Each student is expected to achieve: - a sufficient confidence of the mathematics used to describe the quantum systems studied in the course; - a sufficient understanding of the quantum mechanics underlying the physical systems studied in the course; - a sufficient understanding of the fundamental differences among the classical, semi-classical, and quantum models of solids; - an objectively determinable level of knowledge of the theory of non-equilibrium quantum systems and of their response to perturbations; - an objectively determinable level of knowledge of the models of nano-structured materials of interest in the design of accurate sensors; Each student is expected to gain the following competences and skills: - ability to handle analytic and modeling techniques to describe non-equilibrium systems; - ability to apply the acquired knowledge to the design of sensors; - ability to communicate the theoretical issues related to the design and manufacturing of smart sensors clearly, concisely, rigorously, and unambiguously both in writing and in 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.

Students are required to possess the notions of Mathematics and Physics that are common to the bachelor programs in science and technology as well as in the first year of the present Master program. In particular, it is necessary to be familiar with the fundamentals of classical mechanics and thermodynamics, with the basic notions of quantum physics as well as with the mathematics for quantum mechanics (complex variables, linear algebra, differential equations, integration theory). Notions of statistical mechanics and information theory are useful.

The course consists of a single module in which the following subjects are presented: 1. kinetic theory of quantum gases, photons ,and phonons (15 hours, comprehensive of both lectures and exercises: 12 h + 3 h); 2. density matrix and perturbative expansions (11 hours); 4. fluctuation-dissipation relation and linear response (15 hours); 5. Lindblad equation (4 hours); 6. dissipation and entropy production (6 hours); 7. quantum disordered systems and applications (9 hours).

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

Apart from the teachers' 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.

Lecture notes; Text book;

Exam: Individual essay;

Consistently with the goals of the course, the exam aims at assessing the students' ability in dealing with the mathematical formalism of quantum mechanics at an advanced level, and with its applications to formulate hypotheses and models to solve practical problems of interest in science and technology. The exams consists of a written essay on a subject related to the material of the classes, and it lasts 45 minutes. Two questions will be proposed, and each student will choose one of such questions. Each question will take the form: "Within the framework of (one or two of the six chapters of the course), illustrate the main concepts and equations, and describe applications of interest in science and technology." During the exam, the students will be allowed to consult the material made available during the course. The maximum grade is 32, which corresponds to 30L (30 cum laude). It is obtained by correctly reporting on all of the crucial points of the chosen subject. In the case of a lower grade, students may require to do an oral exam, and their final score will be either incremented or decremented, depending on the quality of their oral part of the exam. This oral part will involve both theoretical questions and exercises, and may contribute three (3) points to the total score at the most, while it may lead to fail the exam if serious flaws in a student's preparation are detected. Note that the professors of the course may require a student to do the oral exam if they find it necessary to ascertain the final mark of the exam of that student. The criteria for assessing the final mark are: (i) the evaluation of the level of understanding reached by each examined student in the proposed topics by determining the clarity, conciseness, and mathematical rigor of the written essay; (ii) the evaluation of the physical insight provided by the description of the potential "applications of interest in science and technology". Both of the above reported criteria apply also to the possible oral exam, which may be required either by a student willing to improve the mark obtained in the written essay or by one or both of the professors, if deemed necessary.

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.