MANY-BODY THEORY AND APPLICATIONS

Module MANY-BODY THEORY 2

The course aims at providing basic concepts and techniques in the theory of many particle physics, at low energies, i.e. in the non-relativistic regime. Selected examples from condensed matter theory will be treated in some detail.

The course requires basic knowledge of standard Quantum mechanics, Complex calculus, as well as Thermodynamics, Statistical mechanics, and Structure of matter.

Knowledge and understanding.

Critical understanding of the most advanced developments of Modern Physics and Condensed Matter Physics, both theoretical and experimental, and their interrelations, also across different subjects.. Adequate knowledge of advanced mathematical and numerical tools, currently used in both basic and applied research. Remarkable acquaintance with the scientific method, understanding of nature, and of the research in Physics. During the course we will present both experimental facts and theoretical models concerning the properties of many-body systems, with reference to modern experiments and novel theoretical interpretations.

Applying knowledge and understanding

Ability to identify the essential elements in a phenomenon, in terms of orders of magnitude and approximation level, and being able to perform the required approximations. Ability to use analogy as a tool to apply known solutions to new problems (problem solving). In presenting a may-body effect, emphasis will be given to the most important magnitudes, introducing all other magnitudes as successive approximations.

Making judgements

Ability to convey own interpretations of physical phenomena, when discussing within a research team. Developing one's own sense of responsibility, through the choice of optional courses and of the final project. In presenting the different topics, both during the course and during the final exam, links will be given with other courses (mainly, but not only, belonging to the same curriculum), some of which optional, and with possible topics for a research final project, both experimental and theoretical.

Communication skills

Ability to discuss about advanced physical concepts, both in Italian and in English.

Learning skills.

Ability to acquire adequate tools for the continuous update of one's knowledge. Ability to access to specialized literature both in the specific field of one's expertise, and in closely related fields. Ability to exploit databases and bibliographical and scientific resources to extract information and suggestions to better frame and develop one's study and research activity. Ability to acquire, through individual study, knowledge in new scientific fields. We will often make reference to scientific papers, both reviews and research articles.

Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course.

-          Fano Anderson model. Exact resolution, application to an impurity and to a qubit in an external bath.

-          Self-energy example applications. Impurities, disordered systems and Green's function in the Born self-consistent approximation. Electron-electron self-energy (1° and 2° order). Electron-phonon self-energy.

-          Response function example calculations.  Electric conductivity (Kubo formula). ARPES response.

-          Magnetic systems. Magnetic impurities and corrections to Green's functions. Kondo effect. Magnetic susceptibility and relation to density-density response function. Ferromagneticm and Stoner criterion.

-          Miscellaneous. BCS theory of superconductors within Green's functions formalism. Adiabatic and isothermal response functions.

[1] C. Berthod, Spectroscopic Probes of Quantum Matter, IOP Publishing Ltd (2018).

[2] G. Rickayzen, Green’s functions and Condensed Matter, Academic Press (1980).

[3] A. L. Fetter, J. D. Walecka, Quantum Theory of Many-Particle Systems, Dover (2003).

[4] H. Bruus, K. Flensberg, Many-body quantum theory in condensed matter physics, Oxford University Press (2004).

[5] G. D. Mahan, Many-Particle Physics, Plenum Press (1990).

[6] G. Giuliani, G. Vignale, Quantum Theory of the Electron Liquid, Cambridge University Press (2005).

[7] H. Haug, A-P. Jauho, Quantum kinetics in transport and optics in semiconductors, Springer (2008).

[8] Instructos's notes.

Evaluation criteria are: relevance of answer wrt question, detail level, ability to stipulate links with other topics of this or other courses, ability to formulate relevant examples, language skills, clarity of presentation.

Evaluation may also take place online, should circumstances require, and current regulations allow that.

To ensure equal opportunities and in compliance with current laws, interested students may request a personal interview in order to plan any compensatory and/or dispensatory measures based on educational objectives and specific needs. Students can also contact the CInAP (Centro per l’integrazione Attiva e Partecipata — Servizi per le Disabilità e/o i DSA) referring teacher within their department (https://www.cinap.unict.it/content/referenti).

- Calculations of Green's functions and self energies

- Feynman diagrams

- Linear response functions