Advanced Workshop on Energy Transport in Low-Dimensional Systems: Achievements and Mysteries October 2012

Size: px
Start display at page:

Download "2371-11. Advanced Workshop on Energy Transport in Low-Dimensional Systems: Achievements and Mysteries. 15-24 October 2012"

Transcription

1 Advanced Workshop on Energy Transport in Low-Dimensional Systems: Achievements and Mysteries October 2012 Thermal Conductance of Uniform Quantum Wires K. MATVEEV Argonne National Laboratory Argonne U.S.A.

2 Konstantin Matveev Trieste, October 18, 2012 In collaboration with A. Levchenko, T. Micklitz, J. Rech, Z. Ristivojevic

3 Motivation: Experiments with quantum wires, quantized conductance Theory: Thermal conductance of quantum wires Non-interacting wires, Wiedemann-Franz law; Classification of electron-electron scattering processes; Small corrections to thermal conductance in short wires; Strong suppression of thermal conductance in long wires.

4 From Berggren & Pepper, 2002 As a function of gate voltage conductance shows multiple steps of height

5 Top view Electron motion across the channel Gate voltage changes the number of parallel channels in the wire Each channel has conductance

6 Current: Conductance:

7 Heat current: Thermal conductance: Wiedemann-Franz law: cf.

8 Uniform quantum wire: No disorder Interactions inside the wire No interactions in the leads What is the thermal conductance?

9 Non-trivial two particle collisions are forbidden by the conservation laws Three particle collisions conserve both energy and momentum

10 Collision integral can be linearized in at

11 (a) (b) (c) fast less fast very slow Scattering rates: These scattering processes relax the electron gas toward different equilibrium states

12 Gibbs distribution: In a uniform wire momentum is conserved, and In general, all conserved quantities enter the exponent of the Gibbs distribution

13 (a) Numbers, momenta, and energies of the left- and right-moving particles are conserved separately The distribution supplied by the leads belongs to this class:

14 (b) Numbers of the left- and right-moving particles are conserved separately, in addition to the total momentum and energy The distribution supplied by the leads does not belong to this class:

15 (c) Only the total number of particles, momentum, and energy are conserved

16 In a long wire electron distribution reaches the equilibrium form corresponding to the dominant scattering process (a) (b) Equilibration due to type (a) processes is more efficient: In wires shorter than, type (b) processes can be accounted for perturbatively At the distribution function has the form The 6 parameters depend on position

17 Integro-differential equation: 6 ordinary differential equations: 4 conservation laws Easily solvable!

18 (b) The correction is due to the curvature of electron spectrum near the Fermi level. Even in long wires it remains small as The equilibration length is model-specific. For unscreened Coulomb interactions we found without spins with spins [Levchenko, Micklitz, Ristivojevic & KM, PRB 84, (2011)]

19 (c) Electron distribution: Heat current depends only on the velocity u

20 Consider the energy current of right-moving electrons The total energy current Exclude the outgoing current Substitute the known expression for the incoming currents

21 Momentum of the electron gas The total momentum is conserved, Momentum change: Energy change: Rate of energy change due to backscattering:

22 (c) In a system without net electric current the electron distribution relaxes towards the usual Fermi function Standard relaxation law: Combining with and we find

23 Old result in a short wire,. Small thermal conductance, but finite thermal conductivity in a long wire, [Micklitz, Rech & KM, PRB 81, (2010)]

24 In long wires the electrical conductance saturates Momentum conservation results in infinite conductivity But the thermal conductance is small: Strong violation of the Wiedemann-Franz law: Thermoelectric figure of merit:

25 Electron-electron scattering reduces thermal conductance of quantum wires Small reduction of thermal conductance in short wires In (exponentially) long wires the thermal conductance is strongly suppressed

Tunneling revisited: the scattering matrix

Tunneling revisited: the scattering matrix he story so far: Semiclassical transport pretty good at duplicating experimental results in regime of validity. Quantum coherence leads to interference effects that can dominate in samples ~ size of coherence

More information

SCIENCE AP Physics B & C. Organizing Topic Benchmark Indicator Forces and Motion A. Explain how the Laws of Motion relate to all forms of motion.

