Introduction to Green s functions


 Edmund Dennis
 1 years ago
 Views:
Transcription
1 Introduction to Green s functions Matteo Gatti ETSF Users Meeting and Training Day Ecole Polytechnique  22 October 2010
2 Outline 1 Motivation 2 Green s functions 3 The GW Approximation 4 The BetheSalpeter Equation
3 Outline 1 Motivation 2 Green s functions 3 The GW Approximation 4 The BetheSalpeter Equation
4 Electronic Spectroscopy Here only two categories: 1 charged excitations: photoemission and inverse photoemission 2 neutral excitations: absorption and electron energy loss
5 Why do we have to study more than DFT? adapted from M. van Schilfgaarde et al., PRL 96 (2006).
6 MBPT vs. TDDFT: different worlds, same physics (TD)DFT based on the density response function χ: neutral excitations moves density around is efficient (simple) MBPT based on Green s functions oneparticle G: electron addition and removal  GW twoparticle L: electronhole excitation  BSE moves (quasi)particles around is intuitive (easy)
7 Table of characters Density: local in space and time ρ(r 1, t 1 ) Density matrix: nonlocal in space γ(r 1, r 2, t) Oneparticle Green s function: nonlocal in space and time: G(r 1, r 2, t 1, t 2 ) G(1, 2) G(r 1, r 2, t 1, t 2 ) G(r 1, r 2, t 1, t 2 ) = G(r 1, r 2, t 1 t 2 ) G(r 1, r 2, ω) ρ(r 1, t 1 ) = ig(r 1, r 1, t 1, t + 1 )
8 Table of characters Density: local in space and time ρ(r 1, t 1 ) Density matrix: nonlocal in space γ(r 1, r 2, t) Oneparticle Green s function: nonlocal in space and time: G(r 1, r 2, t 1, t 2 ) G(1, 2) G(r 1, r 2, t 1, t 2 ) G(r 1, r 2, t 1, t 2 ) = G(r 1, r 2, t 1 t 2 ) G(r 1, r 2, ω) ρ(r 1, t 1 ) = ig(r 1, r 1, t 1, t + 1 )
9 Outline 1 Motivation 2 Green s functions 3 The GW Approximation 4 The BetheSalpeter Equation
10 Photoemission Direct Photoemission Inverse Photoemission
11 Oneparticle Green s function The oneparticle Green s function G Definition and meaning of G: ig(r 1, t 1 ; r 2, t 2 ) = N T [ ψ(r 1, t 1 )ψ (r 2, t 2 ) ] N for t 1 > t 2 ig(r 1, t 1 ; r 2, t 2 ) = N ψ(r 1, t 1 )ψ (r 2, t 2 ) N (1) for t 1 < t 2 ig(r 1, t 1 ; r 2, t 2 ) = N ψ (r 2, t 2 )ψ(r 1, t 1 ) N (2)
12 Oneparticle Green s function The oneparticle Green s function G Definition and meaning of G: ig(r 1, t 1 ; r 2, t 2 ) = N T [ ψ(r 1, t 1 )ψ (r 2, t 2 ) ] N for t 1 > t 2 ig(r 1, t 1 ; r 2, t 2 ) = N ψ(r 1, t 1 )ψ (r 2, t 2 ) N (1) for t 1 < t 2 ig(r 1, t 1 ; r 2, t 2 ) = N ψ (r 2, t 2 )ψ(r 1, t 1 ) N (2)
13 Oneparticle Green s function t 1 > t 2 N ψ(r 1, t 1 )ψ (r 2, t 2 ) N t 1 < t 2 N ψ (r 2, t 2 )ψ(r 1, t 1 ) N
14 Oneparticle Green s function What is G? Definition and meaning of G: h i G(r 1, t 1 ; r 2, t 2 ) = i < N T ψ(r 1, t 1 )ψ (r 2, t 2 ) N > Insert a complete set of N + 1 or N 1particle states. This yields G(r 1, t 1 ; r 2, t 2 ) = i X j f j (r 1 )f j (r 2 )e iε j (t 1 t 2 ) [θ(t 1 t 2 )θ(ε j µ) θ(t 2 t 1 )Θ(µ ε j )]; where: ε j = E(N + 1, j) E(N), ε j > µ E(N) E(N 1, j), ε j < µ f j (r 1 ) = N ψ (r 1) N + 1, j, ε j > µ N 1, j ψ (r 1 ) N, ε j < µ
15 Oneparticle Green s function What is G?  Fourier transform G(x, x, ω) = j Fourier Transform: f j (x)f j (x ) ω ε j + iηsgn(ε j µ). Spectral function: A(x, x ; ω) = 1 π ImG(x, x ; ω) = j f j (x)f j (x )δ(ω ε j ).
