( ) Bose-Einstein condensates in fast rotation. Rotating condensates. Landau levels for a rotating gas. An interesting variant: the r 2 +r 4 potential
|
|
- Dayna Carpenter
- 6 years ago
- Views:
Transcription
1 Bose-instein condensates in fast otation Jean Dalibad Laboatoie Kastle Bossel cole nomale supéieue, Pais xp: Baptiste Battelie, Vincent Betin, Zoan Hadibabic, Sabine Stock Th: Amandine Aftalion, Xavie Blanc + many discussions with Yvan Castin, Sando Stingai, Goa Shlyapnikov Rotating condensates Rotation at angula fequency Ω Boulde: evapoative spin-up ; NS, MIT, Oxfod: stiing Abikosov lattice of votices nh vd. = Feynman, Onsage MIT M Rigid body otation v =Ω fo the coase-gain aveage of the velocity field if the votex suface density is: M Ω ρv = π Landau levels fo a otating gas An inteesting vaiant: the + 4 potential Isotopic hamonic tapping in the xy plane with fequency m=- Hamiltonian in the otating fame: m=- Ω= Ω < m= m= m= m= - - H ΩL When Ω~, one appoaches a situation with a macoscopically degeneate gound state fo the one-body hamiltonian Same physics as fo a chaged paticle in a magnetic field Ω Hamonic potential supeimposed with a small quatic tem (fomed using an additional lase beam popagating along the axis of otation): γ 4 = + in the xy plane ( = x + y ) V() m 4 Stiing fequency Ω of the gas: Ω Tapping + centifugal potential: ( ) γ m Ω Ω < Ω = Ω >
2 Coiolis vs. centifugal foces F = MΩ v Coiolis Fcentif. = MΩ p ( p A) H = + V( ) ΩL = + V( ) MΩ M M A = MΩ. Condensation tempeatue of an ideal otating gas Is the Coiolis foce significant fo fast otating gases?. Condensation tempeatue. quilibium shape of the condensate. Vibation modes of the condensate NO IT DPNDS YS two (little) miacles N = h Condensation theshold in the semi-classical appoximation d d p exp( (, p) / kt) ( p A) (, p) = + V ( ) MΩ M Semi-classical appoximation () Puely hamonic potential (Stingai 999): N =. ( kt / ) - Ω ( Ω ) expeimental check: Boulde Change of vaiables: ' p x = p x + MΩy ' p y = p y MΩx (Landau-Lifshit) Hamonic + quatic potential exactly at Ω = : γ V M M 4 4 () = + Ω γ 4 4 N = d d p' exp( (, p') / kt) p ' (, p') = + V ( ) MΩ M No effect of Coiolis foce Analogous to Boh- van Leeuven theoem: no classical magnetism 5/ M( kt) N =.9 γ Ae these esults compatible with a quantum desciption?
3 Calculation of T c with Landau levels (hamonic case) Calculation of T c with Landau levels ( + γ 4 /4) ' N = levels exp [( ) / kt] =Ω - - Ω 4 m If >> Ω, one can neglect the contibution of the levels with m < Same spectum as a D anisotopic oscillato: Ω,, kt >> ~ γ m 4M m Neglect the levels with m< Same spectum as a D system with: fee motion along diection with an effective mass M eff pop. to M /γ hamonic tap hamonic tap kt >> (class) N =. ( kt / ) ( Ω ) Ω Ω ( Ω) N = ( kt / ). ( Ω) 5/ (class) M( kt) N γ N 5/ Meff ( kt ) xpeimental esults in quadatic+quatic potential /π 65H = 5 atoms T = 5 nk. Ω: quilibium shape of a fast otating condensate Fo Ω=65-67 H, the votices become less and less visible: Not any moe a degeneate gas? T c = 6 nk Bending of the lines? Beakdown of mean-field appoximation? Phys. Rev. Lett. 9, 54 (4) D system: the motion is foen (gaussian of width a = /( m ) ) LLL physics, see also: Fische, Baym Watanabe, Baym, Pethick Komineas, Read, Coope xpeiments by the Boulde goup
4 Physics in the lowest Landau level Gound state in the LLL appoximation Ω /a e / ( x e a n + /a ( x+ e Geneal one-paticle state in the LLL: /a e P( x+ Polynomial o analytic function LLL If the chemical potential is much smalle than, the physics is esticted to the lowest Landau level /a = x + y a = / n j= m e ( u u ) u = x+ iy u j : votices j Minimiation of = + ho + ot + int = ψ int In the LLL: = Ω ψ ψ * ho = ψ ot [ L ] 4 = ψ g = 8 π as / a a s : scatteing length Minimiation of: = ho = + ot Λ =Ω+ ( Ω ) ψ + ψ only one paamete: 4 Ω = M = = LLL vs. centifugal foce appoximation ( = ) Minimiation of Thomas-Femi appoximation: Validity: ( Ω) Λ 4 ψ + ψ atom R ρ Ω R Λ /4 5 Centifugal foce appoximation: Ω D >> : Thomas-Femi egime, simila to LLL ψ + ψ + ψ ψ = µψ ( ) /4 << : Gaussian egime, with a width Ω >> R vey diffeent fom the LLL pediction
5 Physics in the lowest Landau level Gound state in the LLL appoximation Ω /a e / ( x e a n + /a ( x+ e Geneal one-paticle state in the LLL: /a e P( x+ Polynomial o analytic function LLL If the chemical potential is much smalle than, the physics is esticted to the lowest Landau level /a = x + y a = / n j= m e ( u u ) u = x+ iy u j : votices j Minimiation of = + ho + ot + int = ψ int In the LLL: = Ω ψ ψ * ho = ψ ot [ L ] 4 = ψ g = 8 π as / a a s : scatteing length Minimiation of: = ho = + ot Λ =Ω+ ( Ω ) ψ + ψ only one paamete: 4 Ω = M = = LLL vs. centifugal foce appoximation ( = ) LLL solution fo Minimiation of 4 ψ + ψ Thomas-Femi appoximation: Λ atom R ρ Ω R Λ /4 n /a j= ψ ( xy, ) = e ( u u) u = x+ iy j 5 Validity: ( Ω) Centifugal foce appoximation: Ω ψ + ψ + ψ ψ = µψ -5 D >> : Thomas-Femi egime, simila to LLL ( ) /4 << : Gaussian egime, with a width Ω >> R vey diffeent fom the LLL pediction atomic distibution Rb atoms, Ω=.99 / (π) = 5 H votex distibution stong distotion on the edges igid body otation (T.L. Ho)!
