartOne ColdAtomsandMolecules 1
V Contents Preface XIII List of Contributors XVII PartOne ColdAtomsandMolecules 1 1 Cooling and Trapping of Atoms 3 Peter van der Straten and Harold Metcalf 1.1 Introduction 3 1.2 PhaseSpace Density 6
More informationOutline. Magnetic field dependence (e.g. 40 K) Fermionic Alkalis. Creating new states of matter: Experiments with ultracold Fermi gases
Outline Creating new states of matter: Experiments with ultracold Fermi gases Cooling (difficulties) with Fermions Scattering Concept of Feshbach resonances Ultracold molecules Making a BEC of molecules
More informationOne, two, three, many Creating quantum systems one atom at a time. Selim Jochim, Universität Heidelberg
One, two, three, many Creating quantum systems one atom at a time Selim Jochim, Universität Heidelberg One, two, three, many Creating quantum systems one atom at a time Selim Jochim, Universität Heidelberg
More informationTrapping and Interfacing Cold Neutral Atoms Using Optical Nanofibers
Trapping and Interfacing Cold Neutral Atoms Using Optical Nanofibers Wokshop on Cold Atoms and Quantum Engineering, Paris, France, May 30 31, 2013 Arno Rauschenbeutel Vienna Center for Quantum Science
More informationBASICS OF LASER COOLING THEORY. Y. Castin, LKB  ENS, Paris OUTLINE
BASICS OF LASER COOLING THEORY Y. Castin, LKB  ENS, Paris OUTLINE Motivation lightshifts and excitation rates the mean force Doppler cooling the magnetooptical trap Sisyphus cooling Below the recoil
More informationQuantum magnetism with few cold atoms. Gerhard Zürn Graduiertenkolleg Hannover,
Quantum magnetism with few cold atoms Gerhard Zürn Graduiertenkolleg Hannover, 17.12.2015 States of matter http://en.wikipedia.org/wiki/hightemperature_superconductivity What are the key ingredients for
More informationWe consider a hydrogen atom in the ground state in the uniform electric field
Lecture 13 Page 1 Lectures 1314 Hydrogen atom in electric field. Quadratic Stark effect. Atomic polarizability. Emission and Absorption of Electromagnetic Radiation by Atoms Transition probabilities and
More informationAtomic Clocks and Frequency Standards
Atomic Clocks and Frequency Standards The Battel for Exactness Matthias Reggentin HumboldtUniversität zu Berlin, Institut für Physik July 07, 2010 1 Time and Frequency Measurement through the years 2
More informationNonequilibrium spin dynamics in systems of ultracold atoms
Nonequilibrium spin dynamics in systems of ultracold atoms Eugene Demler Harvard University Collaborators: Ehud Altman, Robert Cherng, Vladimir Gritsev, Mikhail Lukin, Anatoli Polkovnikov, Ana Maria Rey
More informationThe Role of Electric Polarization in Nonlinear optics
The Role of Electric Polarization in Nonlinear optics Sumith Doluweera Department of Physics University of Cincinnati Cincinnati, Ohio 45221 Abstract Nonlinear optics became a very active field of research
More informationFinite Fermi systems in the crossover from few to manybody physics
Finite Fermi systems in the crossover from few to manybody physics Andre Wenz Ultracold Quantum Gases group of Prof. Selim Jochim Physikalisches Institut Heidelberg University Germany Fewbody physics
More informationFree Electron Fermi Gas (Kittel Ch. 6)
Free Electron Fermi Gas (Kittel Ch. 6) Role of Electrons in Solids Electrons are responsible for binding of crystals  they are the glue that hold the nuclei together Types of binding (see next slide)
More informationPerpetual motion and driven dynamics of a mobile impurity in a quantum fluid
and driven dynamics of a mobile impurity in a quantum fluid Oleg Lychkovskiy Russian Quantum Center Seminaire du LPTMS, 01.12.2015 Seminaire du LPTMS, 01.12.2015 1 / Plan of the talk 1 Perpetual motion
More informationThe Quantum Harmonic Oscillator Stephen Webb
The Quantum Harmonic Oscillator Stephen Webb The Importance of the Harmonic Oscillator The quantum harmonic oscillator holds a unique importance in quantum mechanics, as it is both one of the few problems
More informationCollapse and Revival of the Matter Wave Field of a BoseEinstein Condensate
Collapse and Revival of the Matter Wave Field of a BoseEinstein Condensate Markus Greiner, Olaf Mandel, Theodor W. Hänsch & Immanuel Bloch * Sektion Physik, LudwigMaximiliansUniversität, Schellingstrasse
More informationTime dependence in quantum mechanics Notes on Quantum Mechanics