SCIENCE AP Physics B & C. Organizing Topic Benchmark Indicator Forces and Motion A. Explain how the Laws of Motion relate to all forms of motion. Forces and Motion A. Explain how the Laws of Motion relate to all forms of 1. Identify and describe one-dimensional 2. Identify and describe two dimensional 3. Use vectors and coordinate systems to solve

More information

6.730 Physics for Solid State Applications

6.730 Physics for Solid State Applications 6.730 Physics for Solid State Applications Lecture 3: Metal as a Free Electron Gas Rajeev J. Ram Generalizations from Molecules to Solids The source of the binding energy is primarily the electrostatic

More information

Free Electron Fermi Gas (Kittel Ch. 6)

Free 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 information

Chapter 9 Center Of Mass, Linear Momentum and Collisions

Chapter 9 Center Of Mass, Linear Momentum and Collisions Chapter 9 Center Of Mass, Linear Momentum and Collisions 9.2 The Center of Mass The center of mass of a system of particles is the point that moves as though (1) all of the system s mass were concentrated

More information

Online Courses for High School Students 1-888-972-6237

Online Courses for High School Students 1-888-972-6237 Online Courses for High School Students 1-888-972-6237 PHYSICS Course Description: This course provides a comprehensive survey of all key areas: physical systems, measurement, kinematics, dynamics, momentum,

More information

Side-by-Side Comparison of the Texas Educational Knowledge and Skills (TEKS) and Louisiana Grade Level Expectations (GLEs) SCIENCE: Physics

Side-by-Side Comparison of the Texas Educational Knowledge and Skills (TEKS) and Louisiana Grade Level Expectations (GLEs) SCIENCE: Physics Side-by-Side Comparison of the Texas Educational Knowledge and Skills (TEKS) and Louisiana Grade Level Expectations () SCIENCE: Physics TEKS Comments Louisiana GLE (Phy.1) Scientific Processes. The student,

More information

8.513 Lecture 3. Microscopic approach; Nonlocal transport; Voltage probes; Resonances

8.513 Lecture 3. Microscopic approach; Nonlocal transport; Voltage probes; Resonances 8.513 Lecture 3 Microscopic approach; Nonlocal transport; Voltage probes; Resonances Derivation of Landauer formulas (multi-lead, multi-channel) from Nazarov & Blanter Second quantization summary from

More information

Welcome to AP Physics

Welcome to AP Physics Welcome to AP Physics Syllabus for 1 st Semester Your teacher will be me, Mr. Dale Brabec. This will be an interesting/exciting/thought provoking class, if you understand the following. Expectations 1.

More information

Phonons Thermal properties

Phonons Thermal properties Phonons Thermal properties Till now everything was classical no quantization, no uncertainty... WHY DO WE NEED QUANTUM THEORY OF LATTICE VIBRATIONS? Classical Dulong Petit law All energy values are allowed

More information

Conceptual Physics 12 th Edition, 2015 Hewitt

Conceptual Physics 12 th Edition, 2015 Hewitt A Correlation of Hewitt To the Next Generation Science Standards A Correlation of, HS-PS1 Matter and Its Interactions HS-PS1-1. Use the periodic table as a model to predict the relative properties of elements

More information

MASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCES IN PHYSICS (MS PHYS) (LIST OF COURSES BY SEMESTER, THESIS OPTION)

MASTER 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 non-physics majors, a GPA of 2.5 or better in at least 15 units in the following advanced

More information

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

More information

NPTEL. Semiconductor Device Modeling - Video course. Electronics & Communication Engineering.

NPTEL. Semiconductor Device Modeling - Video course. Electronics & Communication Engineering. NPTEL Syllabus Semiconductor Device Modeling - Video course COURSE OUTLINE Course Learning Outcomes At the end of this course you should be able to 1. Explain the equations, approximations and techniques

More information

MCEN Fall 2003.

MCEN 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 information

From quantum mechanics, the single particle energy levels are given by

From quantum mechanics, the single particle energy levels are given by The Heat Capacity of a Diatomic Gas 5.1 INTRODUCTION We have seen how statistical thermodynamics provides deep insight into the classical description of a monatomic ideal gas. We might have reason to hope,

More information

Statistical Physics, Part 2 by E. M. Lifshitz and L. P. Pitaevskii (volume 9 of Landau and Lifshitz, Course of Theoretical Physics).