16 Photoemission Direct Photoemission Inverse Photoemission Oneparticle excitations poles of oneparticle Green s function G
17 Oneparticle Green s function Oneparticle Green s function From oneparticle G we can obtain: oneparticle excitation spectra groundstate expectation value of any oneparticle operator: e.g. density ρ or density matrix γ: ρ(r, t) = ig(r, r, t, t + ) γ(r, r, t) = ig(r, r, t, t + ) groundstate total energy
18 Absorption Twoparticle excitations poles of twoparticle Green s function L Excitonic effects = electron  hole interaction
19 Absorption Twoparticle excitations poles of twoparticle Green s function L Excitonic effects = electron  hole interaction
20 Absorption Twoparticle excitations poles of twoparticle Green s function L Excitonic effects = electron  hole interaction
21 Table of characters G(1, 2): oneparticle Green s function (2 points) L(1, 2, 3, 4): twoparticle Green s function (4 points)
22 Outline 1 Motivation 2 Green s functions 3 The GW Approximation 4 The BetheSalpeter Equation
23 GW bandstructure: photoemission additional charge
24 GW bandstructure: photoemission additional charge reaction: polarization, screening GW approximation 1 polarization made of noninteracting electronhole pairs (RPA) 2 classical (Hartree) interaction between additional charge and polarization charge L. Hedin, Phys. Rev. 139 (1965)
25 GW and HartreeFock
26 GW and HartreeFock
27 GW and HartreeFock HartreeFock GW Σ(12) = ig(12)v(1 + 2) Σ(12) = ig(12)w (1 + 2) v infinite range in space v is static Σ is nonlocal, hermitian, static W is short ranged W is dynamical Σ is nonlocal, complex, dynamical
28 GW and HartreeFock from Brice Arnaud
29 GW and HartreeFock M. van Schilfgaarde et al., PRL 96 (2006).
30 Outline 1 Motivation 2 Green s functions 3 The GW Approximation 4 The BetheSalpeter Equation
31 Independent (quasi)particles: GW Independent transitions: ɛ 2 (ω) = 8π2 X ϕ Ωω 2 j e v ϕ i 2 δ(e j E i ω) ij
32 What is wrong? What is missing?
33 Beyond RPA Independent particles (RPA)
34 Beyond RPA Interacting particles (excitonic effects)
35 Absorption spectra in BSE Independent (quasi)particles Abs(ω) vc v D c 2 δ(e c E v ω) Excitonic effects: the BetheSalpeter equation [H el + H hole +H el hole ]A λ = E λ A λ Abs(ω) λ vc A (vc) λ v D c 2 δ(e λ ω) mixing of transitions: v D c 2 vc A(vc) λ v D c 2 modification of excitation energies: E c E v E λ
36 Absorption spectra in BSE Bulk silicon G. Onida, L. Reining, and A. Rubio, RMP 74 (2002).
37 Bound excitons Solid argon F. Sottile, M. Marsili, V. Olevano, and L. Reining, PRB 76 (2007).
38 Exciton analysis Exciton amplitude: Ψ λ (r h, r e ) = vc A (vc) λ φ v(r h )φ c (r e ) Graphene nanoribbon Manganese Oxide D. Prezzi, et al., PRB 77 (2008). C. Rödl, et al., PRB 77 (2008).