Time dependence in quantum mechanics Notes on Quantum Mechanics http://quantum.bu.edu/notes/quantummechanics/timedependence.pdf Last updated Thursday, November 20, 2003 13:22:3705:00 Copyright 2003 Dan
More informationIntroduction to quantum mechanics
Introduction to quantum mechanics Lecture 3 MTX9100 Nanomaterjalid OUTLINE What is electron particle or wave?  How large is a potential well? What happens at nanoscale? What is inside? Matter Molecule
More informationPHYSICAL QUANTITIES AND UNITS
1 PHYSICAL QUANTITIES AND UNITS Introduction Physics is the study of matter, its motion and the interaction between matter. Physics involves analysis of physical quantities, the interaction between them
More information thus, the total number of atoms per second that absorb a photon is
Stimulated Emission of Radiation  stimulated emission is referring to the emission of radiation (a photon) from one quantum system at its transition frequency induced by the presence of other photons
More informationarxiv:quantph/0604019v1 4 Apr 2006
Recurrence Tracking Microscope Farhan Saif Department of Electronics, QuaidiAzam University, Islamabad 4532, Pakistan. Department of Physics, The University of Arizona, Tucson, Arizona 85721, USA. (Dated:
More informationNumerical analysis of Bose Einstein condensation in a threedimensional harmonic oscillator potential
Numerical analysis of Bose Einstein condensation in a threedimensional harmonic oscillator potential Martin Ligare Department of Physics, Bucknell University, Lewisburg, Pennsylvania 17837 Received 24
More informationLecture 6 Scanning Tunneling Microscopy (STM) General components of STM; Tunneling current; Feedback system; Tip  the probe.
Lecture 6 Scanning Tunneling Microscopy (STM) General components of STM; Tunneling current; Feedback system; Tip  the probe. Brief Overview of STM Inventors of STM The Nobel Prize in Physics 1986 Nobel
More informationLecture 3: Optical Properties of Bulk and Nano. 5 nm
Lecture 3: Optical Properties of Bulk and Nano 5 nm The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model) 0 e  n( ) n' n '' n ' = 1 + Nucleus
More informationSolitons and phase domains during the cooling of a onedimensional ultracold gas
Solitons and phase domains during the cooling of a onedimensional ultracold gas Piotr Deuar Emilia Witkowska, Mariusz Gajda Institute of Physics, Polish Academy of Sciences, Warsaw Kazimierz Rzążewski
More informationDesign of 2D waveguide networks for the study of fundamental properties of Quantum Graphs
Design of 2D waveguide networks for the study of fundamental properties of Quantum Graphs Introduction: what is a quantum graph? Areas of application of quantum graphs Motivation of our experiment Experimental
More informationAnderson localization: Metallic behavior in two dimensions?
Anderson localization: Metallic behavior in two dimensions? Vladimir Kuzovkov Institute of Solid State Physics University of Latvia 8 Kengaraga Str., LV1063, RIGA, Latvia September 13, 2005 Page 1 of
More informationThermal unobtainiums? The perfect thermal conductor and the perfect thermal insulator
Thermal unobtainiums? The perfect thermal conductor and the perfect thermal insulator David G. Cahill Materials Research Lab and Department of Materials Science and Engineering, U. of Illinois Gratefully
More information4. The Infinite Square Well
4. The Infinite Square Well Copyright c 215 216, Daniel V. Schroeder In the previous lesson I emphasized the free particle, for which V (x) =, because its energy eigenfunctions are so simple: they re the
More informationChapter 41. One Dimensional Quantum
Chapter 41. One Dimensional Quantum Mechanics Quantum effects are important in nanostructures such as this tiny sign built by scientists at IBM s research laboratory by moving xenon atoms around on a metal
More information5.111 Principles of Chemical Science
MIT OpenCourseWare http://ocw.mit.edu 5.111 Principles of Chemical Science Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.111 Lecture Summary
More informationLecture 3: Electron statistics in a solid
Lecture 3: Electron statistics in a solid Contents Density of states. DOS in a 3D uniform solid.................... 3.2 DOS for a 2D solid........................ 4.3 DOS for a D solid........................
More informationBroadband microwave conductance across the T=0 superconductorresistive magnetic field tuned transition in InO x!
