الجامعة :جامعة المنصورة |
الكلية :كلية العلوم |
القسم :الفيزياء |
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| 1- بيانات المقرر :- |
| | الرمز الكودى: | Phys616 | | اسم المقرر: | ميكانيكا إحصائية | | الفرقة: | درجة الماجستير فى العلوم / الفيزياء / الفيزياء النظرية | | عنوان البرنامج: | - جميع البرامج الاكاديمية
- الماجستير فى الفيزياء النظرية
| | التخصص: | رئيسياً | | عدد الساعات: | نظري: | 2 | فصل: | 1 | عملى: | |
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| 2- أهداف المقرر :- |
| - To introduce statistical mechanics
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| 3- نواتج التعلم المستهدفة للمقرر :- |
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| 4- محتويات المقرر :- |
| | م | الموضوع | الأسبوع |
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| 1 | The Fundamentals of Statistical Mechanics 1 1.1 Introduction 1 1.2 The Microcanonical Ensemble 2 1.2.1 Entropy and the Second Law of Thermodynamics 5 1.2.2 Temperature 8 1.2.3 An Example: The Two State System 11 1.2.4 Pressure, Volume and the First Law of Thermodynamics 14 1.2.5 Ludwig Boltzmann (1844-1906) 16 1.3 The Canonical Ensemble 17 1.3.1 The Partition Function 18 1.3.2 Energy and Fluctuations 19 1.3.3 Entropy 22 1.3.4 Free Energy 25 1.4 The Chemical Potential 26 1.4.1 Grand Canonical Ensemble 27 1.4.2 Grand Canonical Potential 29 1.4.3 Extensive and Intensive Quantities 29 1.4.4 Josiah Willard Gibbs (1839-1903) 30 2. Classical Gases 32 2.1 The Classical Partition Function 32 2.1.1 From Quantum to Classical 33 2.2 Ideal Gas 34 2.2.1 Equipartition of Energy 37 2.2.2 The Sociological Meaning of Boltzmann’s Constant 37 2.2.3 Entropy and Gibbs’s Paradox 39 2.2.4 The Ideal Gas in the Grand Canonical Ensemble 40 2.3 Maxwell Distribution 42 2.3.1 A History of Kinetic Theory 44 2.4 Diatomic Gas 45 2.5 Interacting Gas 48 2.5.1 The Mayer f Function and the Second Virial Coefficient 50 2.5.2 van der Waals Equation of State 53 2.5.3 The Cluster Expansion 55 2.6 Screening and the Debye-H¨uckel Model of a Plasma 60 3. Quantum Gases 62 3.1 Density of States 62 3.1.1 Relativistic Systems 63 3.2 Photons: Blackbody Radiation 64 3.2.1 Planck Distribution 66 3.2.2 The Cosmic Microwave Background Radiation 68 3.2.3 The Birth of Quantum Mechanics 69 3.2.4 Max Planck (1858-1947) 70 3.3 Phonons 70 3.3.1 The Debye Model 70 3.4 The Diatomic Gas Revisited 75 3.5 Bosons 77 3.5.1 Bose-Einstein Distribution 78 3.5.2 A High Temperature Quantum Gas is (Almost) Classical 81 3.5.3 Bose-Einstein Condensation 82 3.5.4 Heat Capacity: Our First Look at a Phase Transition 86 3.6 Fermions 90 3.6.1 Ideal Fermi Gas 91 3.6.2 Degenerate Fermi Gas and the Fermi Surface 92 3.6.3 The Fermi Gas at Low Temperature 93 3.6.4 A More Rigorous Approach: The Sommerfeld Expansion 97 3.6.5 White Dwarfs and the Chandrasekhar limit 100 3.6.6 Pauli Paramagnetism 102 3.6.7 Landau Diamagnetism 104 4. Classical Thermodynamics 108 4.1 Temperature and the Zeroth Law 109 4.2 The First Law 111 4.3 The Second Law 113 4.3.1 The Carnot Cycle 115 4.3.2 Thermodynamic Temperature Scale and the Ideal Gas 117 4.3.3 Entropy 120 4.3.4 Adiabatic Surfaces 123 4.3.5 A History of Thermodynamics 126 4.4 Thermodynamic Potentials: Free Energies and Enthalpy 128 4.4.1 Enthalpy 131 – 1 – 4.4.2 Maxwell’s Relations 131 4.5 The Third Law 133 5. Phase Transitions 135 5.1 Liquid-Gas Transition 135 5.1.1 Phase Equilibrium 137 5.1.2 The Clausius-Clapeyron Equation 140 5.1.3 The Critical Point 142 5.2 The Ising Model 147 5.2.1 Mean Field Theory 149 5.2.2 Critical Exponents 152 5.2.3 Validity of Mean Field Theory 154 5.3 Some Exact Results for the Ising Model 155 5.3.1 The Ising Model in d = 1 Dimensions 156 5.3.2 2d Ising Model: Low Temperatures and Peierls Droplets 157 5.3.3 2d Ising Model: High Temperatures 162 5.3.4 Kramers-Wannier Duality 165 5.4 Landau Theory 170 5.4.1 Second Order Phase Transitions 172 5.4.2 First Order Phase Transitions 175 5.4.3 Lee-Yang Zeros 176 5.5 Landau-Ginzburg Theory 180 5.5.1 Correlations 182 5.5.2 Fluctuations | 1-12 |
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| 5- أساليب التعليم والتعلم :- |
| | م | الاسلوب |
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| - Teaching and Learning Methods 5.1 - Lectures using board. 5.2 - Discussion sessions 5.3 - Problem classes 5.4 - class activity |
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| 6- أساليب التعليم والتعلم للطلاب ذوى القدرات المحدودة :- |