39 Electronic Spectroscopy Here only two categories: 1 charged excitations: photoemission and inverse photoemission = GW 2 neutral excitations: absorption and electron energy loss = BSE
Introduction to manybody Green s functions
Introduction to manybody Green s functions Matteo Gatti European Theoretical Spectroscopy Facility (ETSF) NanoBio Spectroscopy Group  UPV San Sebastián  Spain matteo.gatti@ehu.es  http://nanobio.ehu.es
More informationOptical Properties of Solids. Claudia AmbroschDraxl Chair of Atomistic Modelling and Design of Materials University Leoben, Austria
Optical Properties of Solids Claudia AmbroschDraxl Chair of Atomistic Modelling and Design of Materials University Leoben, Austria Outline Basics Program Examples Outlook light scattering dielectric tensor
More informationTheoretical approaches to the abinitio study of complex systems
Theoretical approaches to the abinitio study of complex systems Olivia Pulci European Theoretical Spectroscopy Facilty (ETSF), and CNRINFM, Dipartimento di Fisica Università di Roma Tor Vergata NASTISM
More informationChapter 2. Theoretical framework
Theoretical framework For studying the properties of thin films and surfaces on the atomic scale a wealth of experimental techniques is available. For brevity, we will introduce only those that will be
More informationarxiv:1006.4085v1 [condmat.mtrlsci] 21 Jun 2010
Quasiparticle and Optical Properties of Rutile and Anatase TiO 2 Wei Kang and Mark S. Hybertsen Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973 (Dated: June 22, 21)
More informationElectronic Structure Methods. by Daniel Rohr Vrije Universiteit Amsterdam
Electronic Structure Methods by Daniel Rohr Vrije Universiteit Amsterdam drohr@few.vu.nl References WFT Szaboo & Ostlund Modern Quantum Chemistry Helgaker, Jørgensen & Olsen Molecular ElectronicStructure
More informationfotoelektronspektroszkópia Rakyta Péter
Spinpálya kölcsönhatás grafénben, fotoelektronspektroszkópia Rakyta Péter EÖTVÖS LORÁND TUDOMÁNYEGYETEM, KOMPLEX RENDSZEREK FIZIKÁJA TANSZÉK 1 Introduction to graphene Sp 2 hybridization p z orbitals
More informationPCV Project: Excitons in Molecular Spectroscopy
PCV Project: Excitons in Molecular Spectroscopy Introduction The concept of excitons was first introduced by Frenkel (1) in 1931 as a general excitation delocalization mechanism to account for the ability
More informationThe electronic and optical properties of conjugated polymers:
The electronic and optical properties of conjugated polymers: predictions from firstprinciples solidstate methods PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven,
More informationChapter 9 Unitary Groups and SU(N)
Chapter 9 Unitary Groups and SU(N) The irreducible representations of SO(3) are appropriate for describing the degeneracies of states of quantum mechanical systems which have rotational symmetry in three
More informationUniversità degli Studi Roma TRE. Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia
Università degli Studi Roma TRE e Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia Dottorato di Ricerca in Scienze Fisiche della Materia XXIII ciclo Challenges for first principles
More informationExciton dissociation in solar cells:
Exciton dissociation in solar cells: Xiaoyang Zhu Department of Chemistry University of Minnesota, Minneapolis t (fs) 3h! E, k h! Pc Bi e  1 Acknowledgement Organic semiconductors: Mutthias Muntwiler,
More informationQuick and Dirty Introduction to Mott Insulators
Quick and Dirty Introduction to Mott Insulators Branislav K. Nikolić Department of Physics and Astronomy, University of Delaware, U.S.A. PHYS 64: Introduction to Solid State Physics http://www.physics.udel.edu/~bnikolic/teaching/phys64/phys64.html
More informationApplied Physics of solar energy conversion
Applied Physics of solar energy conversion Conventional solar cells, and how lazy thinking can slow you down Some new ideas *************************************************************** Our work on semiconductor
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 informationSolid State Detectors = SemiConductor based Detectors
Solid State Detectors = SemiConductor based Detectors Materials and their properties Energy bands and electronic structure Charge transport and conductivity Boundaries: the pn junction Charge collection
More informationarxiv:1404.1715v1 [condmat.mtrlsci] 7 Apr 2014
Fully selfconsistent GW and quasiparticle selfconsistent GW for molecules arxiv:144.1715v1 [condmat.mtrlsci] 7 Apr 214 P. Koval, 1, 2, D. Foerster, 3, 1, 2, and D. SánchezPortal 1 Centro de Física
More informationBroadband THz Generation from Photoconductive Antenna
Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 2226 331 Broadband THz Generation from Photoconductive Antenna Qing Chang 1, Dongxiao Yang 1,2, and Liang Wang 1 1 Zhejiang
More informationGroup Theory and Chemistry
Group Theory and Chemistry Outline: Raman and infrared spectroscopy Symmetry operations Point Groups and Schoenflies symbols Function space and matrix representation Reducible and irreducible representation
More informationElectric Dipole moments as probes of physics beyond the Standard Model
Electric Dipole moments as probes of physics beyond the Standard Model K. V. P. Latha NonAccelerator Particle Physics Group Indian Institute of Astrophysics Plan of the Talk Parity (P) and Timereversal
More informationg 0 = 3 ev Linear a = 0.246nm. constant velocity g 0 ~ 3 ev 0.334nm Interlayer g 1 ~ 0.4 ev Massive Effective mass: Graphene monolayerbilayer junction Theoretical studies Nakanishi, Koshino, Ando, PRB
More informationWhat is molecular dynamics (MD) simulation and how does it work?
