Advanced Statistical Physics
A.Y. 2024/2025
Learning objectives
The course aims to provide an overview of advanced Statistical Physics and its applications to complex systems and physical systems characterized by an enormous number of degrees of freedom, from the classical regime to the quantum degenerate regime. Attention will be given to emerging phenomena such as phase transitions, including topological phases, critical phenomena and universality
Expected learning outcomes
The course aims to provide students with:
· methods for determining the statistical properties of a complex system based on the behavior of its microscopic constituents.
· familiarity with the applications of these methods to important classical and quantum complex systems
· the concept of correlation function and its link with the scattering of radiation from a system
· advanced theories and phenomenological aspects of phase transitions and critical phenomena.
· methods for determining the statistical properties of a complex system based on the behavior of its microscopic constituents.
· familiarity with the applications of these methods to important classical and quantum complex systems
· the concept of correlation function and its link with the scattering of radiation from a system
· advanced theories and phenomenological aspects of phase transitions and critical phenomena.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
· Information entropy and the maximum entropy principle
· Mean field approaches
· Classical and quantum phase transitions
· Order parameter, Goldstone modes, Mermin-Wagner theorem, topological defects, winding number
· Quantum statistical mechanics
· Linear response theory and scattering experiments
· Quantum gases and liquids
· Duality and quantum-classical isomorphism
· Critical phenomena, universality and renormalization group
· The Kosterlitz-Thouless transition, Luttinger liquids
· Mean field approaches
· Classical and quantum phase transitions
· Order parameter, Goldstone modes, Mermin-Wagner theorem, topological defects, winding number
· Quantum statistical mechanics
· Linear response theory and scattering experiments
· Quantum gases and liquids
· Duality and quantum-classical isomorphism
· Critical phenomena, universality and renormalization group
· The Kosterlitz-Thouless transition, Luttinger liquids
Prerequisites for admission
Thermodynamics, Quantum Mechanics and basic concepts of Statistical Mechanics
Teaching methods
Delivery method: traditional, lectures
Attendance: strongly recommended
Attendance: strongly recommended
Teaching Resources
· H. Nishimori and G. Ortiz, "Elements of Phase Transitions and Critical Phenomena", Oxford
· R. K. Pathria, "Statistical mechanics", II ed., Oxford
· L. Pitaevskii, S. Stringari "Bose Einstein Condensation", Clarendon Press - Oxford
· A.J. Leggett, Quantum Liquids, Oxford University Press
· The material presented and discussed in the individual lectures is made available on the Ariel website of the course.
· R. K. Pathria, "Statistical mechanics", II ed., Oxford
· L. Pitaevskii, S. Stringari "Bose Einstein Condensation", Clarendon Press - Oxford
· A.J. Leggett, Quantum Liquids, Oxford University Press
· The material presented and discussed in the individual lectures is made available on the Ariel website of the course.
Assessment methods and Criteria
The exam consists of an oral discussion, of about 60 minutes, which focuses on the topics covered in the lectures with particular attention to a topic chosen by the student. The student's ability to link the main topic of the discussion to the general concepts introduced in the lectures, the deepening and understanding of the topic chosen by the student and the clarity of the presentation will be evaluated.
FIS/03 - PHYSICS OF MATTER - University credits: 6
Lessons: 42 hours
Professors:
Galli Davide Emilio, Kwon Woo Jin
Professor(s)
Reception:
Wednesday 14:30-16:00, or in other days by appointment (contact me by e-mail or telephone)
Dip. di Fisica, stanza A/T/S5b (piano 0 edificio LITA), via Celoria, 16
Reception:
by appointment by email
via celoria 16