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1 = Introduction to Mathematical Physics, Spring 2012 =
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3 = (% style="color: rgb(51,51,51);" %)**Introduction to Statistical Mechanics**(%%) =
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5 === Lecturer ===
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7 [[Antti Kupiainen>>doc:mathstatHenkilokunta.Kupiainen, Antti]]
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9 === Scope ===
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11 10 cu.
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13 === Type ===
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15 Advanced studies
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17 === (% style="color: rgb(51,51,51);" %)**Description**(%%) ===
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19 Statistical mechanics was developed in the 19th century to study mechanical systems
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21 such as gases with a very large number of degrees of freedom. A detailed microscopic
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23 study of such systems is out of question and one has to resort to a probabilistic description.
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25 In the 20th century powerful methods were developed for the study of phenomena such
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27 as phase transitions and non-equilibrium states. The framework of statistical mechanics
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29 is quite universal and can be applied to a variety of problems ranging from quantum
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31 field theory to biological and social systems as well as questions in pure mathematics.
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33 The common feature of all these is the presence of a large number of elementary units
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35 interacting with each other and giving rise to interesting collective behaviour.
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37 The course provides an introduction to some basic topics and techniques of statistical
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39 mechanics from the mathematical point of view. The first half deals with equilibrium
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41 statistical mechanics of "spin systems" where in the simplest case the elementary units
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43 are binary variables. We study low and high temperature behavior as well as critical
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45 behaviour with elements of the renormalization group. The second half adresses
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47 nonequlibrium behavior and introduces Boltzmann equation and hydrodynamic limit.
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49 The course is meant for mathematics students interested in probability who want
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51 to learn the basics of statistical mechanics without physics background and physics
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53 students who want to have a more conceptual and mathematical treatment than
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55 in physics courses.
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57 === (% style="color: rgb(51,51,51);" %)**Contents**(%%) ===
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59 Independent random variables (infinite temperature): ensembles
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61 Ising model: low temperature and high temperature expansion
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63 1st order phase transition
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65 General spin systems
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67 Application to chaotic dynamical systems
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69 2nd order phase transition, critical point
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71 Introduction to renormalization group and scaling limit
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73 Disordered systems: Ising spin glass and random field Ising model
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75 Introduction to non-equlibrium
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77 Boltzmann equation
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79 Hydrodynamic limit
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81 === Prerequisites ===
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83 For the main bulk of the course the mathematics is developed on the spot and
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85 no physics background is assumed. A few lectures deal with more advanced issues
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87 and are not required for the exam.
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89 === Lectures ===
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91 Weeks 3-9 and 11-18, Tuesday 14-16, Thursday 14-16 in room C123.
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93 Easter holiday 5.-11.4.
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95 [[Lecture notes>>attach:book2.pdf]]
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97 [[Extra material on dynamical systems>>attach:MaFy2012SRB.pdf]]
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99 === (% style="color: rgb(51,51,51);" %)**NOTE! - The lecture notes have been updated!**(%%) ===
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101 === (% style="color: rgb(51,51,51);" %)**NEW! There will be no lecture on Tuesday April 24!**(%%) ===
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103 === Exams ===
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105 === (% style="color: rgb(51,51,51);" %)**If you are interesting in taking the exam for the course, let the assistant know what would be a suitable date for you.**(%%) ===
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107 === Bibliography ===
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109 Lecture notes
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111 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57357||shape="rect"]] ===
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113 Did you forget to register? [[What to do>>doc:mathstatOpiskelu.Kysymys4]].
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115 === Exercise groups ===
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117 === (% style="color: rgb(51,51,51);" %)**Note! First exercise session is on Thursday February 2**(%%) ===
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119 === (% style="color: rgb(51,51,51);" %)**Note! The time and place for the exercises changes starting from Friday March 16.**(%%) ===
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121 |=(((
122 Group
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124 Day
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126 Time
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128 Place
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130 Instructor
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133 1.
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135 Fri\\
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137 10-12
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139 C129
140 )))|(((
141 Christian Webb
142 )))
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144 [[Exercise 1>>attach:ex1.pdf]]       [[Solutions 1>>attach:solution1.pdf]]
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146 [[Exercise 2>>attach:ex2.pdf]]       [[Solutions 2>>attach:solution2.pdf]]
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148 [[Exercise 3>>attach:ex3.pdf]]       [[Solutions 3>>attach:solution3.pdf]]
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150 [[Exercise 4>>attach:ex4.pdf]]   [[Solutions 4>>attach:solution4.pdf]]
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152 [[Exercise 5>>attach:ex5.pdf]]   [[Solutions 5>>attach:solution5.pdf]]
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154 [[Exercise 6>>attach:ex6.pdf]]   [[Solutions 6>>attach:solution6.pdf]]
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156 [[Exercise 7>>attach:ex7.pdf]]   [[Solutions 7>>attach:solution7.pdf]]
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158 [[Exercise 8>>attach:ex8.pdf]]   [[Solutions 8>>attach:solution8.pdf]]
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160 [[Exercise 9>>attach:ex9.pdf]]   [[Solutions 9>>attach:solution9.pdf]]
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162 [[Exercise 10>>attach:ex10.pdf]]     [[Solutions 10>>attach:solution10.pdf]]