What is molecular dynamics (MD) simulation and how does it work? A lecture for CHM425/525 Fall 2011 The underlying physical laws necessary for the mathematical theory of a large part of physics and the
More informationQuantum Effects and Dynamics in HydrogenBonded Systems: A FirstPrinciples Approach to Spectroscopic Experiments
Quantum Effects and Dynamics in HydrogenBonded Systems: A FirstPrinciples Approach to Spectroscopic Experiments Dissertation zur Erlangung des Grades Doktor der Naturwissenschaften am Fachbereich Physik
More informationL5. P1. Lecture 5. Solids. The free electron gas
Lecture 5 Page 1 Lecture 5 L5. P1 Solids The free electron gas In a solid state, a few loosely bound valence (outermost and not in completely filled shells) elections become detached from atoms and move
More informationChemistry 102 Summary June 24 th. Properties of Light
Chemistry 102 Summary June 24 th Properties of Light  Energy travels through space in the form of electromagnetic radiation (EMR).  Examples of types of EMR: radio waves, xrays, microwaves, visible
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 informationSpatially separated excitons in 2D and 1D
Spatially separated excitons in 2D and 1D David Abergel March 10th, 2015 D.S.L. Abergel 3/10/15 1 / 24 Outline 1 Introduction 2 Spatially separated excitons in 2D The role of disorder 3 Spatially separated
More informationHard Condensed Matter WZI
Hard Condensed Matter WZI Tom Gregorkiewicz University of Amsterdam VULaserLab Dec 10, 2015 Hard Condensed Matter Cluster Quantum Matter Optoelectronic Materials Quantum Matter Amsterdam Mark Golden Anne
More informationHydrogen Bonds in WaterMethanol Mixture
Bulg. J. Phys. 34 (2007) 103 107 Hydrogen Bonds in WaterMethanol Mixture G.M. Georgiev, K. Vasilev, K. Gyamchev Faculty of Physics, University of Sofia 5J.Bourchier Blvd., 1164 Sofia, Bulgaria Received
More informationExcitons Types, Energy Transfer
Excitons Types, Energy Transfer Wannier exciton Chargetransfer exciton Frenkel exciton Exciton Diffusion Exciton Energy Transfer (Förster, Dexter) Handout (for Recitation Discusssion): J.S. Yang and
More informationNMR SPECTROSCOPY. Basic Principles, Concepts, and Applications in Chemistry. Harald Günther University of Siegen, Siegen, Germany.
NMR SPECTROSCOPY Basic Principles, Concepts, and Applications in Chemistry Harald Günther University of Siegen, Siegen, Germany Second Edition Translated by Harald Günther JOHN WILEY & SONS Chichester
More informationNew magnetism of 3d monolayers grown with oxygen surfactant: Experiment vs. ab initio calculations
New magnetism of 3d monolayers grown with oxygen surfactant: Experiment vs. ab initio calculations 1. Growth and structure 2. Magnetism and MAE 3. Induced magnetism at oxygen Klaus Baberschke Institut
More informationProf. Olivia Pulci Curriculum Vitae
Prof. Olivia Pulci Curriculum Vitae Personal Data: Name: Pulci, Olivia Birth: Civitavecchia (Italy), March 3, 1966 Languages: Italian (mother tongue), English (fluent), German (basic knowledge) Private
More informationMaterials Design and Discovery, and the Challenges of the Materials Genome Nicola Marzari, EPFL
Materials Design and Discovery, and the Challenges of the Materials Genome Nicola Marzari, EPFL The good news: Europe at the forefront in codes for materials simula@ons To name just a few: Quantum ESPRESSO
More informationLecture 2 Semiconductor Physics (I)
Lecture 2 Semiconductor Physics (I) Outline Intrinsic bond model : electrons and holes Generation and recombination Intrinsic semiconductor Doping: Extrinsic semiconductor Charge Neutrality Reading Assignment:
More informationhttp://www.guido.be/intranet/enqueteoverview/tabid/152/ctl/eresults...
1 van 70 20/03/2014 11:55 EnqueteDescription 2 van 70 20/03/2014 11:55 3 van 70 20/03/2014 11:55 4 van 70 20/03/2014 11:55 5 van 70 20/03/2014 11:55 6 van 70 20/03/2014 11:55 7 van 70 20/03/2014 11:55
More informationAnalysis of Riboflavin in a Vitamin Pill by Fluorescence Spectroscopy**
Analysis of Riboflavin in a Vitamin Pill by Fluorescence Spectroscopy** Objectives In this lab, you will use fluorescence spectroscopy to determine the mass and percentage of riboflavin in a vitamin pill.