6 The tansvese monopole oscillation Fo a non otating gas in a hamonic tap, this "beathing mode" coespond to a scaling tansfom of the steady-state distibution. Beathing mode of a otating condensate monopole = Chevy et al, PRL 88, 54 () Guilleumas & Pitaevskii, Jackson et al, Kagan et al Pediction fo a otating gas in a hamonic tap (Coini & Stingai) = and not = Ω monopole xpeiment in a quadatic+ quatic tap.5..5 monopole monopole S. Stock et al, uophys. Lett. 65, 594 (4) Stiing fequency (H) The stuctue of the monopole mode Fo elatively low otation fequencies, usual beathing mode: 6 H Ω /.9 6 ms xcitation of the beathing mode of the fast otating condensate One pictue evey ms Ω /.4 Fo otation fequencies above the tap fequency, stange stuctue of the beathing mode Th: Stingai, Fette, Jackson
7 Conclusions The Coiolis foce plays no ole fo the value of the citical tempeatue of a otating gas, if kt but it is essential to calculate the shape and the modes of the BC Fo fast otations in the mean-field egime, the LLL basis povides a convenient fomalism: deviation fom igid-body otation + 4 : Mexican hat potentials and pesistent cuents Pespectives: Layeed otating supefluid calculation by I. Danaila Reach N votex ~N atomes : coelated states and Factional Quantum Hall effect
11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below.
Fall 2007 Qualifie Pat II 12 minute questions 11) A thin, unifom od of mass M is suppoted by two vetical stings, as shown below. Find the tension in the emaining sting immediately afte one of the stings
More informationPHYSICS 4E FINAL EXAM SPRING QUARTER 2010 PROF. HIRSCH JUNE 11 Formulas and constants: hc =12,400 ev A ; k B. = hf " #, # $ work function.
PHYSICS 4E FINAL EXAM SPRING QUARTER 1 Fomulas and constants: hc =1,4 ev A ; k B =1/11,6 ev/k ; ke =14.4eVA ; m e c =.511"1 6 ev ; m p /m e =1836 Relativistic enegy - momentum elation E = m c 4 + p c ;
More informationNuclear models: Shell model
Lectue 3 Nuclea models: Shell model WS0/3: Intoduction to Nuclea and Paticle Physics,, Pat I Nuclea models Nuclea models Models with stong inteaction between the nucleons Liquid dop model α-paticle model
More informationPreliminary Exam: Quantum Physics 1/14/2011, 9:00-3:00
Peliminay Exam: Quantum Physics /4/ 9:-: Answe a total of SIX questions of which at least TWO ae fom section A and at least THREE ae fom section B Fo you answes you can use eithe the blue books o individual
More informationVortex Lattice in a Rotating Bose-Einstein Condensate
Votex Lattice in a Rotating Bose-Einstein Condensate By: Enikı Madaassy A Bose-Einstein condensate (BEC) is a state of matte of a system of bosons confined in an extenal potential. The atoms ae cooled
More informationChem 453/544 Fall /08/03. Exam #1 Solutions
Chem 453/544 Fall 3 /8/3 Exam # Solutions. ( points) Use the genealized compessibility diagam povided on the last page to estimate ove what ange of pessues A at oom tempeatue confoms to the ideal gas law
More informationLocal Density Functional Theory for Superfluid Fermionic Systems. The Unitary Fermi Gas
Local Density unctional Theoy fo Supefluid emionic Systems The Unitay emi Gas Unitay emi gas in a hamonic tap Chang and Betsch, physics/070390 Outline: What is a unitay emi gas Vey bief/sewed summay of
More informationPhysical Chemistry II (Chapter 4 1) Rigid Rotor Models and Angular Momentum Eigenstates
Physical Chemisty II (Chapte 4 ) Rigid Roto Models and Angula Momentum Eigenstates Tae Kyu Kim Depatment of Chemisty Rm. 30 (tkkim@pusan.ac.k) http://cafe.nave.com/moneo76 SUMMAR CHAPTER 3 A simple QM
More informationChapter 6: Rotational and Rovibrational Spectra. A) General discussion of two- body problem with central potential
Fall 4 Chapte 6: Rotational and Rovibational Specta... 75 Diffeent Appoximations... 8 Spectum fo Hamonic Oscillato + Rigid Rotato... 8 Polyatomic Molecules... 84 Hamonic Oscillato + Rigid Roto Model to
More informationNuclear and Particle Physics - Lecture 20 The shell model
1 Intoduction Nuclea and Paticle Physics - Lectue 0 The shell model It is appaent that the semi-empiical mass fomula does a good job of descibing tends but not the non-smooth behaviou of the binding enegy.