Broadband microwave conductance across the T=0 superconductorresistive magnetic field tuned transition in InO x! N. Peter Armitage! Dept. of Physics and Astronomy! The Johns Hopkins University! Lidong
More information5. Scanning NearField Optical Microscopy 5.1. Resolution of conventional optical microscopy
5. Scanning NearField Optical Microscopy 5.1. Resolution of conventional optical microscopy Resolution of optical microscope is limited by diffraction. Light going through an aperture makes diffraction
More informationF en = mω 0 2 x. We should regard this as a model of the response of an atom, rather than a classical model of the atom itself.
The Electron Oscillator/Lorentz Atom Consider a simple model of a classical atom, in which the electron is harmonically bound to the nucleus n x e F en = mω 0 2 x origin resonance frequency Note: We should
More informationDoes Quantum Mechanics Make Sense? Size
Does Quantum Mechanics Make Sense? Some relatively simple concepts show why the answer is yes. Size Classical Mechanics Quantum Mechanics Relative Absolute What does relative vs. absolute size mean? Why
More informationCoherent control of a short and intensive XUV laser pulse in the spherical symmetric box potential
Coherent control of a short and intensive XUV laser pulse in the spherical symmetric box potential Imre Ferenc Barna and Péter Dombi 1 2 1) KFKI  AEKI Atomic Energy Research Institute of the Hungarian
More informationDOCTOR OF PHILOSOPHY IN PHYSICS
DOCTOR OF PHILOSOPHY IN PHYSICS The Doctor of Philosophy in Physics program is designed to provide students with advanced graduate training in physics, which will prepare them for scientific careers in
More information2. Molecular stucture/basic
2. Molecular stucture/basic spectroscopy The electromagnetic spectrum Spectral region for atomic and molecular spectroscopy E. Hecht (2nd Ed.) Optics, AddisonWesley Publishing Company,1987 Spectral regions
More informationQuantum Computation with BoseEinstein Condensation and. Capable of Solving NPComplete and #P Problems. Abstract
Quantum Computation with BoseEinstein Condensation and Capable of Solving NPComplete and #P Problems Yu Shi Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom Abstract It
More informationProvided by the author(s) and University College Dublin Library in accordance with publisher policies. Please cite the published version when available. Title Bifurcation Scenarios in Electrostatic Vibration
More informationMCEN Fall 2003.
Basic types of solid materials. Overview The theory of bands provides a basis for understanding the classification and physical properties of solid materials such as electrical conductivity, optical behavior
More informationFinite element simulation of ultrasonic wave propagation in anisotropic polycrystalline aggregate
2 nd Workshop on Laser Ultrasonics for Metallurgy (April 2627 th 2016, Vancouver, Canada) Finite element simulation of ultrasonic wave propagation in anisotropic polycrystalline aggregate Thomas Garcin
More informationExcitation transfer and energy exchange processes for modeling the FleischmannPons excess heat effect
Hagelstein, P.L. and I. Chaudhary. Excitation transfer and energy exchange processes for modeling the FleischmannPons excess heat effect. in ICCF14 International Conference on Condensed Matter Nuclear
More informationSyllabus for Chem 359: Atomic and Molecular Spectroscopy
Syllabus for Chem 359: Atomic and Molecular Spectroscopy Instructors: Dr. Reinhard Schweitzer Stenner and Ms. Siobhan E. Toal Of#ice: Disque 605/Disque 306 Tel: (215) 8952268 Email: rschweitzer stenner@drexel.edu
More informationWhat is Nanophysics: Survey of Course Topics. Branislav K. Nikolić
What is Nanophysics: Survey of Course Topics Branislav K. Nikolić Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, U.S.A. http://wiki.physics.udel.edu/phys824 Definition of
More informationLecture 2: Semiconductors: Introduction
Lecture 2: Semiconductors: Introduction Contents 1 Introduction 1 2 Band formation in semiconductors 2 3 Classification of semiconductors 5 4 Electron effective mass 10 1 Introduction Metals have electrical
More informationFYS3410  Vår 2016 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v16/index.html
FYS3410  Vår 2016 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys3410/v16/index.html Pensum: Introduction to Solid State Physics by Charles Kittel (Chapters 19 and 17, 18,
More informationTWODIMENSIONAL XRAY DIFFRACTION
TWODIMENSIONAL XRAY DIFFRACTION BOB B. HE GQ WILEY ,. "'! :~! CONTENTS~\..~..). Preface 1. Introduction 1.1 XRay Technology and Its Brief History, 1.2 Geometry of Crystals, 2 1.2.1 Crystal Lattice
More informationQuantum Computing for Beginners: Building Qubits
Quantum Computing for Beginners: Building Qubits Suzanne Gildert Condensed Matter Physics Research (Quantum Devices Group) University of Birmingham 28/03/2007 Overview of this presentation What is a Qubit?