More informationChapter 8 Molecules. Some molecular bonds involve sharing of electrons between atoms. These are covalent bonds.
Chapter 8 Molecules (We have only three days for chapter 8!) 8.1 The Molecular Bond A molecule is an electrically neutral group of atoms held together strongly enough to behave as a single particle. A
More informationApplications of XRay Absorption Spectroscopy
Applications of XRay Absorption Spectroscopy Bruce Ravel The Naval Research Laboratory ravel@phys.washington.edu http://feff.phys.washington.edu/~ravel/ Version 0.01 5 March, 2001 Abstract This document
More informationAnalysis of Riboflavin in a Vitamin Pill by Fluorescence Spectroscopy
Analysis of Riboflavin in a Vitamin Pill by Fluorescence Spectroscopy Objectives In this lab, you will use fluorescence spectroscopy to determine the mass of riboflavin in a vitamin pill. Riboflavin fluorescence
More informationXray photoelectron spectroscopy  An introduction
1 Xray photoelectron spectroscopy  An introduction Spyros Diplas MENA3100 SINTEF Materials & Chemistry, Department of Materials Physics & Centre of Materials Science and Nanotechnology, Department of
More informationElectronic Structure and Transition Intensities in RareEarth Materials
Electronic Structure and Transition Intensities in RareEarth Materials Michael F Reid Department of Physics and Astronomy and MacDiarmid Institute for Advanced Materials and Nanotechnology University
More informationPHY4604 Introduction to Quantum Mechanics Fall 2004 Practice Test 3 November 22, 2004
PHY464 Introduction to Quantum Mechanics Fall 4 Practice Test 3 November, 4 These problems are similar but not identical to the actual test. One or two parts will actually show up.. Short answer. (a) Recall
More informationPoS(Baldin ISHEPP XXII)026
On the modified Yamaguchitype functions for the BetheSalpeter equation Joint Institute for Nuclear Research, Dubna, Russia Email: bondarenko@jinr.ru V. V. Burov Joint Institute for Nuclear Research,
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 information= N 2 = 3π2 n = k 3 F. The kinetic energy of the uniform system is given by: 4πk 2 dk h2 k 2 2m. (2π) 3 0
Chapter 1 ThomasFermi Theory The ThomasFermi theory provides a functional form for the kinetic energy of a noninteracting electron gas in some known external potential V (r) (usually due to impurities)
More informationMolecular Spectroscopy
Molecular Spectroscopy UVVis Spectroscopy Absorption Characteristics of Some Common Chromophores UVVis Spectroscopy Absorption Characteristics of Aromatic Compounds UVVis Spectroscopy Effect of extended
More informationBasic techniques and tools for the development and maintenance of atomicscale software : the context
CECAM Lyon February 2008 Basic techniques and tools for the development and maintenance of atomicscale software : the context X. Gonze Université Catholique de Louvain CECAM 2008 Developer School : The
More informationApplication of Fourier Transform to PDE (I) Fourier Sine Transform (application to PDEs defined on a semiinfinite domain)
Application of Fourier Transform to PDE (I) Fourier Sine Transform (application to PDEs defined on a semiinfinite domain) The Fourier Sine Transform pair are F. T. : U = 2/ u x sin x dx, denoted as U
More informationQuestion 2: How do you solve a matrix equation using the matrix inverse?
