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. In particular, basic notions of quantum physics, of classical mechanics and thermodynamics, as well as the mathematics for quantum mechanics (algebra, differrential equations, integration theory, complex variables) are required. Notions of statistical mechanics and information theory are also useful.

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

The course consists of blackboard lectures covering the topics described in the Course Topics section, supported at times by projected slides and videos, meant 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

Lecture notes; Text book;

Exam: Optional oral 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 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 the student will choose one. 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, students will be allowed to consult the material made available during the course. The maximum grade is 32, which corresponds to 30L. It is obtained by correctly reporting on all the crucial points of the chosen subject. In case of lower grade, the student may require to continue the exam orally, and the result will be either incremented or decremented, depending on the oral part of the exam. This oral part will involve both theoretical questions and exercises, and may at most contribute three (3) points to the total, while it may lead to fail the exam, if it reveals serious flaws in the student's preparation.

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.