Statistical Physics, Part 2 by E. M. Lifshitz and L. P. Pitaevskii (volume 9 of Landau and Lifshitz, Course of Theoretical Physics). Fermi liquids The electric properties of most metals can be well understood from treating the electrons as non-interacting. This free electron model describes the electrons in the outermost shell of the

More information

Computational Astrophysics 2 The Equations of Hydrodyamics

Computational Astrophysics 2 The Equations of Hydrodyamics Computational Astrophysics 2 The Equations of Hydrodyamics Oscar Agertz Outline - The Boltzmann equation - The Collision Integral - The Local Thermodynamical Equilibrium - The Euler equations - The Equation-Of-State

More information

BETA DECAY. Beta decays are nuclear processes mediated by the weak interaction. The three types of beta decay are

BETA DECAY. Beta decays are nuclear processes mediated by the weak interaction. The three types of beta decay are BETA DECAY Beta decays are nuclear processes mediated by the weak interaction. The three types of beta decay are a. The conversion of a neutron to a proton along with the emission of an electron and an

More information

Chapter 38 Quantum Mechanics

Chapter 38 Quantum Mechanics Chapter 38 Quantum Mechanics Units of Chapter 38 Quantum Mechanics A New Theory The Wave Function and Its Interpretation; the Double-Slit Experiment The Heisenberg Uncertainty Principle Philosophic Implications;

More information

Charge Carriers in Semiconductors

Charge Carriers in Semiconductors Charge Carriers in Semiconductors At T = 0K, a semiconductor is an insulator with no free charge carriers. At T > 0K, some electrons in the valence band are excited to the conduction band, where they are

More information

Diamagnetism and Paramagnetism. Magnetization M(H) in the presence of an uniform magnetic field H at T=0 is defined as:

Diamagnetism and Paramagnetism. Magnetization M(H) in the presence of an uniform magnetic field H at T=0 is defined as: Diamagnetism and Paramagnetism Definitions: Magnetization M(H) in the presence of an uniform magnetic field H at T=0 is defined as: where is the ground state energy. Note that H is the magnetic field felt

More information

Inertial frame of reference: The frame of reference in which Newton`s first law is valid is called inertial frame of reference.

Inertial frame of reference: The frame of reference in which Newton`s first law is valid is called inertial frame of reference. Dynamics Newton`s first law: If no net force acts on a body, it will move on a straight line at constant velocity or will stay at rest if it stays initially at rest. Inertial frame of reference: The frame

More information

Statistical Mechanics: Lecture 1

Statistical Mechanics: Lecture 1 1 Statistical Mechanics: Lecture 1 Tabish Qureshi Thermodynamics and microscopic laws Thermodynamics describes the macroscopic properties of matter phenomenologically with the aid of equations of state

More information

COMPETENCY GOAL 1: The learner will develop abilities necessary to do and understand scientific inquiry.

COMPETENCY GOAL 1: The learner will develop abilities necessary to do and understand scientific inquiry. North Carolina Standard Course of Study and Grade Level Competencies, Physics I Revised 2004 139 Physics PHYSICS - Grades 9-12 Strands: The strands are: Nature of Science, Science as Inquiry, Science and

More information

3.15 Electrical, Optical, and Magnetic Materials and Devices Caroline A. Ross Fall Term, Problem Set #1 Semiconductor Fundamentals Solutions

3.15 Electrical, Optical, and Magnetic Materials and Devices Caroline A. Ross Fall Term, Problem Set #1 Semiconductor Fundamentals Solutions 3.15 Electrical, Optical, and Magnetic Materials and Devices Caroline A. Ross Fall Term, 2003 Problem Set #1 Semiconductor Fundamentals Solutions Released Tuesday, September 23, 2003 Reference: Chapters

More information

Dynamics of a mobile impurity in a one-dimensional quantum gas

Dynamics of a mobile impurity in a one-dimensional quantum gas Dynamics of a mobile impurity in a one-dimensional quantum gas O. Lychkovskiy Russian Quantum Center, Skolkovo In collaboration with E. Burovski, V. Cheianov and O. Gamayun. Work in progress also with

More information

High Performance Computing II Lecture 3

High Performance Computing II Lecture 3 Topic : Molecular Dynamics of Lennard-Jones System Molecular Dynamics (MD) is widely used to simulate many particle systems ranging from solids, liquids, gases, and biomolecules on Earth, to the motion

More information

Chapter 6 (part 1) Ideal Gas: Fermions and Bosons

Chapter 6 (part 1) Ideal Gas: Fermions and Bosons Last Time LECTURE 10 Gibbs Factor (Boltzmann factor with N) Gibbs Sum (Partition function with N) Adsorption (O 2 - myoglobin ) Semiconductor Impurity Sites Today LECTURE 10 Chapter 6 (part 1) Ideal Gas:

More information

Electrons in Quantum Wires

Electrons in Quantum Wires Electrons in Quantum Wires L.I. Glazman Yale University Chernogolovka 07 Outline Electrical resistance Sharvin resistance and Landauer formula Interaction effects: scattering of electron waves off a Friedel

More information

Monte Carlo Simulation technique. S. B. Santra Department of Physics Indian Institute of Technology Guwahati

Monte Carlo Simulation technique. S. B. Santra Department of Physics Indian Institute of Technology Guwahati Monte Carlo Simulation technique S. B. Santra Department of Physics Indian Institute of Technology Guwahati What is Monte Carlo (MC)? Introduction Monte Carlo method is a common name for a wide variety

More information

The Quantum Hall Effect

The Quantum Hall Effect The Quantum Hall Effect File from a talk given at the International School "Quantum Metrology and Fundamental constants, 'Ecole de Physique des Houches" (France) from October 1st to October 12 th, 2007.

