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    Lucilla DE ARCANGELIS

    Insegnamento di STATISTICAL MECHANICS

    Corso di laurea magistrale in PHYSICS

    SSD: FIS/02

    CFU: 8,00

    ORE PER UNITÀ DIDATTICA: 72,00

    Periodo di Erogazione: Secondo Semestre

    Italiano

    Lingua di insegnamento

    INGLESE

    Contenuti

    Synthetic Program:

    1) Short Review of statistical ensembles
    2) Phase Transitions and Critical Phenomena
    3) Mean Field Theories
    4) Renormalization Group
    5) Kinetic Theory and Boltzmann Equation
    6) Markovian processes

    Testi di riferimento

    General reference books
    - Statistical Mechanics- Author: K. Huang, WILEY
    - Meccanica Statistica Elementare – Authors: M. Falcioni and A. Vulpiani,
    Springer-Verlag Mailand
    -Statistical Mechanics - Authors: R K Pathria, Paul D. Beale, AP

    For the part on Critical Phenomena
    - Introduction to Phase Transitions and Critical Phenomena -
    Author: E. Stanley, Oxford Science
    For the recalls of statistical ensembles
    - Introduction to Modern Statistical Mechanics - Author: D. Chandler,
    Oxford University Press

    Obiettivi formativi

    The course is aimed at providing basic notions and methods of statistical physics and at the same time at presenting its modern applications in physics and beyond.
    The course is therefore finalized to a learning process at the end of which the student will be able to manage a broad range of theoretical methods of general use in many branches of science
    Concerning communicative skills, the course is aimed at developing the student's ability in presenting in a clear and rigorous ways statistical methods

    Prerequisiti

    Statistical ensembles, basic probability theory, operator formalism

    Metodologie didattiche

    The course is structured in 52 hours of frontal lectures (6h for recalls of introductory concepts, 24h for Phase Transitions and Critical Phenomena, Mean Field Theories, Renormalization Group, 22 h for Kinetic Theory and Boltzmann Equation and Markovian processes)
    16 hours for classroom exercises and 4 hours of assisted study.
    Attendance is not compulsory but strongly recommended.

    Metodi di valutazione

    The examination is oral interview based on the discussion of the arguments illustrated during the course with a typical duration of 45 minutes. Together with the evaluation of the degree of knowledge reached by the student, the interview is aimed to evaluate the students' ability in managing statistical methods and in demonstrating theorems at their basis.

    Programma del corso

    1) A short review of statistical ensembles (1 CFU)


    2) Kinetic Theory and Markov Chains (2 CFU)
    The Boltzmann Equation- H theorem and its objections – The Master Equation – The Fokker-Plank Equation – The Langevin Equation

    3) Fluctuation-Dissipation theorems (1CFU) - Einstein Fluctuation theory – Linear Response Theory – Onsager Relations

    4) Phase Transitions and Critical Phenomena (2 CFU)
    The order parameter – The Correlation function – critical exponents – Scale invariance – The Ising and granular gas model – The Onsager Solution in one dimension. Random percolation.

    5) Mean field theories (1CFU): Landau theory, Weiss theory and Ornstein-Zernicke theory.
    6) Renormalization Group (1CFU) Block spins – The one-dimensional Ising model – The gaussian model - Migdal-Kadanoff method for the two-dimensional Ising model. Random Percolation on the triangular lattice.

    English

    Teaching language

    English

    Contents

    Synthetic Program:

    1) Short Review of statistical ensembles
    2) Phase Transitions and Critical Phenomena
    3) Mean Field Theories
    4) Renormalization Group
    5) Kinetic Theory and Boltzmann Equation
    6) Markovian processes

    Textbook and course materials

    General reference books
    - Statistical Mechanics- Author: K. Huang, WILEY
    - Meccanica Statistica Elementare – Authors: M. Falcioni and A. Vulpiani,
    Springer-Verlag Mailand
    -Statistical Mechanics - Authors: R K Pathria, Paul D. Beale, AP

    For the part on Critical Phenomena
    - Introduction to Phase Transitions and Critical Phenomena -
    Author: E. Stanley, Oxford Science
    For the recalls of statistical ensembles
    - Introduction to Modern Statistical Mechanics - Author: D. Chandler,
    Oxford University Press

    Course objectives

    The course is aimed at providing basic notions and methods of statistical physics and at the same time at presenting its modern applications in physics and beyond.
    The course is therefore finalized to a learning process at the end of which the student will be able to manage a broad range of theoretical methods of general use in many branches of science
    Concerning communicative skills, the course is aimed at developing the student's ability in presenting in a clear and rigorous ways statistical methods

    Prerequisites

    Statistical ensembles, basic probability theory, operator formalism

    Teaching methods

    The course is structured in 52 hours of frontal lectures (6h for recalls of introductory concepts, 24h for Phase Transitions and Critical Phenomena, Mean Field Theories, Renormalization Group, 22 h for Kinetic Theory and Boltzmann Equation and Markovian processes)
    16 hours for classroom exercises and 4 hours of assisted study.
    Attendance is not compulsory but strongly recommended.

    Evaluation methods

    The examination is oral interview based on the discussion of the arguments illustrated during the course with a typical duration of 45 minutes. Together with the evaluation of the degree of knowledge reached by the student, the interview is aimed to evaluate the students' ability in managing statistical methods and in demonstrating theorems at their basis.

    Course Syllabus

    1) A short review of statistical ensembles (1 CFU)


    2) Kinetic Theory and Markov Chains (2 CFU)
    The Boltzmann Equation- H theorem and its objections – The Master Equation – The Fokker-Plank Equation – The Langevin Equation

    3) Fluctuation-Dissipation theorems (1CFU) - Einstein Fluctuation theory – Linear Response Theory – Onsager Relations

    4) Phase Transitions and Critical Phenomena (2 CFU)
    The order parameter – The Correlation function – critical exponents – Scale invariance – The Ising and granular gas model – The Onsager Solution in one dimension. Random percolation.

    5) Mean field theories (1CFU): Landau theory, Weiss theory and Ornstein-Zernicke theory.
    6) Renormalization Group (1CFU) Block spins – The one-dimensional Ising model – The gaussian model - Migdal-Kadanoff method for the two-dimensional Ising model. Random Percolation on the triangular lattice.

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