i) basic concepts of out-of-equilibrium statistical mechanics, ii) open quantum systems, iii) thermodynamics of quantum dynamical processes.
Course Prerequisites
Fundamental notions of thermodynamics. Quantum mechanics. Mathematical methods for physics.
Teaching Methods
Lectures at the blackboard.
Assessment Methods
Oral examination, in order to verify the knowledge of the basic concepts of out-of-equilibrium statistical mechanics, and the comprehension of the methods to study open quantum systems and the thermodynamics of quantum dynamical processes. We recommend focusing on the comprehension of the physics of the subjects, addressing the different approaches (classical, semi-classical, and quantum) to the course topics and the validity regime of the assumptions and approximations involved in different contexts.
Texts
Suggested books: The theory of open quantum systems, H.-P. Breuer and Petruccione (Oxford University Press); The quantum statistics of dynamic processes, E. Fick and G. Sauermann (Springer); Quantum Thermodynamics, P. P. Potts (SciPost Physics Lecture Notes).
Contents
Concepts of out-of-equilibrium statistical physics: open quantum systems, Born-Markoff approximation, Master Equation; semi-group dynamics and Lindblad form; representation of discrete-time dynamics: completely positive maps and Jamiolkowski isomorphism. Langevin equations; Fokker-Planck equations; Green functions method. Quantum regression theorem and correlation functions. Einstein relations between diffusion and drift. Generalized Wigner functions. Numerical methods: cumulative distribution function method; Monte Carlo and Metropolis algorithm; quantum jump approach. Applications: Lorenzian line shape for spontaneous emission; complete Bloch equations for two-level systems, T1 and T2 relaxation times. Radiation in cavity; (nonrelativistic) temperature-dependent Lamb shift. Master equation and Fokker-Planck equation for amplification and loss of radiation. Generalized canonical statistical operator and response theory: observation level and entropy. 1st and 2nd laws of thermodynamics for quantum dynamic processes. Mori scalar product (canonical correlation) and Kubo identity. Operators of the generalized forces. Linear response theory for classical and quantum systems: isothermal and adiabatic suscettibility; dynamic suscettibility; Kubo formula. Relaxation functions. Wiener-Khintchine theorem; Kramers-Kronig relations; Johnson-Nyquist theorem. Langevin-Mori equations. Memory matrix and dynamic Onsager coefficients. 1st and 2nd fluctuation-dissipation theorem. Generalized Master equation: projector method (Nakajima-Zwanzig equation). Entropy irreversible production. Work for out-of-equilibrium trasformations: Crooks relation and Jarzynski's equality. Quantum Carnot and Otto cycles.