More informationWave Interference and Modes in Random Media
Chapter 9 Wave Interference and Modes in Random Media Azriel Z. Genack, Sheng Zhang Queens College of CUNY, Queens, NY, USA 9.1 Introduction 9.2 Wave Interference 9.2.1 Weak localization 9.2.2 Coherent
More informationMagnetic dynamics driven by spin current
Magnetic dynamics driven by spin current Sergej O. Demokritov University of Muenster, Germany Giant magnetoresistance Spin current Group of NonLinear Magnetic Dynamics Charge current vs spin current Electron:
More informationRutgers  Physics Graduate Qualifying Exam Quantum Mechanics: September 1, 2006
Rutgers  Physics Graduate Qualifying Exam Quantum Mechanics: September 1, 2006 QA J is an angular momentum vector with components J x, J y, J z. A quantum mechanical state is an eigenfunction of J 2 J
More informationProblem Set 1 Solutions
Chemistry 36 Dr. Jean M. Standard Problem Set Solutions. The first 4 lines in the visible region of atomic line spectrum of hydrogen atom occur at wavelengths of 656., 486., 434.0, and 40. nm (this is
More informationGravity measurements with atom interferometry
Gravity measurements with atom interferometry F. Sorrentino Dipartimento di Fisica & LENS, Università di Firenze & INFN with support from Outline AI differential gravity measurements in space An example
More informationFrom quantum fields to ecosystems
From quantum fields to ecosystems Dynamics on extended phasespaces P. D. Drummond ACQAO COE, University of Queensland Moyal medal lecture, 2007 Outline Exponential complexity 1 Exponential complexity
More informationQuantum Monte Carlo and the negative sign problem
Quantum Monte Carlo and the negative sign problem or how to earn one million dollar Matthias Troyer, ETH Zürich UweJens Wiese, Universität Bern Complexity of many particle problems Classical 1 particle:
More informationComputers in Science Education A new Way to teach Science?
Computers in Science Education A new Way to teach Science? Morten HjorthJensen 1,2 1 Department of Physics and Center of Mathematics for Applications, University of Oslo, Norway 2 Department of Physics
More informationTHEORETICAL PHYSICS @TCD
THEORETICAL PHYSICS @TCD 1 2 4 3 5 6 TR035 Theoretical Physics String Theory 1 Subatomic Collision at CERN 2 Magnetic Molecules Showing Opposite Spin States 3 Crystal Lattice 4 Foam Structure 5 Cosmic
More informationarxiv:condmat/9811359v1 [condmat.disnn] 25 Nov 1998
arxiv:condmat/9811359v1 [condmat.disnn] 25 Nov 1998 Energy Levels of Quasiperiodic Hamiltonians, Spectral Unfolding, and Random Matrix Theory M. Schreiber 1, U. Grimm, 1 R. A. Römer, 1 and J. X. Zhong
More informationAMPLIFICATION OF ATOMIC WAVES BY STIMULATED EMISSION OF ATOMS. Christian J. Borde
AMPLIFIATION OF ATOMI WAVES BY STIMULATED EMISSION OF ATOMS hristian J. Borde Laboratoire de Physique des Lasers, NRS/URA 8, Universite ParisNord, Villetaneuse, France. INTRODUTION: The recent development
More informationConcept 2. A. Description of lightmatter interaction B. Quantitatities in spectroscopy
Concept 2 A. Description of lightmatter interaction B. Quantitatities in spectroscopy Dipole approximation Rabi oscillations Einstein kinetics in twolevel system B. Absorption: quantitative description
More informationBlackbody Radiation References INTRODUCTION
Blackbody Radiation References 1) R.A. Serway, R.J. Beichner: Physics for Scientists and Engineers with Modern Physics, 5 th Edition, Vol. 2, Ch.40, Saunders College Publishing (A Division of Harcourt
More informationMASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCES IN PHYSICS (MS PHYS) (LIST OF COURSES BY SEMESTER, THESIS OPTION)
MASTER OF SCIENCE IN PHYSICS Admission Requirements 1. Possession of a BS degree from a reputable institution or, for nonphysics majors, a GPA of 2.5 or better in at least 15 units in the following advanced
More informationSIMPLE HARMONIC MOTION
SIMPLE HARMONIC MOTION PURPOSE The purpose of this experiment is to investigate one of the fundamental types of motion that exists in nature  simple harmonic motion. The importance of this kind of motion
More informationPower and Energy Characteristics of Continuous Waves / Pulsed CO 2 Laser Application in CNGDI Ignition
