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.
Lesson period: Second semester
(In case of multiple editions, please check the period, as it may vary)
· 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
Prerequisites for admission
Thermodynamics, Quantum Mechanics and basic concepts of Statistical Mechanics
· 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: http://dgallifs.ariel.ctu.unimi.it/v3/Home/
Assessment methods and Criteria
The exam consists of an oral discussion, of about 60 minutes, which focuses on the topics covered in the course 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 course, the deepening and understanding of the topic chosen by the student and the clarity of the presentation will be evaluated.