More information

b) Write down the Hamiltonian using the generalized coordinates.

b) Write down the Hamiltonian using the generalized coordinates. Classical Mechanics 500 Two masses m 1 and m 2 are joined by a massless spring (force constant k and natural length l 0 ) and are confined to move in a frictionless horizontal plane, with center of mass

More information

4/25/2016. Great Job! PHYS 342 Modern Physics Course Review. The research projects are fantastic!

4/25/2016. Great Job! PHYS 342 Modern Physics Course Review. The research projects are fantastic! PHYS 34 Modern Physics Course Review Great Job! The research projects are fantastic! In the end (current points + final exam), passing 60% points means at least C. Currently, almost everyone has more than

More information

Chapter 7- Linear Momentum

Chapter 7- Linear Momentum Chapter 7- Linear Momentum Assignment 6 Textbook (Giancoli, 6 th edition), Chapter 6: Due on Thursday, November 12 1. On page 163 of Giancoli, problem 38. 2. On page 165 of Giancoli, problem 69. 3. On

More information

Lab 9 CONSERVATION OF LINEAR MOMENTUM

Lab 9 CONSERVATION OF LINEAR MOMENTUM Lab 9 CONSERVATION OF LINEAR MOMENTUM In this experiment, you will try to verify the Law of Conservation of Linear Momentum using a collision between two cars on the air track. Here are the important concepts

More information

Morgan Hill Unified School District Course Outline Advanced Placement Physics (AP) Grades: Recommended: Completion of Algebra 2.

Morgan Hill Unified School District Course Outline Advanced Placement Physics (AP) Grades: Recommended: Completion of Algebra 2. Course Title: Course Length: Morgan Hill Unified School District Course Outline Advanced Placement Physics (AP) One year Grades: 10-12 Recommended: Completion of Algebra 2. Course Goals Students will demonstrate

More information

Momentum, Impulse, and Collisions

Momentum, Impulse, and Collisions Nicholas J. Giordano www.cengage.com/physics/giordano Momentum, Impulse, and Collisions Introduction Objects have been treated as point particles Mass is located at a single point in space This assumption

More information

COLLEGE PHYSICS. Chapter 29 INTRODUCTION TO QUANTUM PHYSICS

COLLEGE PHYSICS. Chapter 29 INTRODUCTION TO QUANTUM PHYSICS COLLEGE PHYSICS Chapter 29 INTRODUCTION TO QUANTUM PHYSICS Quantization: Planck s Hypothesis An ideal blackbody absorbs all incoming radiation and re-emits it in a spectrum that depends only on temperature.

More information

Spectroscopic Notation

Spectroscopic Notation Spectroscopic Notation Most of the information we have about the universe comes to us via emission lines. However, before we can begin to understand how emission lines are formed and what they tell us,

More information

Foundations of Chemical Kinetics. Lecture 20: The master equation

Foundations of Chemical Kinetics. Lecture 20: The master equation Foundations of Chemical Kinetics Lecture 20: The master equation Marc R. Roussel Department of Chemistry and Biochemistry Transition rates Suppose that Ps (t) is the probability that a system is in a state

More information

Potential Energy and Energy Diagrams Concept Questions

Potential Energy and Energy Diagrams Concept Questions Potential Energy and Energy Diagrams Concept Questions Question 1 You lift a ball at constant velocity from a height h i to a greater height h f. Considering the ball and the earth together as the system,

More information

Molecular electronics

Molecular electronics Molecular electronics Karsten Flensberg Niels Bohr Institute University of Copenhagen Molecular electronics I Introduction to experiments on molecular transistors (random selection) from mono-layers to

More information

Torque, Angular momentum and Equilibrium

Torque, Angular momentum and Equilibrium Torque, Angular momentum and Equilibrium 1. Torque: the moment of force Consider a particle M of position vector r moving in a force field F, then we can define the torque of the force F about the origin

More information

Lecture #17 Today: 1. The Sommerfeld expansion and the calculation of properties near the Fermi level 2. Calculating the electronic contribution to

Lecture #17 Today: 1. The Sommerfeld expansion and the calculation of properties near the Fermi level 2. Calculating the electronic contribution to Lecture #17 Today: 1. The Sommerfeld expansion and the calculation of properties near the ermi level. Calculating the electronic contribution to the heat capacity of a metal at moderate temperatures. 3.

