01HEQUU

A.A. 2023/24

Course Language

Inglese

Degree programme(s)

Course structure

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Lecturers

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2023/24

The course is meant to give the theoretical basis needed to understand nonequilibrium quantum phenomena, particularly concerning electrons, photons and phonons. The corresponding evolution equations will be derived, and the linear response to perturbations, which includes fluctuation-dissipation relations, and the modern theory of fluctuations of observables in nonequilibrium systems will be illustrated. These results are of particular interest in the study of systems in conditions far away from equilibrium, and in the modern bio- and nano-technology.

The course is meant to give the theoretical basis needed to understand nonequilibrium quantum phenomena, particularly concerning electrons, photons and phonons. The corresponding evolution equations will be derived, and the linear response to perturbations, which includes fluctuation-dissipation relations, and the modern theory of fluctuations of observables in nonequilibrium systems will be illustrated. These results are of particular interest in the study of systems in conditions far away from equilibrium, and in the modern bio- and nano-technology.

Expected knowledge:
- theory of nonequilibrium quantum systems and of their response to perturbations
- models of nano-structured materials of interest in the design of accurate sensors
Expected competences and skills:
- ability to handle analytic and modeling techniques to treat nonequilibrium systems
- ability to apply the acquired knowledge to the design of sensors
- ability to communicate in a clear and unambiguous way theoretical issues related to the design and manufacture of smart sensors both in writing and oral form to both specialists and non- specialists;
- development of self-learning skills, allowing the students to continue to autonomously learn new techniques and to design methodologies of investigation not necessarily during the classes.

Expected knowledge:
- theory of nonequilibrium quantum systems and of their response to perturbations
- models of nano-structured materials of interest in the design of accurate sensors
Expected competences and skills:
- ability to handle analytic and modeling techniques to treat nonequilibrium systems
- ability to apply the acquired knowledge to the design of sensors
- ability to communicate in a clear and unambiguous way theoretical issues related to the design
and manufacture of smart sensors both in writing and oral form to both specialists and non-
specialists;
- development of self-learning skills, allowing the students to continue to autonomously learn
new techniques and to design methodologies of investigation not necessarily during the
classes.

Mathematics and physics notions common to the bachelor programs in science and technology, as well as in the first year of the present Master program. For instance, basic notions of quantum physics, of classical mechanics and thermodynamics, and the mathematics for quantum mechanics (algebra, differrential equations, integration theory, complex variables) are required. Also, notions of statistical mechanics and information theory will be useful.

Mathematics and physics notions common to the bachelor programs in science and technology, as well as in the first year of the present Master program. For instance, basic notions of quantum physics, of classical mechanics and thermodynamics, and the mathematics for quantum mechanics (algebra, differrential equations, integration theory, complex variables) are required. Also, notions of statistical mechanics and information theory will be useful.

The course consists of a single module in which the following subjects are treated:
1. density matrix and Lindblad equation;
2. kinetic theory of quantum gases, photons and phonons;
3. perturbative expansions;
4. fluctuation-dissipation relation and linear response;
5. dissipation and entropy production;
6. quantum disordered systems and applications.

The course consists of a single module in which the following subjects are treated:
1. density matrix and Lindblad equation;
2. kinetic theory of quantum gases, photons and phonons;
3. perturbative expansions;
4. fluctuation-dissipation relation and linear response;
5. dissipation and entropy production;
6. quantum disordered systems and applications.

The course consists of blackboard lectures covering the topics described in the Course Topics section, supported at times by projected slides and videos, mean to exemplify the theory. The teacher’s notes and slides will be made available to students in pdf format on the Internet Didactic Portal, together with all presented material.

The course consists of blackboard lectures covering the topics described in the Course Topics section, supported at times by projected slides and videos, mean to exemplify the theory. The teacher’s notes and slides will be made available to students in pdf format on the Internet Didactic Portal, together with all presented material.

Apart from the teacher’s notes and slides, the following texts are useful to deepen the topics of the course:
- Ryogo Kubo, Morikazu Toda; Natsuki Hashitsume, Statistical Physics II, Nonequilibrium Statistical Mechanics; Springer Verlag, 1991
- D. A. Kirzhnits, Field Theoretical Methods in Many-Body Systems, Pergamon Press (1967)
- Supriyo Datta; Quantum Transport: Atom to Transistor; Cambridge University Press, 2005
- A. Jungel, Transport Equations for Semiconductors, Springer, 2009
- Research papers on subjects of interest to the students will be provided

Apart from the teacher’s notes and slides, the following texts are useful to deepen the topics of the course:
- Ryogo Kubo, Morikazu Toda; Natsuki Hashitsume, Statistical Physics II, Nonequilibrium
Statistical Mechanics; Springer Verlag, 1991
- D. A. Kirzhnits, Field Theoretical Methods in Many-Body Systems, Pergamon Press (1967)
- Supriyo Datta; Quantum Transport: Atom to Transistor; Cambridge University Press, 2005
- A. Jungel, Transport Equations for Semiconductors, Springer, 2009
- Research papers on subjects of interest to the students will be provided

...
Written essay on a subject related to the material of the classes.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

Written essay on a subject related to the material of the classes.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.

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