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Quantum mechanics of many-body systems

01MLOKG

A.A. 2019/20

Course Language

Inglese

Course degree

Doctorate Research in Physics - Torino

Course structure
Teaching Hours
Lezioni 30
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Penna Vittorio Professore Associato FIS/03 30 0 0 0 9
Teaching assistant
Espandi

Context
SSD CFU Activities Area context
*** N/A ***    
2019/20
PERIOD: NOVEMBER - JANUARY This course presents the quantum-field theory approach to many-body systems. The main topics discussed are: the lagrangian/hamiltonian formulation of classical mechanics and the Hamilton approach to classical field theory, the quantization of nonrelativistic Schroedinger equation and the definition of creation, destruction, and number operators, the properties of bosonic/fermionic fields (and, in particular, the notion of Fermi-Dirac and Bose-Einstein statistics, the Pauli principle and the spin-statistics theorem), and the Bose-Einstein gas of interacting particles within the Bogoliubov scheme. The field-theory approach is then applied to derive the Bose-Hubbard model currently employed to describe condensed bosons trapped in optical lattices. Finally, the statistical-mechanics approach to the ideal Bose-Einstein and Fermi-Dirac gases is discussed.
PERIOD: NOVEMBER - JANUARY This course presents the quantum-field theory approach to many-body systems. The main topics discussed are: the lagrangian/hamiltonian formulation of classical mechanics and the Hamilton approach to classical field theory, the quantization of nonrelativistic Schroedinger equation and the definition of creation, destruction, and number operators, the properties of bosonic/fermionic fields (and, in particular, the notion of Fermi-Dirac and Bose-Einstein statistics, the Pauli principle and the spin-statistics theorem), and the Bose-Einstein gas of interacting particles within the Bogoliubov scheme. The field-theory approach is then applied to derive the Bose-Hubbard model currently employed to describe condensed bosons trapped in optical lattices. Finally, the statistical-mechanics approach to the ideal Bose-Einstein and Fermi-Dirac gases is discussed.
Course contents: The Lagrange and Hamilton formulation of classical dynamics; Hamilton approaches to Classical field theory. Nonrelativistic quantum field theory of many-body systems: Quantization of Schroedinger equation; the N representation, creation, destruction and number operators. Properties of bosonic and fermionic fields; Bose-Einstein and Fermi-Dirac statistics; Pauli principle and spin statistics theorem; From many-body systems to quantum field theory; nearly-ideal, degenerate BE gases: Bogoliubov approach; superfluidity. The Bose-Hubbard model for condensed bosons trapped in optical lattices. Statistical mechanics of ideal Bose-Einstein and Fermi-Dirac gases.
Course contents: The Lagrange and Hamilton formulation of classical dynamics; Hamilton approaches to Classical field theory. Nonrelativistic quantum field theory of many-body systems: Quantization of Schroedinger equation; the N representation, creation, destruction and number operators. Properties of bosonic and fermionic fields; Bose-Einstein and Fermi-Dirac statistics; Pauli principle and spin statistics theorem; From many-body systems to quantum field theory; nearly-ideal, degenerate BE gases: Bogoliubov approach; superfluidity. The Bose-Hubbard model for condensed bosons trapped in optical lattices. Statistical mechanics of ideal Bose-Einstein and Fermi-Dirac gases.
ModalitÓ di esame:
Exam:


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