Proceedings of the th WSEAS International Conference on Applications of Electrical Engineering, Istanbul, Turkey, May 79, 7 17 Power and Energy Characteristics of Continuous Waves / Pulsed CO Laser Application
More informationNDSU Department of Physics. Graduate Student Handbook
NDSU Department of Physics Graduate Student Handbook Department of Physics North Dakota State University Fargo, ND 581086050 History Draft: August 24, 2014 Table of Contents 1. Contact 2 2. Graduate Program
More informationQUANTUM COMPUTATION AND MULTIPARTICLE ENTANGLEMENT WITH TRAPPED ATOMS AND IONS. Ph.D. Thesis Anders Søndberg Sørensen
QUANTUM COMPUTATION AND MULTIPARTICLE ENTANGLEMENT WITH TRAPPED ATOMS AND IONS Ph.D. Thesis Anders Søndberg Sørensen Institute of Physics and Astronomy University of Aarhus July 2001 ii Preface This thesis
More informationVortices and Solitons in Fermi Superfluids or rather: Our search for an easy, yet versatile way to describe them
Ultracold Quantum Gases Current Trends and Future Perspectives 616 th WE Heraus Seminar Bad Honnef, May 9 th 13 th 2016 Theory of Quantum and Complex systems Vortices and Solitons in Fermi Superfluids
More informationFundamentals of grain boundaries and grain boundary migration
1. Fundamentals of grain boundaries and grain boundary migration 1.1. Introduction The properties of crystalline metallic materials are determined by their deviation from a perfect crystal lattice, which
More informationLecture 3: Optical Properties of Bulk and Nano. 5 nm
Lecture 3: Optical Properties of Bulk and Nano 5 nm First H/W#1 is due Sept. 10 Course Info The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model)
More informationPHYSICS FOUNDATIONS SOCIETY THE DYNAMIC UNIVERSE TOWARD A UNIFIED PICTURE OF PHYSICAL REALITY TUOMO SUNTOLA
PHYSICS FOUNDATIONS SOCIETY THE DYNAMIC UNIVERSE TOWARD A UNIFIED PICTURE OF PHYSICAL REALITY TUOMO SUNTOLA Published by PHYSICS FOUNDATIONS SOCIETY Espoo, Finland www.physicsfoundations.org Printed by
More informationDamping in a variable mass on a spring pendulum
Damping in a variable mass on a spring pendulum Rafael M. Digilov, a M. Reiner, and Z. Weizman Department of Education in Technology and Science, TechnionIsrael Institute of Technology, Haifa 32000, Israel
More informationThomson and Rayleigh Scattering
Thomson and Rayleigh Scattering Initial questions: What produces the shapes of emission and absorption lines? What information can we get from them regarding the environment or other conditions? In this
More informationAnderson localization of a Majorana fermion
Anderson localization of a Majorana fermion Dmitri Ivanov1,2, Pavel Ostrovsky3,4, Mikhail Skvortsov4,5, and Yakov Fominov4,5 1 ETH Zürich 2 University of Zürich 3 Max Planck Institute, Stuttgart 4 Landau
More informationBackbone and elastic backbone of percolation clusters obtained by the new method of burning
J. Phys. A: Math. Gen. 17 (1984) L261L266. Printed in Great Britain LE ITER TO THE EDITOR Backbone and elastic backbone of percolation clusters obtained by the new method of burning H J HerrmanntS, D
More information develop a theory that describes the wave properties of particles correctly
Quantum Mechanics Bohr's model: BUT: In 192526: by 1930s:  one of the first ones to use idea of matter waves to solve a problem  gives good explanation of spectrum of single electron atoms, like hydrogen
More informationSpatial and temporal coherence of polariton condensates
Spatial and temporal coherence of polariton condensates R. Spano Dpt. Fisica de Materiales, Universidad Autónoma Madrid. SPAIN XIV JORNADA DE JÓVENES CIENTÍFICOS DEL INSTITUTO DE CIENCIA DE MATERIALES
More informationThe Physics Degree. Graduate Skills Base and the Core of Physics
The Physics Degree Graduate Skills Base and the Core of Physics Version date: September 2011 THE PHYSICS DEGREE This document details the skills and achievements that graduates of accredited degree programmes
More information1.5 Light absorption by solids
1.5 Light absorption by solids BlochBrilloin model L e + + + + + allowed energy bands band gaps p x In a unidimensional approximation, electrons in a solid experience a periodic potential due to the positively
