samedi 26 janvier 2019

Statistical field theory

Giorgio Parisi

A comprehensive text book covering the field of statistical physics.

Categories:Physics\\Thermodynamics and Statistical Mechanics

Year:1988

Language:english

Pages:368

ISBN 10:0738200514

ISBN 13:9781429485852

Series:Frontiers in Physics 66

File:DJVU, 4.10 MB

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Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics

Giuseppe Mussardo

This book provides a thorough introduction to the fascinating world of phase transitions as well as many related topics, including random walks, combinatorial problems, quantum field theory and S-matrix. Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry, and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides an excellent introduction to frontier topics of exactly solved models in statistical mechanics and quantum field theory, renormalization group, conformal… Read more →

Categories:Physics\\Thermodynamics and Statistical Mechanics

Year:2009

Language:english

Pages:672

ISBN 13:978-0-19-954758-6

Series:Oxford Graduate Texts

File:PDF, 4.34 MB

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Introduction to Statistical Field Theory

Edouard Brézin

Knowledge of the renormalization group and field theory is a key part of physics, and is essential in condensed matter and particle physics. Written for advanced undergraduate and beginning graduate students, this textbook provides a concise introduction to this subject. The textbook deals directly with the loop-expansion of the free-energy, also known as the background field method. This is a powerful method, especially when dealing with symmetries, and statistical mechanics. In focussing on free-energy, the author avoids long developments on field theory techniques. The necessity of renormalization then follows.

Categories:Physics\\Thermodynamics and Statistical Mechanics

Year:2010

Edition:1

Language:english

Pages:176

ISBN 10:0511789548

ISBN 13:9780511789540

File:PDF, 1.28 MB

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jeudi 17 janvier 2019

Experimental procedure to deduce the Stefan-Boltzmann law

Object:

Measure how the current through an electric light bulb varies as the applied voltage is changed. This will allow you to establish Stephan's Law for Black Body Radiation.

Introduction:

When an electric current flows through the filament in a light bulb the filament heats up. The filament loses heat in two ways: electromagnetic radiation (mainly visible light and invisible heat radiation) and conduction (through the base of the bulb). The heat conducted away from the filament increases linearly with filament temperature. The air in the bulb is pumped out during manufacture so little heat is lost by convection.

To download the file click on the link below:

http://www.iiserpune.ac.in/~bhasbapat/phy221_files/StephansLaw.pdf

Mathematical Physics of BlackBody Radiation

Contents

I Old Picture 3
1 Blackbody Radiation 5
1.1 Birth of Modern Physics . . . . . . . . . . . . . . . . . . . . . 5
1.2 Planck, Einstein and Schr¨odinger . . . . . . . . . . . . . . . . 6
1.3 Finite Precision Computation . . . . . . . . . . . . . . . . . . 7
2 Blackbody as Blackpiano 9
3 Interaction Light-Matter 13
4 Planck-Stefan-Boltzmann Laws 17
4.1 Planck’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 Stefan-Boltzmann’s Law . . . . . . . . . . . . . . . . . . . . . 18
4.3 The Enigma of the Photoelectric Effect . . . . . . . . . . . . . 23
4.4 The Enigma of Blackbody Radiation . . . . . . . . . . . . . . 24
4.5 Confusion in Media . . . . . . . . . . . . . . . . . . . . . . . . 24
4.6 Confessions by Confused Scientists . . . . . . . . . . . . . . . 25
4.7 Towards Enigma Resolution . . . . . . . . . . . . . . . . . . . 27
5 Planck/Einstein Tragedy 29
5.1 James Jeans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2 Max Planck . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.3 Planck and Einstein . . . . . . . . . . . . . . . . . . . . . . . . 32
6 Classical Derivation of Rayleigh-Jeans Law 35
6.1 Counting Cavity Degrees of Freedom . . . . . . . . . . . . . . 35
6.2 Dependence of Space Dimension . . . . . . . . . . . . . . . . . 36
7 Statistics vs Computation 37
7.1 Cut-Off by Statistics . . . . . . . . . . . . . . . . . . . . . . . 37
7.2 Cut-Off by Finite Precision Computation . . . . . . . . . . . . 37