More informationElectromagnetic scattering. Graduate Course Electrical Engineering (Communications) 1 st Semester, Sharif University of Technology
Electomagnetic scatteing Gaduate Couse Electical Engineeing (Communications) 1 st Semeste, 1390-1391 Shaif Univesity of Technology Geneal infomation Infomation about the instucto: Instucto: Behzad Rejaei
More informationGermán Sierra Instituto de Física Teórica CSIC-UAM, Madrid, Spain
Gemán Siea Instituto de Física Teóica CSIC-UAM, Madid, Spain Wo in pogess done in collaboation with J. Lins and S. Y. Zhao (Univ. Queensland, Austalia) and M. Ibañez (IFT, Madid) Taled pesented at the
More informationPhysics 221 Lecture 41 Nonlinear Absorption and Refraction
Physics 221 Lectue 41 Nonlinea Absoption and Refaction Refeences Meye-Aendt, pp. 97-98. Boyd, Nonlinea Optics, 1.4 Yaiv, Optical Waves in Cystals, p. 22 (Table of cystal symmeties) 1. Intoductoy Remaks.
More informationRydberg-Rydberg Interactions
Rydbeg-Rydbeg Inteactions F. Robicheaux Aubun Univesity Rydbeg gas goes to plasma Dipole blockade Coheent pocesses in fozen Rydbeg gases (expts) Theoetical investigation of an excitation hopping though
More information13. Adiabatic Invariants and Action-Angle Variables Michael Fowler
3 Adiabatic Invaiants and Action-Angle Vaiables Michael Fowle Adiabatic Invaiants Imagine a paticle in one dimension oscillating back and foth in some potential he potential doesn t have to be hamonic,
More informationQuantum vortices and competing orders
Talk online: Google Sachdev Quantum votices and competing odes cond-mat/0408329 and cond-mat/0409470 Leon Balents (UCSB) Loenz Batosch (Yale) Anton Bukov (UCSB) Subi Sachdev (Yale) Kishnendu Sengupta (Toonto)
More informationDEMONSTRATION OF INADEQUACY OF FFOWCS WILLIAMS AND HAWKINGS EQUATION OF AEROACOUSTICS BY THOUGHT EXPERIMENTS. Alex Zinoviev 1
ICSV14 Cains Austalia 9-12 July, 27 DEMONSTRATION OF INADEQUACY OF FFOWCS WILLIAMS AND HAWKINGS EQUATION OF AEROACOUSTICS BY THOUGHT EXPERIMENTS Alex Zinoviev 1 1 Defence Science and Technology Oganisation
More information, and the curve BC is symmetrical. Find also the horizontal force in x-direction on one side of the body. h C
Umeå Univesitet, Fysik 1 Vitaly Bychkov Pov i teknisk fysik, Fluid Dynamics (Stömningsläa), 2013-05-31, kl 9.00-15.00 jälpmedel: Students may use any book including the textbook Lectues on Fluid Dynamics.
More informationPendulum in Orbit. Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ (December 1, 2017)
1 Poblem Pendulum in Obit Kik T. McDonald Joseph Heny Laboatoies, Pinceton Univesity, Pinceton, NJ 08544 (Decembe 1, 2017) Discuss the fequency of small oscillations of a simple pendulum in obit, say,
More informationMultipole Radiation. February 29, The electromagnetic field of an isolated, oscillating source
Multipole Radiation Febuay 29, 26 The electomagnetic field of an isolated, oscillating souce Conside a localized, oscillating souce, located in othewise empty space. We know that the solution fo the vecto
More informationPROBLEM SET #1 SOLUTIONS by Robert A. DiStasio Jr.
