Lecture notes provided on the moodle page of the course https://e-l.unifi.it/course/view.php?id=15894
Recommended books:
Steven Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Westview Press 1994, ISBN-13: 9780738204536; Crispin W. Gardiner, Handbook of Stochastic Methods, Springer 2009, ISBN-13: 9783540707127 (for the lectures devoted to the physics of complex systems)
E. Hecht, Optics (for the lectures on waves and optics)
“Quantum Chance: Nonlocality, Teleportation and Other Quantum Marvels”
Nicolas Gisin – Springer 2014
Learning Objectives
To provide students the elements to understand some aspects of quantum physics of complex systems, wave phenomena, mechanics and their applications.
Prerequisites
Basic knowledge of mechanics, thermodynamics and electromagnetism. Basic knowledge of mathematical analysis and geometry.
Teaching Methods
Lectures, computer sessions and visit to the labs.
Further information
Moodle page of the course:https://e-l.unifi.it/course/view.php?id=15894
Type of Assessment
Oral exam on the covered topics, with emphasis on a specific item agreed with the lecturers.
Course program
Phyics of Complex Systems
Low dimensional models. Fixed points, limit cycles, chaos. Bifurcaton theory. Applications. Stochastic processes. Markov processes. Master equation. Fokker-Planck and Langevin equations. From stochastic to deterministic models: mean-field approximations and the role of fluctuations. Montecarlo simulations.
-Waves and Optics-
Harmonic oscillations, resonance, quality factor, tuning circuits, linewidth of a transition
Vibrating string, d'Alembert equation, Fourier analysis, sould waves, electromagnetic waves, electromagnetic spectrum. Plane and spherical waves. Poynting Theorem. Absorption, emission, linewidth. Dispersion in optical materials. Reflection in metals.
Interference, spatial and temporal coherence. Fraunhofer and Fresnel diffraction. Geometrical optics. Optical instruments
Elements of Quantum Mechanics: wave-particle duality, 2 levels systems; Quantum states superpositions (single particle): introduction of the Bloch sphere (Q-bit), no cloning theorem and quantum cryptography (BB84); Two particles superpositions (EPR): Entanglement, Bell inequalities (and experimental verification), quantum teleportation;
Lasers: working principles, applications in mechanics (laser cutting, 3D-printing, sensors)