More information

Topic 3b: Kinetic Theory

Topic 3b: Kinetic Theory Topic 3b: Kinetic Theory What is temperature? We have developed some statistical language to simplify describing measurements on physical systems. When we measure the temperature of a system, what underlying

More information

Physics - SC1117. Revised 8/31/10 Page 1 of 11

Physics - SC1117. Revised 8/31/10 Page 1 of 11 Introduction to Physics Mathematics and Physics Demonstrate scientific methods. Use the metric system. Evaluate answers using dimensional analysis. Perform arithmetic operations using scientific notation.

More information

Equilibrium Versus Nonequilibrium

Equilibrium Versus Nonequilibrium Equilibrium Versus Nonequilibrium What do we mean by the terms equilibrium, far from equilibrium, local equilibrium, etc.? It is first important to point out that we mean more by equilibrium than ust steady

More information

Chapter 8- Rotational Motion

Chapter 8- Rotational Motion Chapter 8- Rotational Motion Textbook (Giancoli, 6 th edition): Assignment 9 Due on Thursday, November 26. 1. On page 131 of Giancoli, problem 18. 2. On page 220 of Giancoli, problem 24. 3. On page 221

More information

STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE

STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE PHYS 121 - COLLEGE PHYSICS I Prepared By: Dr. Lawretta Ononye CANINO SCHOOL OF ENGINEERING TECHNOLOGY PHYSICS MAY2015

More information

The Revised Syllabus for Basic Academic Abilities in the EJU (To be applied to the questions of the 2015 EJU 1st Session (June))

The Revised Syllabus for Basic Academic Abilities in the EJU (To be applied to the questions of the 2015 EJU 1st Session (June)) December 2013 The Revised Syllabus for Basic Academic Abilities in the EJU (To be applied to the questions of the 2015 EJU 1st Session (June)) [Purpose of the Examination] The purpose

More information

Simple models of plasma turbulence

Simple models of plasma turbulence ASDEX Upgrade Max-Planck-Institut für Plasmaphysik Simple models of plasma turbulence D. Strintzi Outline The Hasegawa-Mima model derivation comparison with 2D fluid classical drift wave energy spectrum

More information

Introduction to Many-Body Perturbation Theory

Introduction to Many-Body Perturbation Theory Chapter 10 Introduction to Many-Body Perturbation Theory c 2006 by Harvey Gould and Jan Tobochnik 2 January 2006 We introduce the language of second quantization in the context of quantum many body systems

More information

5.62 Physical Chemistry II Spring 2008

5.62 Physical Chemistry II Spring 2008 MIT OpenCourseWare http://ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.62 Spring 2008 Lecture

More information

Decay Rates, Cross Sections and Phase Space. H. A. Tanaka

Decay Rates, Cross Sections and Phase Space. H. A. Tanaka Decay Rates, Cross Sections and Phase Space H. A. Tanaka Overview Decay rates and lifetimes relation to half-life, total decay rates, etc. Fermi s golden rule how phase space affects interactions/transitions/reactions/decays

More information

Kern- und Teilchenphysik I Lecture 4: Nuclear Decay

Kern- und Teilchenphysik I Lecture 4: Nuclear Decay Kern- und Teilchenphysik I Lecture 4: Nuclear Decay Prof. Dr. Patrick Owen, Dr. Silva Coutinho http://www.physik.uzh.ch/de/lehre/phy211/hs2016.html Gamma Decay We want to compute the lifetime of nuclei

More information

Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena

Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena Ya. B. Zel'dovich and Yu. P. Raizer Academy of Sciences, Moscow Edited by Wallace D. Hayes and Ronald F. Probstein Princeton University

More information

An Introduction to Cross Sections

An Introduction to Cross Sections An Introduction to Cross Sections 1. Definition of cross section for scattering or reactions Let A = mass number of target (assuming a single pure isotope) If we assume that (a) the probability of interaction

More information

1 of 8 11/10/ :20 AM

1 of 8 11/10/ :20 AM 1 of 8 11/10/2009 11:20 AM Chapter 12 Homework Due: 9:00am on Wednesday, November 11, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment

More information

Electrical Conductivity in Metals

Electrical Conductivity in Metals Electrical Conductivity in Metals V H Satheeshkumar Department of Physics and Center for Advanced Research and Development Sri Bhagawan Mahaveer Jain College of Engineering Jain Global Campus Kanakapura