| - 1. Giving them more chance through the office hours to raise their competencies 2. class activity
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| 7- تقويم الطلاب :- |
| أ- التوقيت |
| | م | الطريقة | الأسبوع |
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| 1 | final exam | 12 | | 2 | oral exam | 12 | | 3 | med term exam | 6 |
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| ب- توزيع الدرجات |
| | م | الطريقة | الدرجة |
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| 1 | final exam | 70 | | 2 | oral exam | 10 | | 3 | med term exam | 10 | | 4 | repoort | 10 | | المجموع | 100% |
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| 8- قائمة الكتب الدراسية والمراجع |
| | م | العنصر | النوع |
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| 1 | statistical mechanics | كتب ملزمة |
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| 9- مصفوفة المعارف والمهارات المستهدفة من المقرر الدراسي |
| | م | المحتوى | أسبوع الدراسة |
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| The Fundamentals of Statistical Mechanics 1 1.1 Introduction 1 1.2 The Microcanonical Ensemble 2 1.2.1 Entropy and the Second Law of Thermodynamics 5 1.2.2 Temperature 8 1.2.3 An Example: The Two State System 11 1.2.4 Pressure, Volume and the First Law of Thermodynamics 14 1.2.5 Ludwig Boltzmann (1844-1906) 16 1.3 The Canonical Ensemble 17 1.3.1 The Partition Function 18 1.3.2 Energy and Fluctuations 19 1.3.3 Entropy 22 1.3.4 Free Energy 25 1.4 The Chemical Potential 26 1.4.1 Grand Canonical Ensemble 27 1.4.2 Grand Canonical Potential 29 1.4.3 Extensive and Intensive Quantities 29 1.4.4 Josiah Willard Gibbs (1839-1903) 30 2. Classical Gases 32 2.1 The Classical Partition Function 32 2.1.1 From Quantum to Classical 33 2.2 Ideal Gas 34 2.2.1 Equipartition of Energy 37 2.2.2 The Sociological Meaning of Boltzmann’s Constant 37 2.2.3 Entropy and Gibbs’s Paradox 39 2.2.4 The Ideal Gas in the Grand Canonical Ensemble 40 2.3 Maxwell Distribution 42 2.3.1 A History of Kinetic Theory 44 2.4 Diatomic Gas 45 2.5 Interacting Gas 48 2.5.1 The Mayer f Function and the Second Virial Coefficient 50 2.5.2 van der Waals Equation of State 53 2.5.3 The Cluster Expansion 55 2.6 Screening and the Debye-H¨uckel Model of a Plasma 60 3. Quantum Gases 62 3.1 Density of States 62 3.1.1 Relativistic Systems 63 3.2 Photons: Blackbody Radiation 64 3.2.1 Planck Distribution 66 3.2.2 The Cosmic Microwave Background Radiation 68 3.2.3 The Birth of Quantum Mechanics 69 3.2.4 Max Planck (1858-1947) 70 3.3 Phonons 70 3.3.1 The Debye Model 70 3.4 The Diatomic Gas Revisited 75 3.5 Bosons 77 3.5.1 Bose-Einstein Distribution 78 3.5.2 A High Temperature Quantum Gas is (Almost) Classical 81 3.5.3 Bose-Einstein Condensation 82 3.5.4 Heat Capacity: Our First Look at a Phase Transition 86 3.6 Fermions 90 3.6.1 Ideal Fermi Gas 91 3.6.2 Degenerate Fermi Gas and the Fermi Surface 92 3.6.3 The Fermi Gas at Low Temperature 93 3.6.4 A More Rigorous Approach: The Sommerfeld Expansion 97 3.6.5 White Dwarfs and the Chandrasekhar limit 100 3.6.6 Pauli Paramagnetism 102 3.6.7 Landau Diamagnetism 104 4. Classical Thermodynamics 108 4.1 Temperature and the Zeroth Law 109 4.2 The First Law 111 4.3 The Second Law 113 4.3.1 The Carnot Cycle 115 4.3.2 Thermodynamic Temperature Scale and the Ideal Gas 117 4.3.3 Entropy 120 4.3.4 Adiabatic Surfaces 123 4.3.5 A History of Thermodynamics 126 4.4 Thermodynamic Potentials: Free Energies and Enthalpy 128 4.4.1 Enthalpy 131 – 1 – 4.4.2 Maxwell’s Relations 131 4.5 The Third Law 133 5. Phase Transitions 135 5.1 Liquid-Gas Transition 135 5.1.1 Phase Equilibrium 137 5.1.2 The Clausius-Clapeyron Equation 140 5.1.3 The Critical Point 142 5.2 The Ising Model 147 5.2.1 Mean Field Theory 149 5.2.2 Critical Exponents 152 5.2.3 Validity of Mean Field Theory 154 5.3 Some Exact Results for the Ising Model 155 5.3.1 The Ising Model in d = 1 Dimensions 156 5.3.2 2d Ising Model: Low Temperatures and Peierls Droplets 157 5.3.3 2d Ising Model: High Temperatures 162 5.3.4 Kramers-Wannier Duality 165 5.4 Landau Theory 170 5.4.1 Second Order Phase Transitions 172 5.4.2 First Order Phase Transitions 175 5.4.3 Lee-Yang Zeros 176 5.5 Landau-Ginzburg Theory 180 5.5.1 Correlations 182 5.5.2 Fluctuations | 1-12 |
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| اساتذة المادة: - |
| - السيد عبد العاطى حسن الوكيل
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| رئيس مجلس القسم العلمى: - |
| عادل محمد صادق عجور |