More informationDarrick Chang ICFO The Institute of Photonic Sciences Barcelona, Spain. April 2, 2014
Darrick Chang ICFO The Institute of Photonic Sciences Barcelona, Spain April 2, 2014 ICFO The Institute of Photonic Sciences 10 minute walk 11 years old 22 Research Groups 300 people Research themes: Quantum
More informationPHYS 1624 University Physics I. PHYS 2644 University Physics II
PHYS 1624 Physics I An introduction to mechanics, heat, and wave motion. This is a calculus based course for Scientists and Engineers. 4 hours (3 lecture/3 lab) Prerequisites: Credit for MATH 2413 (Calculus
More informationOnline Courses for High School Students 18889726237
Online Courses for High School Students 18889726237 PHYSICS Course Description: This course provides a comprehensive survey of all key areas: physical systems, measurement, kinematics, dynamics, momentum,
More informationSUPERCONDUCTIVITY. PH 318 Introduction to superconductors 1
SUPERCONDUCTIVITY property of complete disappearance of electrical resistance in solids when they are cooled below a characteristic temperature. This temperature is called transition temperature or critical
More informationFLAP P11.2 The quantum harmonic oscillator
F L E X I B L E L E A R N I N G A P P R O A C H T O P H Y S I C S Module P. Opening items. Module introduction. Fast track questions.3 Ready to study? The harmonic oscillator. Classical description of
More informationStructure Factors 59553 78
78 Structure Factors Until now, we have only typically considered reflections arising from planes in a hypothetical lattice containing one atom in the asymmetric unit. In practice we will generally deal
More informationDO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS
DO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS Quantum Mechanics or wave mechanics is the best mathematical theory used today to describe and predict the behaviour of particles and waves.
More informationSpinor Bose gases lecture outline
Spinor Bose gases lecture outline 1. Basic properties 2. Magnetic order of spinor BoseEinstein condensates 3. Imaging spin textures 4. Spinmixing dynamics We re here 5. Magnetic excitations Citizens,
More informationSurprising pairing properties around the drip line and in the crust of neutron stars
Surprising pairing properties around the drip line and in the crust of neutron stars J. Margueron, IPN Lyon, France. I Superfluidity and neutron stars II Surprising features of superfluidity In collaboration
More informationDYNAMICS OF MOMENTUM DISTRIBUTIONS OF VACUUM EXCITATION IN FOCAL SPOT OF MODERN SUPERPOWER LASERS COUNTER BEAMS
DYNAMICS OF MOMENTUM DISTRIBUTIONS OF VACUUM EXCITATION IN FOCAL SPOT OF MODERN SUPERPOWER LASERS COUNTER BEAMS A.S. Dubinin Saratov State University, Russia S.A. Smolyansky, A.V. Prozorkevich, (Saratov
More informationBandwidth statistics from the eigenvalue moments for the Harper Hofstadter problem
J Phys A: Math Gen 33 (000) 6875 6888 Printed in the UK PII: S03054470(00)11389 Bandwidth statistics from the eigenvalue moments for the Harper Hofstadter problem O Lipan Division of Physics, Mathematics,
More informationHeat Transfer and Energy
What is Heat? Heat Transfer and Energy Heat is Energy in Transit. Recall the First law from Thermodynamics. U = Q  W What did we mean by all the terms? What is U? What is Q? What is W? What is Heat Transfer?
More informationLecture 3: Line broadening mechanisms in NMR
Lecture 3: Line broadening mechanisms in NMR Lecture aims to explain: 1. Fourier transform limit (or energytime uncertainty principle) 2. Resonance broadening due to interaction with neighbouring nuclei
More informationBoltzmann Distribution Law
Boltzmann Distribution Law The motion of molecules is extremely chaotic Any individual molecule is colliding with others at an enormous rate Typically at a rate of a billion times per second We introduce
More informationSimulation of collisional relaxation of trapped ion clouds in the presence of space charge fields
Simulation of collisional relaxation of trapped ion clouds in the presence of space charge fields J. H. Parks a) and A. Szöke Rowland Institute for Science, Cambridge, Massachusetts 14197 Received 1 January
More information