More information

Assessment Plan for Learning Outcomes for BA/BS in Physics

Assessment Plan for Learning Outcomes for BA/BS in Physics Department of Physics and Astronomy Goals and Learning Outcomes 1. Students know basic physics principles [BS, BA, MS] 1.1 Students can demonstrate an understanding of Newton s laws 1.2 Students can demonstrate

More information

Lecture 18. Wave Transmission of Pressure and Sound. BENG 221: Mathematical Methods in Bioengineering. References

Lecture 18. Wave Transmission of Pressure and Sound. BENG 221: Mathematical Methods in Bioengineering. References BENG 1: Mathematical Methods in Bioengineering Lecture 18 Wave Transmission of Pressure and Sound References Haberman APDE, Ch. 1. http://en.wikipedia.org/wiki/wave_equation http://en.wikipedia.org/wiki/longitudinal_wave

More information

Making Sense of the Equation Sheet. Physics 213

Making Sense of the Equation Sheet. Physics 213 Fundamental Laws/Principles: First Law: Making Sense of the Equation Sheet Physics 213 Energy is conserved the change in the internal energy of a system is equal to the heat that flows into or out of the

More information

Energy Transport. Focus on heat transfer. Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids)

Energy Transport. Focus on heat transfer. Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids) Energy Transport Focus on heat transfer Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids) Conduction Conduction heat transfer occurs only when there is physical contact

More information

Spin-electronics: a new challenge in science and technology ``Teaching electrons new tricks

Spin-electronics: a new challenge in science and technology ``Teaching electrons new tricks Spin-electronics: a new challenge in science and technology ``Teaching electrons new tricks P. Bruno Max-Planck Institute of Microstructure Physics, Halle, Germany Summary: Introduction: what is spin-electronics?

More information

Scattering Theory of Waves and Particles

Scattering Theory of Waves and Particles Scattering Theory of Waves and Particles Roger G. Newton DOVER PUBLICATIONS, INC. Mineola, New York Contents PART I SCATTERING OF ELECTROMAGNETIC WAVES 1 1 Formalism and General Results 3 1.1 The Maxwell

More information

Midterm Review. GEOG/ENST 2331 Lecture 13 Ahrens et al., Chapters 1-8 Labs 1-3

Midterm Review. GEOG/ENST 2331 Lecture 13 Ahrens et al., Chapters 1-8 Labs 1-3 Midterm Review GEOG/ENST 2331 Lecture 13 Ahrens et al., Chapters 1-8 Labs 1-3 Midterm Wednesday: 30 multiple choice, three short answer Bring a pencil for Scantron cards Bring a non-programmable calculator

More information

Lasing Principles & Conditions

Lasing Principles & Conditions Lasing Principles & Conditions Dr. BC Choudhary, Professor NITTTR, Sector-26, Chandigarh-160019 Content Outlines Quantum Nature of light Photon-Electron Interactions Thermal Equilibrium & Einstein Prediction

More information

Electronic transport in a ferromagnetic single-electron transistor with non-collinear magnetizations in the co-tunnelling regime

Electronic transport in a ferromagnetic single-electron transistor with non-collinear magnetizations in the co-tunnelling regime Materials Science-Poland, Vol. 5, No., 007 Electronic transport in a ferromagnetic single-electron transistor with non-collinear magnetizations in the co-tunnelling regime J. WIŚNIEWSKA *, J. BARNAŚ, Department

More information

- develop a theory that describes the wave properties of particles correctly

- develop a theory that describes the wave properties of particles correctly Quantum Mechanics Bohr's model: BUT: In 1925-26: 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 information

METALS-Drude s classical theory

METALS-Drude s classical theory METALS-Drude s classical theory Theory by Paul Drude in 1900, only three years after the electron was discovered. Drude treated the (free) electrons as a classical ideal gas but the electrons should collide

More information

Chapter 6. Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws

Chapter 6. Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws Chapter 6. Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws 6.1 Displacement Current The magnetic field due to a current distribution satisfies Ampere s law, (5.45) Using Stokes s theorem

More information

Fermi gas. V (R i R j ), (1.2) i j i r j, (1.3) 2m + 1 e 2. v(r i R j ). (1.4)

Fermi gas. V (R i R j ), (1.2) i j i r j, (1.3) 2m + 1 e 2. v(r i R j ). (1.4) 51573 - Electron Correlation in Metals 1 Fermi gas The basic properties of free electron systems are introduced. Then, the many-body effects of electron gas are discussed. The ground state energy is obtained

More information

Collisions. Nucleosynthesis and Distribution of Elements. Simon Fraser University Fall NUCS 344 October 18, 2010

Collisions. Nucleosynthesis and Distribution of Elements. Simon Fraser University Fall NUCS 344 October 18, 2010 Collisions Nucleosynthesis and Distribution of Elements Simon Fraser University Fall 2010 NUCS 344 October 18, 2010 NUCS 344 (Tutorial 4) October 18, 2010 1 / 18 Outline 1 Binary collisions NUCS 344 (Tutorial

More information

Harald Ibach Hans Lüth. Solid-State Physics. An Introduction to Principles of Materials Science. Second Edition. With 232 Figures.