II New Analysis 39
8 Wave Equation with Radiation 41
8.1 A Basic Radiation Model . . . . . . . . . . . . . . . . . . . . . 41
9 Spectral Analysis of Radiation 45
9.1 Basic Energy Balance R = F . . . . . . . . . . . . . . . . . . . 45
9.2 Rayleigh-Jeans Law . . . . . . . . . . . . . . . . . . . . . . . . 48
9.3 Radiation from Near-Resonance . . . . . . . . . . . . . . . . . 49
9.4 Thermal Equilibrium from Near-Resonance . . . . . . . . . . . 49
9.5 The Poynting Vector vs ∥f∥ 2 . . . . . . . . . . . . . . . . . . . 50
10 Acoustic Near-Resonance 53
10.1 Radiation vs Acoustic Resonance . . . . . . . . . . . . . . . . 53
10.2 Resonance in String Instrument . . . . . . . . . . . . . . . . . 53
10.3 Fourier Analysis of Near-Resonance . . . . . . . . . . . . . . . 55
10.4 Application to Acoustical Resonance . . . . . . . . . . . . . . 56
10.5 Computational Resonance . . . . . . . . . . . . . . . . . . . . 57
11 Model of Blackbody Radiation 63
11.1 Finite Precision Computation . . . . . . . . . . . . . . . . . . 63
11.2 Radiation and Heating . . . . . . . . . . . . . . . . . . . . . . 64
11.3 Planck as Rayleigh-Jeans with Cut-off . . . . . . . . . . . . . 65
11.4 Planck’s Law: R + H = F . . . . . . . . . . . . . . . . . . . . 65
11.5 Connection to Uncertainty Principle . . . . . . . . . . . . . . . 66
11.6 Stefan-Boltzmann’s Law . . . . . . . . . . . . . . . . . . . . . 66
11.7 Radiative Interaction . . . . . . . . . . . . . . . . . . . . . . . 67
11.8 Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
11.9 Radiative Cooling . . . . . . . . . . . . . . . . . . . . . . . . . 69
11.10Interaction by Shared Force . . . . . . . . . . . . . . . . . . . 69
11.11Generic Nature of Blackbody . . . . . . . . . . . . . . . . . . 70
11.12Cut-Off by Residual Stabilization . . . . . . . . . . . . . . . . 71
11.13Cordination Length . . . . . . . . . . . . . . . . . . . . . . . . 71
12 Universal Blackbody 73
12.1 Kirchhoff and Universality . . . . . . . . . . . . . . . . . . . . 73
12.2 Blackbody as Cavity with Graphite Walls . . . . . . . . . . . 75
13 Model of Universal Blackbody 77
14 Radiative Heat Transfer 79
14.1 Stefan-Boltzmann for Two Blackbodies . . . . . . . . . . . . . 79
14.2 Non-Physical Two-Way Heat Transfer . . . . . . . . . . . . . . 80
15 Greybody vs Blackbody 83
16 2nd Law of Radiation 85
16.1 Irreversible Heating . . . . . . . . . . . . . . . . . . . . . . . . 85
16.2 Mystery of 2nd Law . . . . . . . . . . . . . . . . . . . . . . . 86
16.3 Stefan-Boltzmann Law as 2nd Law . . . . . . . . . . . . . . . 86
17 Reflection vs Blackbody Absorption/Emission 87
18 Blackbody as Transformer of Radiation 89
19 Hot Sun and Cool Earth 91 19.1 Emission Spectra . . . . . . . . . . . . . . . . . . . . . . . . . 91
20 Blackbody Dynamics 93
20.1 Recollection of Model . . . . . . . . . . . . . . . . . . . . . . . 93
20.2 Radiative Interaction of Two Blackbodies . . . . . . . . . . . . 95
21 The Photoelectric Effect 97
21.1 Nobel Prize to Einstein . . . . . . . . . . . . . . . . . . . . . . 97
21.2 The photoelectric effect I . . . . . . . . . . . . . . . . . . . . . 97
21.3 Remark on Viscosity Models . . . . . . . . . . . . . . . . . . . 101
21.4 The Photolelectric Effect II . . . . . . . . . . . . . . . . . . . 101
22 The Compton Effect 103
22.1 The Compton Effect I . . . . . . . . . . . . . . . . . . . . . . 103
22.2 The Compton Effect II . . . . . . . . . . . . . . . . . . . . . . 103