POBLM S # SOLUIONS by obet A. DiStasio J. Q. he Bon-Oppenheime appoximation is the standad way of appoximating the gound state of a molecula system. Wite down the conditions that detemine the tonic and
More informationChapter 9. Spintransport in Semiconductors. Spinelektronik: Grundlagen und Anwendung spinabhängiger Transportphänomene 1
Chapte 9 Spintanspot in Semiconductos : Gundlagen und Anwendung spinabhängige Tanspotphänomene 1 Winte 05/06 Why ae semiconductos of inteest in spintonics? They povide a contol of the chage as in conventional
More informationLecture 24 Stability of Molecular Clouds
Lectue 4 Stability of Molecula Clouds 1. Stability of Cloud Coes. Collapse and Fagmentation of Clouds 3. Applying the iial Theoem Refeences Oigins of Stas & Planetay Systems eds. Lada & Kylafis http://cfa-www.havad.edu/cete
More informationyou of a spring. The potential energy for a spring is given by the parabola U( x)
Small oscillations The theoy of small oscillations is an extemely impotant topic in mechanics. Conside a system that has a potential enegy diagam as below: U B C A x Thee ae thee points of stable equilibium,
More informationis the instantaneous position vector of any grid point or fluid
Absolute inetial, elative inetial and non-inetial coodinates fo a moving but non-defoming contol volume Tao Xing, Pablo Caica, and Fed Sten bjective Deive and coelate the govening equations of motion in
More informationThree dimensional flow analysis in Axial Flow Compressors
1 Thee dimensional flow analysis in Axial Flow Compessos 2 The ealie assumption on blade flow theoies that the flow inside the axial flow compesso annulus is two dimensional means that adial movement of
More informationON THE TWO-BODY PROBLEM IN QUANTUM MECHANICS
ON THE TWO-BODY PROBLEM IN QUANTUM MECHANICS L. MICU Hoia Hulubei National Institute fo Physics and Nuclea Engineeing, P.O. Box MG-6, RO-0775 Buchaest-Maguele, Romania, E-mail: lmicu@theoy.nipne.o (Received
More informationLecture 7: Angular Momentum, Hydrogen Atom
Lectue 7: Angula Momentum, Hydogen Atom Vecto Quantization of Angula Momentum and Nomalization of 3D Rigid Roto wavefunctions Conside l, so L 2 2 2. Thus, we have L 2. Thee ae thee possibilities fo L z
More informationVibration Analysis of a Two-Dimensional Tire Cross-Section Model
Pudue Univesity Pudue e-pubs Publications of the Ray W. Heick Laboatoies School of Mechanical Engineeing 8-28-2017 Vibation Analysis of a Two-Dimensional Tie Coss-Section Model Rui Cao Pudue Univesity,
More informationThe second law of thermodynamics - II.
Januay 21, 2013 The second law of themodynamics - II. Asaf Pe e 1 1. The Schottky defect At absolute zeo tempeatue, the atoms of a solid ae odeed completely egulaly on a cystal lattice. As the tempeatue
More informationPlasmonics and non-local interactions from TDDFT: graphene and metal surfaces
Plasmonics and non-local inteactions fom TDDFT: gaphene and metal sufaces Thomas Olsen Cente fo Atomic-scale Mateials Design CAMD Depatment of Physics Technical Univesity of Denmak Outline Linea esponse
More informationAdiabatic evolution of the constants of motion in resonance (I)
Adiabatic evolution of the constants of motion in esonance (I) BH Gavitational 重 力力波 waves Takahio Tanaka (YITP, Kyoto univesity) R. Fujita, S. Isoyama, H. Nakano, N. Sago PTEP 013 (013) 6, 063E01 e-pint:
More informationANALYSIS OF QUANTUM EIGENSTATES IN A 3-MODE SYSTEM
AAYSIS OF QUATUM EIGESTATES I A 3-MODE SYSTEM SRIHARI KESHAVAMURTHY AD GREGORY S. EZRA Depatment of Chemisty, Bake aboatoy Conell Univesity, Ithaca, Y 14853, USA. Abstact. We study the quantum eigenstates
More informationME 425: Aerodynamics
ME 5: Aeodynamics D ABM Toufique Hasan Pofesso Depatment of Mechanical Engineeing, BUET Lectue- 8 Apil 7 teachebuetacbd/toufiquehasan/ toufiquehasan@mebuetacbd ME5: Aeodynamics (Jan 7) Flow ove a stationay
More informationLecture 1. 2D quantum gases: the static case. Low dimension quantum physics. Physics in Flatland. The 2D Bose gas:
Lecture 1 2D quantum gases: the static case Low dimension quantum physics Quantum wells and MOS structures Jean Dalibard, Laboratoire Kastler Brossel*, ENS Paris * Research unit of CNRS, ENS, and UPMC
More informationINFLUENCE OF GROUND INHOMOGENEITY ON WIND INDUCED GROUND VIBRATIONS. Abstract
INFLUENCE OF GROUND INHOMOGENEITY ON WIND INDUCED GROUND VIBRATIONS Mohammad Mohammadi, National Cente fo Physical Acoustics, Univesity of Mississippi, MS Caig J. Hicey, National Cente fo Physical Acoustics,
More informationParticle Physics. From Monday: Summary. Lecture 9: Quantum Chromodynamics (QCD) q 2 m 2 Z. !q q!q q scattering
Paticle Physics Lectue 9: Quantum Chomodynamics (QCD)!Colou chage and symmety!gluons!qcd Feynman Rules!! scatteing!jets! 1 Fom Monday: Summay Weak Neutal Cuent Caied by the massive Z-boson: acts on all