Harald Ibach Hans Lüth. Solid-State Physics. An Introduction to Principles of Materials Science. Second Edition. With 232 Figures. Harald Ibach Hans Lüth Solid-State Physics An Introduction to Principles of Materials Science Second Edition With 232 Figures Springer Contents 1 Chemical Bonding in Solids 1 1.1 The Periodic Table of

More information

Finite square well. Announcements:

Finite square well. Announcements: Finite square well Announcements: 2 nd exam is next Thursday, Nov. 7 7:30pm-9:00pm Homework due today. Homework #7 to return A practice exam will be posted on CULearn sometime on Friday. Today I will try

More information

Complex Variables in Classical Hamiltonian Mechanics

Complex Variables in Classical Hamiltonian Mechanics Complex Variables in Classical Hamiltonian Mechanics In the classical Hamiltonian formalism, the state of a mechanical system is given by a set of pairs of conjugated variables, of variables {q j, p j

More information

PHYS 1624 University Physics I. PHYS 2644 University Physics II

PHYS 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 information

Decay Widths and Scattering Cross Sections

Decay Widths and Scattering Cross Sections Chapter 4 Decay Widths and Scattering Cross Sections We are now ready to calculate the rates of some simple scattering and decay processes. The former is expressed in terms of cross section, σ, which is

More information

F ij = Gm im j r i r j 3 ( r j r i ).

F ij = Gm im j r i r j 3 ( r j r i ). Physics 3550, Fall 2012 Newton s Third Law. Multi-particle systems. Relevant Sections in Text: 1.5, 3.1, 3.2, 3.3 Newton s Third Law. You ve all heard this one. Actioni contrariam semper et qualem esse

More information

PC1141 Physics I Conservation of Momentum in Collisions

PC1141 Physics I Conservation of Momentum in Collisions PC1141 Physics I Conservation of Momentum in Collisions 1 Purpose Determination of the velocity and this momentum of each glider before and after the collision from which the total momentum of the system

More information

Particle Physics and the Universe

Particle Physics and the Universe Particle Physics and the Universe This is a rather active research area right now and we have to change numbers rather often. An example here is that the Hubble constant which was only know to within a

More information

جامعة البلقاء التطبيقية

جامعة البلقاء التطبيقية AlBalqa Applied University تا سست عام 997 The curriculum of associate degree in Air Conditioning, Refrigeration and Heating Systems consists of (7 credit hours) as follows: Serial No. Requirements First

More information

PHYSICS UNIT 1: METHODS OF SCIENCE AND FORCE EQUILIBRIUM

PHYSICS UNIT 1: METHODS OF SCIENCE AND FORCE EQUILIBRIUM UNIT 1: METHODS OF SCIENCE AND FORCE EQUILIBRIUM 1. What are the methods, processes and tools used by scientists and engineers? 2. What are the differences and similarities between vectors and scalars?

More information

Solid-State Physics. 421 Springer. An Introduction to Principles of Materials Science. Fourth Extensively Updated and Enlarged Edition

Solid-State Physics. 421 Springer. An Introduction to Principles of Materials Science. Fourth Extensively Updated and Enlarged Edition Harald Ibach Hans Lüth Solid-State Physics An Introduction to Principles of Materials Science Fourth Extensively Updated and Enlarged Edition With 286 Figures, 18 Panels and 104 Problems 421 Springer Contents

More information

Physics 122 Class #23 (4/7/15)

Physics 122 Class #23 (4/7/15) Physics 122 Class #23 (4/7/15) Announcements / Equation Abuse Resistance and Resistivity Drude Model of Conduction Series and Parallel Circuits RC Circuits Homework assignment from Hell Week of 4/6/2015

More information

Electrons in Solids. Drude Model. Resistivity and Conductivity V = IR R = "L A. j = I A. E = j" j = #E V = EL

Electrons in Solids. Drude Model. Resistivity and Conductivity V = IR R = L A. j = I A. E = j j = #E V = EL Electrons in Solids Drude Model Resistivity and Conductivity R = "L A V = IR j = I A V = EL E = j" j = #E 1 Conductivity Drude Model of Conductivity E = j" j = #E 2 Drude Model of Conductivity Classical

