Dipartimento di Fisica

Advanced Statistical Mechanics

- Course:
- Laurea magistrale in Scienze fisiche
- Teachers:
- Massimiliano Sacchi (CNR)
- Academic year:
- 2017/2018 (Altri: 2016/2017 2015/2016 2014/2015 2013/2014)
- Semester:
- I
- Language:
- Italiano / english friendly
- Code:
- 500599
- SSD:
- FIS/02
- Credits:
- 6
- Hours:
- 48

Educational goals

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

Prerequisites

Quantum mechanics; mathematical methods for physics.

Programme

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 equality.

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 equality.

Bibliography

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).

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).

Exam

Oral examination.