More informationClassical Mechanics Homework set 7, due Nov 8th: Solutions
Classical Mechanics Homewok set 7, due Nov 8th: Solutions 1. Do deivation 8.. It has been asked what effect does a total deivative as a function of q i, t have on the Hamiltonian. Thus, lets us begin with
More informationField emission of Electrons from Negatively Charged Cylindrical Particles with Nonlinear Screening in a Dusty Plasma
Reseach & Reviews: Jounal of Pue and Applied Physics Field emission of Electons fom Negatively Chaged Cylindical Paticles with Nonlinea Sceening in a Dusty Plasma Gyan Pakash* Amity School of Engineeing
More informationIntroduction to Nuclear Forces
Intoduction to Nuclea Foces One of the main poblems of nuclea physics is to find out the natue of nuclea foces. Nuclea foces diffe fom all othe known types of foces. They cannot be of electical oigin since
More informationarxiv: v1 [physics.gen-ph] 18 Aug 2018
Path integal and Sommefeld quantization axiv:1809.04416v1 [physics.gen-ph] 18 Aug 018 Mikoto Matsuda 1, and Takehisa Fujita, 1 Japan Health and Medical technological college, Tokyo, Japan College of Science
More informationQuantum Mechanics II
Quantum Mechanics II Pof. Bois Altshule Apil 25, 2 Lectue 25 We have been dicussing the analytic popeties of the S-matix element. Remembe the adial wave function was u kl () = R kl () e ik iπl/2 S l (k)e
More informationSupporting information
Electonic Supplementay Mateial (ESI) fo Physical Chemisty Chemical Physics. This jounal is the Owne Societies 18 Suppoting infomation Nonstoichiometic oxides as a continuous homologous seies: linea fee-enegy
More informationLecture 2: Basic plasma equations, self-focusing, direct laser acceleration
Lectue : Basic plasma equations, self-focusing, diect lase acceleation Pukhov, Meye-te-Vehn, PRL 76, 3975 (1996) plasma box (ne/nc=0.6) Lase 10 19 pulse W/cm B ~ mcωp/e ~ 108 Gauss Relat ivistic elect
More informationThe Unitary Fermi Gas
Local Density unctional Theoy fo Supefluid emionic Systems The Unitay emi Gas A. Bulgac, Univesity of Washington axiv:cond-mat/070356, PRA, R, in pess (007 Unitay emi gas in a hamonic tap Chang and Betsch,
More information5.111 Lecture Summary #6 Monday, September 15, 2014
5.111 Lectue Summay #6 Monday, Septembe 15, 014 Readings fo today: Section 1.9 Atomic Obitals. Section 1.10 Electon Spin, Section 1.11 The Electonic Stuctue of Hydogen. (Same sections in 4 th ed.) Read
More informationReview: Electrostatics and Magnetostatics
Review: Electostatics and Magnetostatics In the static egime, electomagnetic quantities do not vay as a function of time. We have two main cases: ELECTROSTATICS The electic chages do not change postion
More informationIntroduction to Arrays
Intoduction to Aays Page 1 Intoduction to Aays The antennas we have studied so fa have vey low diectivity / gain. While this is good fo boadcast applications (whee we want unifom coveage), thee ae cases
More informationTeoría del Funcional de la Densidad (Density Functional Theory)
Teoía del Funcional de la Densidad (Density Functional Theoy) Motivation: limitations of the standad appoach based on the wave function. The electonic density n() as the key vaiable: Functionals & Thomas-Femi
More informationHawking Radiation Seminar Talk
Hawking Radiation Semina Talk Julius Eckhad, Max Lautsch June 9, 205 In this talk on Hawking Radiation we will fist motivate why we have to intoduce the counteintuitive concept of a black hole tempeatue
More informationNuclear reactions of heavy ions
Autho: Facultat de Física, Univesitat de Bacelona, Diagonal 645, 08028 Bacelona, Spain. Adviso: Xavie Vinyes Abstact: In this wok nuclea eactions of heavy ions ae studied, focusing on elastic scatteing.
More informationCurrent Balance Warm Up
PHYSICS EXPERIMENTS 133 Cuent Balance-1 Cuent Balance Wam Up 1. Foce between cuent-caying wies Wie 1 has a length L (whee L is "long") and caies a cuent I 0. What is the magnitude of the magnetic field
More informationChapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
More information3. Electromagnetic Waves II
Lectue 3 - Electomagnetic Waves II 9 3. Electomagnetic Waves II Last time, we discussed the following. 1. The popagation of an EM wave though a macoscopic media: We discussed how the wave inteacts with
More informationDILUTE QUANTUM DROPLETS
DILUTE QUANTUM DROPLETS Auel Bulgac Phys. Rev. Lett. 89, 54 Quantum Fluids at T Liquid 4 He and He Electons but only embedded in an ion backgound BEC in alkali atoms and hydogen and the Femi-Diac countepats
More informationIntroduction to Dielectric Properties and Magnetism
Intoduction to Dielectic opeties and Magnetism At the end of the last lectue we looked at some of the electical popeties of matte and intoduces the notions of electic field and electical conductivity.