More information

Chapter 8 Conservation of Linear Momentum. Conservation of Linear Momentum

Chapter 8 Conservation of Linear Momentum. Conservation of Linear Momentum Chapter 8 Conservation of Linear Momentum Physics 201 October 22, 2009 Conservation of Linear Momentum Definition of linear momentum, p p = m v Linear momentum is a vector. Units of linear momentum are

More information

Chapter 18 Statistical mechanics of classical systems

Chapter 18 Statistical mechanics of classical systems Chapter 18 Statistical mechanics of classical systems 18.1 The classical canonical partition function When quantum effects are not significant, we can approximate the behavior of a system using a classical

More information

physics 100 prac exam#3

physics 100 prac exam#3 physics 100 prac exam#3 Student: 1. An isolated object is initially spinning at a constant speed. Then, although no external forces act upon it, its rotational speed increases. This must be due to A. an

More information

The student applies the concepts and principles of simple motion including vectors to the solution of everyday situations. Unit 1

The student applies the concepts and principles of simple motion including vectors to the solution of everyday situations. Unit 1 Unit 1 Outcomes The student applies the concepts and principles of simple motion including vectors to the solution of everyday situations. The student applies the concepts and principles of force, work,

More information

3. CURRENT ELECTRICITY

3. CURRENT ELECTRICITY 3. CURRENT ELECTRICITY ONE MARK QUESTIONS WITH ANSWERS 1. What constitutes an electric current? Ans. Charges in motion constitutes an electric current. 2. Define electric current. Ans. The amount of charge

More information

Physics of fusion power. Lecture 6: Conserved quantities / Mirror device / tokamak

Physics of fusion power. Lecture 6: Conserved quantities / Mirror device / tokamak Physics of fusion power Lecture 6: Conserved quantities / Mirror device / tokamak Reminder Perpendicular forces lead to drifts of the particles Electric field acceleration Inertia connected with a change

More information

Electric Potential Energy versus Electric Potential

Electric Potential Energy versus Electric Potential [ Assignment View ] Eðlisfræði 2, vor 2007 23a. Electric Potential Assignment is due at 2:00am on Wednesday, January 31, 2007 Credit for problems submitted late will decrease to 0% after the deadline has

More information

Gas Discharge Physics

Gas Discharge Physics Yuri P. Raizer Gas Discharge Physics With 209 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest Contents 1. Introduction 1 1.1 What Is the Subject of Gas

More information

Laboratory experiment on quantized conductance Autumn 2010

Laboratory experiment on quantized conductance Autumn 2010 Laboratory experiment on quantized conductance Autumn 010 IH654 Nanoelectronics Ilse de Moffarts April 010 1 1. Introduction The first experiment on ballistic transport goes back to 1965, when Yuri Sharvin

More information

Collision Theory. 8.01t Nov 1, 2004

Collision Theory. 8.01t Nov 1, 2004 Collision Theory 8.01t Nov 1, 004 Momentum and Impulse momentum p = mv change in momentum p = m v average impulse I = F t ave ave = p Conservation of Momentum The total change in momentum of a system and

More information

PHYSICS 100A Second Exam (75 minutes, Chapters 7 12) Fall 2007 PART I - MULTIPLE CHOICE. EACH QUESTION IS WORTH 5 POINTS FOR A TOTAL OF 40 POINTS.

PHYSICS 100A Second Exam (75 minutes, Chapters 7 12) Fall 2007 PART I - MULTIPLE CHOICE. EACH QUESTION IS WORTH 5 POINTS FOR A TOTAL OF 40 POINTS. PHYSICS 100A Second Exam (75 minutes, Chapters 7 1) Fall 007 NAME: SCORE: Note: All quantities without explicit units are in SI units. PART I - MULTIPLE CHOICE. EACH QUESTION IS WORTH 5 POINTS FOR A TOTAL

More information

Lecture 31: Angular Momentum

Lecture 31: Angular Momentum Lecture 31: Angular Momentum For linear motion, we learned that momentum was a useful quantity In particular, Newton s Second Law could be written as d F p dt For rotational motion, we define the angular

More information

Order of Magnitude Astrophysics - a.k.a. Astronomy 111. Radiation Basics

Order of Magnitude Astrophysics - a.k.a. Astronomy 111. Radiation Basics 1 Order of Magnitude Astrophysics - a.k.a. Astronomy 111 Radiation Basics To relate the information received from electromagnetic waves to the properties of the emitting system, it is necessary to first

More information