2017/2018

2017/2018

DM270

FIS/02 (THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS)

DEPARTMENT OF PHYSICS

Fisica della materia

1°

1st semester (02/10/2017 - 19/01/2018)

6

48 lesson hours

Italian (or English, if requested).

ORAL TEST

SACCHI MASSIMILIANO (titolare) - 6 ECTS

Quantum mechanics; mathematical methods for physics.

i) basic concepts of out-of-equilibrium statistical mechanics, ii) open quantum systems iii) thermodynamics of quantum dynamical processes.

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.

Lectures at the blackboard.

Suggested books:
The theory of open quantum systems, H.-P. Breuer and Petruccione (Oxford University Press);
Statistical physics II: Nonequilibrium statistical mechanics, R. Kubo, M, Toda, and N. Hashitsume (Spinger);
The quantum statistics of dynamic processes, E. Fick and G. Sauermann (Springer).

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.

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.