More informationElectromagnetic Waves
Chapte 32 Electomagnetic Waves PowePoint Lectues fo Univesity Physics, Twelfth Edition Hugh D. Young and Roge A. Feedman Lectues by James Pazun Modified P. Lam 8_11_2008 Topics fo Chapte 32 Maxwell s equations
More informationA new force Magnetic force. Today. Force Fields: A disturbance of space. The correspondence of a loop of current and magnet.
Today A new foce Magnetic foce Announcements HW#6 and HW#7 ae both due Wednesday Mach 18th. Thanks to my being WAY behind schedule, you 2nd exam will be a take-home exam! Stay tuned fo details Even if
More informationThe Apparent Mystery of the Electron:
The Appaent Mystey of the Electon: Thee is no mystey! The electon can be physically undestood! Since the middle of the 9s physicists have been stuggling to undestand the electon. om expeiments it was concluded
More informationResearch by Jack Sarfatti, San Francisco, 7/28/09, 2:02 PM, page 1 of 6
Reseach by Jack Safatti, San Fancisco, 7/8/09, :0 PM, page 1 of 6 Wheele-Feynman Genealized Bohm Quantum Potential fo Open Fa-Fom-Equilibium Biological Dissipative Stuctues with Non-Unitay Post-Quantum
More informationSupporting Information Wedge Dyakonov Waves and Dyakonov Plasmons in Topological Insulator Bi 2 Se 3 Probed by Electron Beams
Suppoting Infomation Wedge Dyakonov Waves and Dyakonov Plasmons in Topological Insulato Bi 2 Se 3 Pobed by Electon Beams Nahid Talebi, Cigdem Osoy-Keskinboa, Hadj M. Benia, Klaus Ken, Chistoph T. Koch,
More informationII. MRI Technology. B. Localized Information. Lorenz Mitschang Physikalisch-Technische Bundesanstalt, 29 th June 2009
Magnetic Resonance Imaging II. MRI Technology A. Limitations to patial Infomation B. Localized Infomation Loenz Mitschang Physikalisch-Technische Bundesanstalt, www.ptb.de 9 th June 009 A. Limitations
More informationarxiv:gr-qc/ v1 29 Jan 1998
Gavitational Analog of the Electomagnetic Poynting Vecto L.M. de Menezes 1 axiv:g-qc/9801095v1 29 Jan 1998 Dept. of Physics and Astonomy, Univesity of Victoia, Victoia, B.C. Canada V8W 3P6 Abstact The
More informationDepartment of Chemistry Chapter 4 continued
Chapte 4 continued Chial o not chial esponse functions otational aveages linea and nonlinea signals Undestanding this And maybe this Non-linea signal signal ( ( ( ( f E( tn sf... E( t2 q E( t 0q aveage
More informationσ = neμ = v D = E H, the Hall Field B Z E Y = ee y Determining n and μ: The Hall Effect V x, E x I, J x E y B z F = qe + qv B F y
Detemining n and μ: The Hall Effect V x, E x + + + + + + + + + + + --------- E y I, J x F = qe + qv B F y = ev D B z F y = ee y B z In steady state, E Y = v D B Z = E H, the Hall Field Since v D =-J x
More informationCHEM1101 Worksheet 3: The Energy Levels Of Electrons
CHEM1101 Woksheet 3: The Enegy Levels Of Electons Model 1: Two chaged Paticles Sepaated by a Distance Accoding to Coulomb, the potential enegy of two stationay paticles with chages q 1 and q 2 sepaated
More informationLecture 5 Solving Problems using Green s Theorem. 1. Show how Green s theorem can be used to solve general electrostatic problems 2.