Question : How do you solve a matrix equation using the matrix inverse? In the previous question, we wrote systems of equations as a matrix equation AX B. In this format, the matrix A contains the coefficients
More informationThree Pictures of Quantum Mechanics. Thomas R. Shafer April 17, 2009
Three Pictures of Quantum Mechanics Thomas R. Shafer April 17, 2009 Outline of the Talk Brief review of (or introduction to) quantum mechanics. 3 different viewpoints on calculation. Schrödinger, Heisenberg,
More informationION ENERGY DISTRIBUTION FUNCTION MEASURED BY RETARDING FIELD ENERGY ANALYZERS
ION ENERGY DISTRIBUTION FUNCTION MEASURED BY RETARDING FIELD ENERGY ANALYZERS Laboratoire de Physique des Plasmas Ane Aanesland CNRS Ecole Polytechnique France Overview 1. Principle and requirements for
More informationThermal transport in the anisotropic Heisenberg chain with S = 1/2 and nearestneighbor interactions
Thermal transport in the anisotropic Heisenberg chain with S = 1/2 and nearestneighbor interactions D. L. Huber Department of Physics, University of WisconsinMadison, Madison, WI 53706 Abstract The purpose
More informationarxiv:1512.02410v1 [condmat.meshall] 8 Dec 2015
Corelevel spectra from bilayer graphene Bo E. Sernelius Division of Theory and Modeling, Department of Physics, Chemistry and Biology, Linköping University, SE58 83 Linköping, Sweden arxiv:5.4v condmat.meshall
More informationChemical Synthesis. Overview. Chemical Synthesis of Nanocrystals. SelfAssembly of Nanocrystals. Example: Cu 146 Se 73 (PPh 3 ) 30
Chemical Synthesis Spontaneous organization of molecules into stable, structurally welldefined aggregates at the nanometer length scale. Overview The 1100 nm nanoscale length is in between traditional
More information3.003 Lab 4 Simulation of Solar Cells
Mar. 9, 2010 Due Mar. 29, 2010 3.003 Lab 4 Simulation of Solar Cells Objective: To design a silicon solar cell by simulation. The design parameters to be varied in this lab are doping levels of the substrate
More informationBlackbody radiation derivation of Planck s radiation low
Blackbody radiation derivation of Planck s radiation low 1 Classical theories of Lorentz and Debye: Lorentz (oscillator model): Electrons and ions of matter were treated as a simple harmonic oscillators
More informationPolynomials and the Fast Fourier Transform (FFT) Battle Plan
Polynomials and the Fast Fourier Transform (FFT) Algorithm Design and Analysis (Wee 7) 1 Polynomials Battle Plan Algorithms to add, multiply and evaluate polynomials Coefficient and pointvalue representation
More informationPina Romaniello Department of Physics Phone: +39 02 50317377 Università degli Studi di Milano Fax: +39 02 503174 82 via Celoria 16
Curriculum Vitae Pina Romaniello Department of Physics Phone: +39 02 50317377 Università degli Studi di Milano Fax: +39 02 503174 82 via Celoria 16 pina.romaniello@mi.infn.it 20133 Milano, Italy http://www.etsf.it/milan_group_link1.html/
More informationXRays and Magnetism From Fundamentals to Nanoscale Dynamics
XRays and Magnetism From Fundamentals to Nanoscale Dynamics Joachim Stöhr Stanford Synchrotron Radiation Laboratory Xrays have come a long way 1895 1993 10 cm 10 µm 100 nm Collaborators: SSRL Stanford:
More informationComparison of approximations to the transition rate in the DDHMS preequilibrium model
EPJ Web of Conferences 69, 0 00 24 (204) DOI: 0.05/ epjconf/ 2046900024 C Owned by the authors, published by EDP Sciences, 204 Comparison of approximations to the transition rate in the DDHMS preequilibrium
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 informationCircular dichroism elucidates spinorbit interaction in magnets
Circular dichroism elucidates spinorbit interaction in magnets HansJoachim Elmers nstitut für Physik, Universität Mainz, 55128 Mainz M P Folie Nr. 1 DOS Halfmetallic ferromagnets Metal De Groot, 1983
More informationSolid State Theory. (Theorie der kondensierten Materie) Wintersemester 2015/16
Martin Eckstein Solid State Theory (Theorie der kondensierten Materie) Wintersemester 2015/16 MaxPlanck Research Departement for Structural Dynamics, CFEL Desy, Bldg. 99, Rm. 02.001 Luruper Chaussee 149
More informationCENTER OF GRAVITY, CENTER OF MASS AND CENTROID OF A BODY
CENTER OF GRAVITY, CENTER OF MASS AND CENTROID OF A BODY Dr. Amilcar RinconCharris, MSME Mechanical Engineering Department MECN 3005  STATICS Objective : Students will: a) Understand the concepts of
More informationNanoparticle Enhanced Thin Film Solar Cells
Nanoparticle Enhanced Thin Film Solar Cells Solar Cells Solar cells convert visible light to electricity. It is one of the clean sources of energy. In theory a 100 square mile area covered with solar panels
More informationInduction Motor Theory
PDHonline Course E176 (3 PDH) Induction Motor Theory Instructor: Jerry R. Bednarczyk, P.E. 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 220306658 Phone & Fax: 7039880088 www.pdhonline.org
More informationElectron density is complex!
