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Course unit
THEORY OF STRONGLY CORRELATED SYSTEMS
SCP7081742, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type |
Scientific-Disciplinary Sector |
Credits allocated |
Educational activities in elective or integrative disciplines |
FIS/03 |
Material Physics |
6.0 |
Course unit organization
Period |
First semester |
Year |
2nd Year |
Teaching method |
frontal |
Type of hours |
Credits |
Teaching hours |
Hours of Individual study |
Shifts |
Lecture |
6.0 |
48 |
102.0 |
No turn |
Examination board
Board |
From |
To |
Members of the board |
2 THEORY OF STRONGLY CORRELATED SYSTEMS |
01/10/2019 |
30/11/2020 |
DELL'ANNA
LUCA
(Presidente)
UMARI
PAOLO
(Membro Effettivo)
SALASNICH
LUCA
(Supplente)
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1 THEORY OF STRONGLY CORRELATED SYSTEMS |
01/10/2018 |
30/11/2019 |
DELL'ANNA
LUCA
(Presidente)
UMARI
PAOLO
(Membro Effettivo)
SALASNICH
LUCA
(Supplente)
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Target skills and knowledge:
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Learning of some phenomena in condensed matter physics by means of the path integral approach |
Examination methods:
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Oral examination |
Assessment criteria:
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Knowledge of the topics of the course, ability of analytic calculus and oral exposition. |
Course unit contents:
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Part 1: Introduction to the path integral
- Brief review of quantum mechanics for single particle and identical particles
- Second quantization: annihilation and creation operators
- Single-particle and double-particle operators
- Bosonic coherent states
- Grassmann algebra
- Fermionic coherent states
- Gaussian integrals with complex and grassmannian variables
- Feynmann integrals
- Patition function and imaginary time
- Equation of motion and stationary phase approximation
- Application of Feynman integrals for a double-well: instanton gas
- Functional integrals with coherent states
- Interacting particles: perturbation theory
- Functional integral for the electromagnetic field
Part 2: Applications
- Coulomb gas
* Perturbative approach
* Random Phase Approximation
* Functional integral method
- Non-interacting bosons: Bose-Einsten condensation
- Goldstone theorem
- Interacting bosons: Superfluidity
* Bogoliubov spectrum
* Landau criterion
* Action for the Goldstone mode
* Phenomenology
- Superconductivity
* Phenomenology and London equations
* Electron-phonon interaction
* Cooper problem
* BCS theory by functional approach: gap equation and critical temperature
* Ginzburg-Landau theory
* Action for the Goldstone mode
* Meissner effect and Higgs mechanism |
Planned learning activities and teaching methods:
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Lectures on blackboard |
Textbooks (and optional supplementary readings) |
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J.W. Negele, H. Orland, Quantum Many-Particle Systems. --: --, --.
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N. Nagaosa, Quantum Field Theory in Condensed Matter Physics. --: --, --.
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A. Altland, B. Simons, Condensed Matter Field Theory. --: --, --.
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Innovative teaching methods: Teaching and learning strategies
Innovative teaching methods: Software or applications used
- Moodle (files, quizzes, workshops, ...)
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