Lectue 5 Solving Poblems using Geen s Theoem Today s topics. Show how Geen s theoem can be used to solve geneal electostatic poblems. Dielectics A well known application of Geen s theoem. Last time we
More informationRigid Body Dynamics 2. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018
Rigid Body Dynamics 2 CSE169: Compute Animation nstucto: Steve Rotenbeg UCSD, Winte 2018 Coss Poduct & Hat Opeato Deivative of a Rotating Vecto Let s say that vecto is otating aound the oigin, maintaining
More informationSuperfluid LDA (SLDA)
Supefluid LDA SLDA Local Density Appoximation / Kohn-Sham fo Systems with Supefluid Coelations Auel Bulgac Seattle and Yongle Yu Seattle Lund Slides will be posted shotly at http://www.phys.washington.edu/~bulgac/
More information1 Fundamental Solutions to the Wave Equation
1 Fundamental Solutions to the Wave Equation Physical insight in the sound geneation mechanism can be gained by consideing simple analytical solutions to the wave equation. One example is to conside acoustic
More informationLecture 2 Date:
Lectue 2 Date: 5.1.217 Definition of Some TL Paametes Examples of Tansmission Lines Tansmission Lines (contd.) Fo a lossless tansmission line the second ode diffeential equation fo phasos ae: LC 2 d I
More information20th Century Atomic Theory - Hydrogen Atom
0th Centuy Atomic Theoy - Hydogen Atom Ruthefod s scatteing expeiments (Section.5, pp. 53-55) in 1910 led to a nuclea model of the atom whee all the positive chage and most of the mass wee concentated
More informationThe Schrödinger Equation in Three Dimensions
The Schödinge Equation in Thee Dimensions Paticle in a Rigid Thee-Dimensional Box (Catesian Coodinates) To illustate the solution of the time-independent Schödinge equation (TISE) in thee dimensions, we
More informationPhysics 505 Homework No. 9 Solutions S9-1
Physics 505 Homewok No 9 s S9-1 1 As pomised, hee is the tick fo summing the matix elements fo the Stak effect fo the gound state of the hydogen atom Recall, we need to calculate the coection to the gound
More informationModal MAC Analysis vs. Sine Vibe A Case Study
Modal MAC Analysis vs. Sine Vibe A Case Study Bing C. Chen, Walte S. Tsuha and Chia-Yen Peng Jet Populsion Laboatoy Califonia Institute of Technology Mechanical Systems Engineeing, Fabication and Test
More informationPhysics 598 ESM Term Paper Giant vortices in rapidly rotating Bose-Einstein condensates
Physics 598 ESM Term Paper Giant vortices in rapidly rotating Bose-Einstein condensates Kuei Sun May 4, 2006 kueisun2@uiuc.edu Department of Physics, University of Illinois at Urbana- Champaign, 1110 W.
More informationMOLECULES BONDS. ENERGY LEVELS electronic vibrational rotational. P461 - Molecules 1
BONDS MOLECULES Ionic: closed shell (+) o open shell (-) Covalent: both open shells neutal ( shae e) Othe (skip): van de Waals (He- He) Hydogen bonds (in DNA, poteins, etc) ENERGY LEVELS electonic vibational
More informationc n ψ n (r)e ient/ h (2) where E n = 1 mc 2 α 2 Z 2 ψ(r) = c n ψ n (r) = c n = ψn(r)ψ(r)d 3 x e 2r/a0 1 πa e 3r/a0 r 2 dr c 1 2 = 2 9 /3 6 = 0.
Poblem {a} Fo t : Ψ(, t ψ(e iet/ h ( whee E mc α (α /7 ψ( e /a πa Hee we have used the gound state wavefunction fo Z. Fo t, Ψ(, t can be witten as a supeposition of Z hydogenic wavefunctions ψ n (: Ψ(,
More informationRole of the Mean Field in Bloch Oscillations of a Bose-Einstein Condensate in an Optical Lattice and Harmonic Trap
Role of the Mean Field in Bloch Oscillations of a Bose-Einstein Condensate in an Optical Lattice and Hamonic Tap R. Zhang, R. E. Sapio, R. R. Mhaska, G. Raithel FOCUS Cente, Depatment of Physics, Univesity
More information? this lecture. ? next lecture. What we have learned so far. a Q E F = q E a. F = q v B a. a Q in motion B. db/dt E. de/dt B.
PHY 249 Lectue Notes Chapte 32: Page 1 of 12 What we have leaned so fa a a F q a a in motion F q v a a d/ Ae thee othe "static" chages that can make -field? this lectue d/? next lectue da dl Cuve Cuve
More informationPhysics 506 Winter 2006 Homework Assignment #9 Solutions
Physics 506 Winte 2006 Homewok Assignment #9 Solutions Textbook poblems: Ch. 12: 12.2, 12.9, 12.13, 12.14 12.2 a) Show fom Hamilton s pinciple that Lagangians that diffe only by a total time deivative
More informationSection 11. Timescales Radiation transport in stars
Section 11 Timescales 11.1 Radiation tanspot in stas Deep inside stas the adiation eld is vey close to black body. Fo a black-body distibution the photon numbe density at tempeatue T is given by n = 2
More informationPROBLEM SET #3A. A = Ω 2r 2 2 Ω 1r 2 1 r2 2 r2 1
PROBLEM SET #3A AST242 Figue 1. Two concentic co-axial cylindes each otating at a diffeent angula otation ate. A viscous fluid lies between the two cylindes. 1. Couette Flow A viscous fluid lies in the
More informationPhysics 2020, Spring 2005 Lab 5 page 1 of 8. Lab 5. Magnetism
Physics 2020, Sping 2005 Lab 5 page 1 of 8 Lab 5. Magnetism PART I: INTRODUCTION TO MAGNETS This week we will begin wok with magnets and the foces that they poduce. By now you ae an expet on setting up
More informationCoarse Mesh Radiation Transport Code COMET Radiation Therapy Application*
Coase Mesh Radiation Tanspot Code COMT Radiation Theapy Application* Fazad Rahnema Nuclea & Radiological ngineeing and Medical Physics Pogams Geogia Institute of Technology Computational Medical Physics
More informationPhysics 121 Hour Exam #5 Solution
Physics 2 Hou xam # Solution This exam consists of a five poblems on five pages. Point values ae given with each poblem. They add up to 99 points; you will get fee point to make a total of. In any given
More informationEnd-to-end statistical model for maximum expected vibration response under aero-acoustic loading
End-to-end statistical model fo maximum expected vibation esponse unde aeo-acoustic loading Paul Bemne 1 Outline Motivation Vaiation in flight test data Ensemble Mean vibation esponse Ensemble Vaiance
More informationChapter 7-8 Rotational Motion
Chapte 7-8 Rotational Motion What is a Rigid Body? Rotational Kinematics Angula Velocity ω and Acceleation α Unifom Rotational Motion: Kinematics Unifom Cicula Motion: Kinematics and Dynamics The Toque,
More informationMolecular dynamics simulation of ultrafast laser ablation of fused silica
IOP Publishing Jounal of Physics: Confeence Seies 59 (27) 1 14 doi:1.188/1742-6596/59/1/22 Eighth Intenational Confeence on Lase Ablation Molecula dynamics simulation of ultafast lase ablation of fused
More informationby numerous studies); ii) MSWT spectrum is symmetric with respect to point while numerical methods give asymmetrical spectrum with gap = = 2.
