Physics

GENERAL OBJECTIVES: The aim of the course 'Computational Solid State Physics' is to provide both theoretical and practical understanding with the two main numerical approaches currently in use for the solution of the quantum many body problem in condensed matter physics: a) Density Functional Theory, which allows to obtain predictions from first principles of electronic states, structural energies, and interatomic forces in molecules and solids; b) Quantum Monte Carlo methods - variational, diffusion, path-integral – which can be applied to the numerical study of various many-body quantum systems (liquid or solid helium, electron gas, electrons in atoms and molecules). SPECIFIC OBJECTIVES: A- Knowledge and Understanding: OF1: To know and understand the fundamentals of Hartree-Fock (H-F) theory. OF2: To know and understand the fundamentals of Density Functional Theory (DFT). OF3: To know and understand the fundamentals of Pseudopotential theory (PPT). OF4: To know and understand the DFT+PPT theory of crystalline systems. OF5: To know and understand the variational Monte Carlo (MC) method for identical particles. OF6: To know and understand the "projection MC" method for identical particles. OF7: To know and understand the path integral Monte Carlo (PIMC) method. OF8: To know and understand the "sign problem" for systems of many identical fermions. B- Application Skills: OF9: To apply DFT+PPT to simple solid-state systems (using software like Quantum Espresso). OF10: To apply various quantum Monte Carlo methods to simple systems of many identical bosons or fermions (writing simple C codes and using large pre-existing FORTRAN codes). C- Autonomy of Judgement: OF11: To be able to assess, for a real quantum solid or fluid, which theories and algorithms presented in the course are suitable for describing and/or predicting which physical properties. OF12: To be able to evaluate the feasibility, in terms of memory and CPU time, of a numerical project in molecular or solid-state physics. D- Communication Skills: OF13: To be able to present the results of a theoretical-numerical project. OF14: To be able to write concise reports on the results of a theoretical-numerical project. Ability to Learn: OF15: To progress autonomously in C programming skills. OF16: To progress autonomously in the use of existing software and codes. OF17: To progress in graphical visualization skills of one's own results. OF18: To progress in the ability to read reviews and research articles.