Electron density is complex! Göttingen, November 13 th 2008 George M. Sheldrick, Göttingen University http://shelx.uniac.gwdg.de/shelx/ Friedel s Law F h,k,l = F h, k, l and φ h,k,l = φ h, k, l Friedel
More informationDETECTION OF CHARGED PARTICLES WITH SILICON DETECTORS
DETECTION OF CHARGED PARTICLES WITH SILICON DETECTORS A) DESCRIPTION OF SILICON CHARGED PARTICLE DETECTOR The silicon charged particle detector is a wafer of silicon having surface contacts forming a pn
More informationMolecular Dynamics Simulations
Molecular Dynamics Simulations Yaoquan Tu Division of Theoretical Chemistry and Biology, Royal Institute of Technology (KTH) 201106 1 Outline I. Introduction II. Molecular Mechanics Force Field III. Molecular
More informationElectromagnetic Radiation
Activity 17 Electromagnetic Radiation Why? Electromagnetic radiation, which also is called light, is an amazing phenomenon. It carries energy and has characteristics of both particles and waves. We can
More information2.5 Quantum expressions for conductance: Realspace
54 2.5 Quantum expressions for conductance: Realspace Green function technique The iconolaters of Byzantium were subtle folk, who claimed to represent God to his great glory, but who, simulating God in
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 information* Present address: Department of Physics, Clark University, Worcester, MA 01610.
(solid curve) radiations are searched to minimize x2. The inclusion of one E3 partial wave lowers X2 from 19.8 to 1.6 and is strongly influenced by the data near to 0" and 180". At 39 MeV excitation the
More informationEnhanced Charge Separation in Organic Photovoltaic Films Doped with Ferroelectric Dipoles. Supporting Information
Enhanced Charge Separation in Organic Photovoltaic Films Doped with Ferroelectric Dipoles Kanwar S. Nalwa, a John A. Carr, a Rakesh C. Mahadevapuram, b Hari K. Kodali, c Sayantan Bose, d Yuqing Chen, a
More information221A Lecture Notes Variational Method
1 Introduction 1A Lecture Notes Variational Method Most of the problems in physics cannot be solved exactly, and hence need to be dealt with approximately. There are two common methods used in quantum
More informationRate of convergence towards Hartree dynamics
Rate of convergence towards Hartree dynamics Benjamin Schlein, LMU München and University of Cambridge Universitá di Milano Bicocca, October 22, 2007 Joint work with I. Rodnianski 1. Introduction boson
More informationCoefficient of Potential and Capacitance
Coefficient of Potential and Capacitance Lecture 12: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay We know that inside a conductor there is no electric field and that
More informationBOX. The density operator or density matrix for the ensemble or mixture of states with probabilities is given by
2.4 Density operator/matrix Ensemble of pure states gives a mixed state BOX The density operator or density matrix for the ensemble or mixture of states with probabilities is given by Note: Once mixed,
More informationThe Central Equation
The Central Equation Mervyn Roy May 6, 015 1 Derivation of the central equation The single particle Schrödinger equation is, ( H E nk ψ nk = 0, ) ( + v s(r) E nk ψ nk = 0. (1) We can solve Eq. (1) at given
More informationarxiv:1204.4608v1 [condmat.mtrlsci] 20 Apr 2012
arxiv:1204.4608v1 [condmat.mtrlsci] 20 Apr 2012 GW quasiparticle band gaps of anatase TiO 2 starting from DFT+U Christopher E. Patrick and Feliciano Giustino Department of Materials, University of Oxford,
More informationSemiconductor Physics
10p PhD Course Semiconductor Physics 18 Lectures NovDec 2011 and Jan Feb 2012 Literature Semiconductor Physics K. Seeger The Physics of Semiconductors Grundmann Basic Semiconductors Physics  Hamaguchi
More informationImproved predictive modeling of white LEDs with accurate luminescence simulation and practical inputs
Improved predictive modeling of white LEDs with accurate luminescence simulation and practical inputs TracePro OptoMechanical Design Software s Fluorescence Property Utility TracePro s Fluorescence Property
More information3. Derive the partition function for the ideal monoatomic gas. Use Boltzmann statistics, and a quantum mechanical model for the gas.