To download the course click on the link below:

http://www.csc.kth.se/~cgjoh/ambsblack.pdf

jeudi 10 janvier 2019

The Theory Of Heat Radiation (1914)

Author: Max Planck

Translator: Morton Masius

Release Date: June 18, 2012

[EBook #40030]

Language: English

PART I FUNDAMENTAL FACTS AND DEFINITIONS

I. General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
II. Radiation at Thermodynamic Equilibrium. Kirchhoff’s Law. Black Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

PART II DEDUCTIONS FROM ELECTRODYNAMICS AND THERMODYNAMICS

I. Maxwell’s Radiation Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
II. Stefan-Boltzmann Law of Radiation . . . . . . . . . . . . . . . . . . . . . . . . 69
III. Wien’s Displacement Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
IV. Radiation of Any Arbitrary Spectral Distribution of Energy. Entropy and Temperature of Monochromatic Radiation . . . . 104
V. Electrodynamical Processes in a Stationary Field of Radiation 124

PART III ENTROPY AND PROBABILITY

I. Fundamental Definitions and Laws. Hypothesis of Quanta . . 133
II. Ideal Monatomic Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
III. Ideal Linear Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
IV. Direct Calculation of the Entropy in The Case of Thermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

PART IV A SYSTEM OF OSCILLATORS IN A STATIONARY FIELD OF RADIATION

I. The Elementary Dynamical Law for The Vibrations of an Ideal Oscillator. Hypothesis of Emission of Quanta . . . . . . . . . . . . . . 177
II. Absorbed Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
III. Emitted Energy. Stationary State . . . . . . . . . . . . . . . . . . . . . . . . . . 189
IV. The Law of the Normal Distribution Of Energy. Elementary Quanta Of Matter and Electricity . . . . . . . . . . . . . . . . . . . . . . . . . . 197

PART V IRREVERSIBLE RADIATION PROCESSES

I. Fields of Radiation in General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
II. One Oscillator in the Field of Radiation . . . . . . . . . . . . . . . . . . . . 230
III. A System of Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
IV. Conservation of Energy and Increase Of Entropy. Conclusion 241
List of Papers on Heat Radiation and the Hypothesis of Quanta by the Author . . . . . . . . . . . . 255
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

To download the book click on the link below:

https://www.gutenberg.org/files/40030/40030-pdf.pdf

dimanche 6 janvier 2019

Courses of Mechanics

(UCSD Physics 110B)

Jim Branson 2012-10-21

Review of Hamiltonian Mechanics (Lecture)

Andy Wolski

University of Liverpool, and the Cockcroft Institute, Daresbury, UK.

November, 2012

Course Outline

Part I (Lectures 1 – 5): Dynamics of a relativistic charged particle in the electromagnetic field of an accelerator beamline.

1. Review of Hamiltonian mechanics
2. The accelerator Hamiltonian in a straight coordinate system
3. The Hamiltonian for a relativistic particle in a general electromagnetic field using accelerator coordinates
4. Dynamical maps for linear elements
5. Three loose ends: edge focusing; chromaticity; beam rigidity.

To download the lecture click on the following link:

https://www.cockcroft.ac.uk/wp-content/uploads/2014/12/wolski-1.pdf

Lagrangian and Hamiltonian Mechanics

Lagrange has perhaps done more than any other to give extent and harmony to such deductive researches by showing that the most varied consequences … may be derived from one radical formula, the beauty of the method so suiting the dignity of the results as to make his great work a kind of scientific poem.

