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Coherent-state approach to complex quantum systems

01MLPKG

A.A. 2018/19

Course Language

Inglese

Course degree

Doctorate Research in Physics - Torino

Course structure
Teaching Hours
Lezioni 20
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Penna Vittorio Professore Associato FIS/03 20 0 0 0 9
Teaching assistant
Espandi

Context
SSD CFU Activities Area context
*** N/A ***    
2018/19
PERIOD: NOVEMBER This course presents different methods to approach the dynamics of quantum systems whose complex behavior is due to both their many-body and nonlinear character. Different topics are discussed such as the coherent-state method, the dynamical-algebra method, the solution of Schroedinger problems by means of the Time-dependent variational principle, and the adiabatic approximation. Such theoretic techniques are applied to physical systems of condensed-matter Physics and of Quantum Optics such as the parametric-amplifier models, the interaction of two-level atom with radiation, superfluids confined in optical lattices, arrays of Bose-Einstein condensates and the fermion Hubbard model.
PERIOD: NOVEMBER This course presents different methods to approach the dynamics of quantum systems whose complex behavior is due to both their many-body and nonlinear character. Different topics are discussed such as the coherent-state method, the dynamical-algebra method, the solution of Schroedinger problems by means of the Time-dependent variational principle, and the adiabatic approximation. Such theoretic techniques are applied to physical systems of condensed-matter Physics and of Quantum Optics such as the parametric-amplifier models, the interaction of two-level atom with radiation, superfluids confined in optical lattices, arrays of Bose-Einstein condensates and the fermion Hubbard model.
1. Three independent definitions of Coherent States (CS). Definition of Dynamical Algebra and spectrum generating algebra. 2. Solution of the Schroedinger equation for the harmonic oscillator (HO) within the CS picture. Semiclassical charcter of CS and of CS Manifold. 3. Generalized HO Hamiltonian with time-dependent parameters as a model for the interaction between radiation and atomic systems. The model dynamics in terms of CS. 4. Solution of problems involving time-dependent Hamiltonian within the adiabatic approximation scheme. Berry's phase and geometric correction. Applications. 5. Generalized CS for algebras with a more complex structure. CS of group SU(2) and SU(3). Arbitrariness of the extremal vector. CS of su(1,1) and squeezing effect. 6. Isotropy Group and of Maximal Isotropy subalgebra. Semiclassical character of generalized CS and the extremal-vector choice. Applications. 7. Quantum dynamics of many-particle lattice models based on the CS picture and the time-dependent variational principle (TDVP). Applications. 8. Semiclassical approach to the dynamics of Bose condensates in a 2/3-well system. 9. Interacting bosons in optical lattices: the Bose-Hubbard model. Properties. CS variational approach. The Hubbard model and spin coherent states.
1. Three independent definitions of Coherent States (CS). Definition of Dynamical Algebra and spectrum generating algebra. 2. Solution of the Schroedinger equation for the harmonic oscillator (HO) within the CS picture. Semiclassical charcter of CS and of CS Manifold. 3. Generalized HO Hamiltonian with time-dependent parameters as a model for the interaction between radiation and atomic systems. The model dynamics in terms of CS. 4. Solution of problems involving time-dependent Hamiltonian within the adiabatic approximation scheme. Berry's phase and geometric correction. Applications. 5. Generalized CS for algebras with a more complex structure. CS of group SU(2) and SU(3). Arbitrariness of the extremal vector. CS of su(1,1) and squeezing effect. 6. Isotropy Group and of Maximal Isotropy subalgebra. Semiclassical character of generalized CS and the extremal-vector choice. Applications. 7. Quantum dynamics of many-particle lattice models based on the CS picture and the time-dependent variational principle (TDVP). Applications. 8. Semiclassical approach to the dynamics of Bose condensates in a 2/3-well system. 9. Interacting bosons in optical lattices: the Bose-Hubbard model. Properties. CS variational approach. The Hubbard model and spin coherent states.
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