SPIN-WAVE THEORY FOR S= ANTIFERROMAGNETIC ISOTROPIC CHAIN D. V. Spiin V.I. Venadsii Tauida National Univesity, Yaltinsaya st. 4, Simfeopol, 957, Cimea, Uaine E-mail: spiin@cimea.edu, spiin@tnu.cimea.ua
More informationFrom a few to many electrons in quantum dots under strong magnetic fields: Properties of rotating electron molecules with multiple rings
Fom a few to many electons in quantum dots unde stong magnetic fields: Popeties of otating electon molecules with multiple ings Yuesong Li, Constantine Yannouleas, and Uzi Landman School of Physics, Geogia
More informationQUASI-STATIONARY ELECTRON STATES IN SPHERICAL ANTI-DOT WITH DONOR IMPURITY * 1. INTRODUCTION
ATOMIC PHYSICS QUASI-STATIONARY ELECTRON STATES IN SPHERICAL ANTI-DOT ITH DONOR IMPURITY * V. HOLOVATSKY, O. MAKHANETS, I. FRANKIV Chenivtsi National Univesity, Chenivtsi, 581, Ukaine, E-mail: ktf@chnu.edu.ua
More informationDiffusion and Transport. 10. Friction and the Langevin Equation. Langevin Equation. f d. f ext. f () t f () t. Then Newton s second law is ma f f f t.
Diffusion and Tanspot 10. Fiction and the Langevin Equation Now let s elate the phenomena of ownian motion and diffusion to the concept of fiction, i.e., the esistance to movement that the paticle in the
More informationModeling Fermi Level Effects in Atomistic Simulations
Mat. Res. Soc. Symp. Poc. Vol. 717 Mateials Reseach Society Modeling Femi Level Effects in Atomistic Simulations Zudian Qin and Scott T. Dunham Depatment of Electical Engineeing, Univesity of Washington,
More information1) Consider an object of a parabolic shape with rotational symmetry z
Umeå Univesitet, Fysik 1 Vitaly Bychkov Pov i teknisk fysik, Fluid Mechanics (Stömningsläa), 01-06-01, kl 9.00-15.00 jälpmedel: Students may use any book including the tetbook Lectues on Fluid Dynamics.
More information2 Lecture 2: The Bohr atom (1913) and the Schrödinger equation (1925)
1 Lectue 1: The beginnings of quantum physics 1. The Sten-Gelach expeiment. Atomic clocks 3. Planck 1900, blackbody adiation, and E ω 4. Photoelectic effect 5. Electon diffaction though cystals, de Boglie
More informationGeometry and statistics in turbulence
Geomety and statistics in tubulence Auoe Naso, Univesity of Twente, Misha Chetkov, Los Alamos, Bois Shaiman, Santa Babaa, Alain Pumi, Nice. Tubulent fluctuations obey a complex dynamics, involving subtle
More informationGeneralized functions and statistical problems of. orbital mechanics
Genealized functions and statistical poblems of obital mechanics Meshcheyakov TSNIIMASH OSKOSMOS 4// 8th US/ussian Space Suveillance Wokshop, Intoduction Thee is discussed a new method fo solution of statistical
More informationNovel Orbital Phases of Fermions in p-band Optical Lattices
Novel Obital Phases of Femions in p-band Optical Lattices Congjun Wu Depatment of Physics, UC San Diego W. C. Lee, C. Wu, S. Das Sama, in pepaation. C. Wu, PRL 0, 68807 008. C. Wu, PRL 00, 00406 008. C.
More informationHyperfine Interactions
Hypefine Inteactions Inteaction between the electomagnetic moments of a nucleus and electomagnetic fields acting on the nucleus e- μ, Q, I I nuclea spin µ magn. dipole moment Q electic quadupole moment
More information