Tentamen i Statistisk Fysik I den tjugosjunde februari 2009, under tiden 9.0015.00. Lärare: Ingemar Bengtsson. Hjälpmedel: Penna, suddgummi och linjal. Bedömning: 3 poäng/uppgift. Betyg: 03 = F, 46
More informationElectronic transport properties of nanoscale Si films: an ab initio study
Electronic transport properties of nanoscale Si films: an ab initio study Jesse Maassen, Youqi Ke, Ferdows Zahid and Hong Guo Department of Physics, McGill University, Montreal, Canada Motivation (of
More informationModeling Dye Sensitized Solar Cells Filippo De Angelis
Modeling Dye Sensitized Solar Cells Filippo De Angelis Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO) Istituto CNR di Scienze e Tecnologie Molecolari (ISTM), I06123 Perugia, Italy Computational
More informationLecture 29. Introduction to Fluorescence Spectroscopy
Lecture 29 Introduction to Fluorescence Spectroscopy Introduction When a molecule absorbs light, an electron is promoted to a higher excited state (generally a singlet state, but may also be a triplet
More informationThe plasmoelectric effect: optically induced electrochemical potentials in resonant metallic structures
The plasmoelectric effect: optically induced electrochemical potentials in resonant metallic structures Matthew T. Sheldon and Harry A. Atwater Thomas J. Watson Laboratories of Applied Physics, California
More informationPhotoinduced volume change in chalcogenide glasses
Photoinduced volume change in chalcogenide glasses (Ph.D. thesis points) Rozália Lukács Budapest University of Technology and Economics Department of Theoretical Physics Supervisor: Dr. Sándor Kugler 2010
More informationMATH 105: Finite Mathematics 26: The Inverse of a Matrix
MATH 05: Finite Mathematics 26: The Inverse of a Matrix Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Outline Solving a Matrix Equation 2 The Inverse of a Matrix 3 Solving Systems of
More informationTheory of Light Scattering in Condensed Matter
Proceedings of the First Joint USA USSR Symposium Theory of Light Scattering in Condensed Matter Edited by Bernard Bendow Solid State Sciences Division Rome Air Development Center Hanscom AFB, Massachusetts
More informationAUTOMATED THREEANTENNA POLARIZATION MEASUREMENTS USING DIGITAL SIGNAL PROCESSING
AUTOMATED THREEANTENNA POLARIZATION MEASUREMENTS USING DIGITAL SIGNAL PROCESSING John R. Jones and Doren W. Hess Abstract In this paper we present a threeantenna measurement procedure which yields the
More informationTDS. Dirk Rosenthal Department of Inorganic Chemistry FritzHaberInstitut der MPG Faradayweg 46, DE 14195 Berlin dirkrose@fhiberlin.mpg.
Modern Methods in Heterogeneous Catalysis Research TDS Dirk Rosenthal Department of Inorganic Chemistry FritzHaberInstitut der MPG Faradayweg 46, DE 14195 Berlin dirkrose@fhiberlin.mpg.de TDS = TPD
More informationDIRECT CURRENT GENERATORS
DIRECT CURRENT GENERATORS Revision 12:50 14 Nov 05 INTRODUCTION A generator is a machine that converts mechanical energy into electrical energy by using the principle of magnetic induction. This principle
More informationAtomic Structure: Chapter Problems
Atomic Structure: Chapter Problems Bohr Model Class Work 1. Describe the nuclear model of the atom. 2. Explain the problems with the nuclear model of the atom. 3. According to Niels Bohr, what does n stand
More informationIntroduction to spectroscopy
Introduction to spectroscopy How do we know what the stars or the Sun are made of? The light of celestial objects contains much information hidden in its detailed color structure. In this lab we will separate
More informationhypothesis of Louis de Broglie (1924): particles may have wavelike properties
Wave properties of particles hypothesis of Louis de Broglie (1924): particles may have wavelike properties note: it took almost 20 years after noting that waves have particle like properties that particles
More informationSymmetric Stretch: allows molecule to move through space
BACKGROUND INFORMATION Infrared Spectroscopy Before introducing the subject of IR spectroscopy, we must first review some aspects of the electromagnetic spectrum. The electromagnetic spectrum is composed
More informationMultiple Choice (4 points each): Answer on blue form; be sure to code in your name and ID.
Multiple Choice (4 points each): Answer on blue form; be sure to code in your name and ID. 1. The Bohr model of the atom works reasonably well in the calculation of energy levels in hydrogen. What other
More informationDr.B.R.AMBEDKAR OPEN UNVERSITY FACULTY OF SCIENCE M.Sc. I year CHEMISTRY (201314) Course I: Inorganic Chemistry
M.Sc. I year CHEMISTRY (201314) Course I: Inorganic Chemistry Maximum Marks 15 Minimum Marks  06 Section A 1X10=10 Answer any One question from the following Two questions a. What is symmetry operation?
More information