W. R. Hamilton

According to Newton's laws, the incremental work dW done by a force f on a particle moving an incremental distance dx, dy, dz in 3-dimensional space is given by the dot product

Now suppose the particle is constrained in such a way that its position has only two degrees of freedom. In other words, there are two generalized position coordinates X and Y such that the position coordinates x, y, and z of the particle are each strictly functions of these two generalized coordinates. We can then define a generalized force F with the components F_X and F_Y such that

To continue reading click on the following link:

https://www.mathpages.com/home/kmath523/kmath523.htm

Joseph-Louis Lagrange

William Rowan Hamilton

samedi 5 janvier 2019

Vanadium - A Transition Element (1962)

Molecular Spectroscopy (1962)

Lagrangian Mechanics

For other videos click on the following link:

https://www.youtube.com/watch?v=4uJaKJASKnY&list=PLX2gX-ftPVXWK0GOFDi7FcmIMMhY_7fU9

Hamiltonian Mechanics

For the other videos click on the following link:

https://www.youtube.com/watch?v=R_N_2Q4v9jA&list=PLX2gX-ftPVXX6ctceuUBuClP83K5wJtGt

vendredi 4 janvier 2019

Intro to Chemistry, Basic Concepts - Periodic Table, Elements, Metric System & Unit Conversion

Atomic Radius - Basic Introduction - Periodic Table Trends, Chemistry

Bohr Model of the Hydrogen Atom, Electron Transitions, Atomic Energy Levels, Lyman & Balmer Series

Energy Levels of Electrons of Hydrogen atom

As you may remember from chemistry, an atom consists of electrons orbiting around a nucleus. However, the electrons cannot choose any orbit they wish. They are restricted to orbits with only certain energies. Electrons can jump from one energy level to another, but they can never have orbits with energies other than the allowed energy levels.

Let's look at the simplest atom, a neutral hydrogen atom. Its energy levels are given in the diagram below. The x-axis shows the allowed energy levels of electrons in a hydrogen atom, numbered from 1 to 5. The y-axis shows each level's energy in electron volts (eV). One electron volt is the energy that an electron gains when it travels through a potential difference of one volt (1 eV = 1.6 x 10^-19 Joules).

Click on the image for a larger view

Electrons in a hydrogen atom must be in one of the allowed energy levels. If an electron is in the first energy level, it must have exactly -13.6 eV of energy. If it is in the second energy level, it must have -3.4 eV of energy. An electron in a hydrogen atom cannot have -9 eV, -8 eV or any other value in between.

Let's say the electron wants to jump from the first energy level, n = 1, to the second energy level n = 2. The second energy level has higher energy than the first, so to move from n = 1 to n = 2, the electron needs to gain energy. It needs to gain (-3.4) - (-13.6) = 10.2 eV of energy to make it up to the second energy level.

The electron can gain the energy it needs by absorbing light. If the electron jumps from the second energy level down to the first energy level, it must give off some energy by emitting light. The atom absorbs or emits light in discrete packets called photons, and each photon has a definite energy. Only a photon with an energy of exactly 10.2 eV can be absorbed or emitted when the electron jumps between the n = 1 and n = 2 energy levels.

The energy that a photon carries depends on its wavelength. Since the photons absorbed or emitted by electrons jumping between the n = 1 and n = 2 energy levels must have exactly 10.2 eV of energy, the light absorbed or emitted must have a definite wavelength. This wavelength can be found from the equation

E = hc/l,

where E is the energy of the photon (in eV), h is Planck's constant (4.14 x 10^-15 eV s) and c is the speed of light (3 x 10⁸ m/s). Rearranging this equation to find the wavelength gives

l = hc/E.

A photon with an energy of 10.2 eV has a wavelength of 1.21 x 10^-7 m, in the ultraviolet part of the spectrum. So when an electron wants to jump from n = 1 to n = 2, it must absorb a photon of ultraviolet light. When an electron drops from n = 2 to n = 1, it emits a photon of ultraviolet light.

The step from the second energy level to the third is much smaller. It takes only 1.89 eV of energy for this jump. It takes even less energy to jump from the third energy level to the fourth, and even less from the fourth to the fifth.

What would happen if the electron gained enough energy to make it all the way to 0eV? The electron would then be free of the hydrogen atom. The atom would be missing an electron, and would become a hydrogen ion.

The table below shows the first five energy levels of a hydrogen atom.