- 27.04.2017 -
PhD Course in Modena by Stefano Baroni, Sissa from 28/4/2017

Prof. Stefano Baroni, from Sissa Trieste, will start his course on April 28 at 2 pm, Aula A, Physics Building, Unimore.

Title: **"Classical and quantum linear response: from lattice dynamics, to optical spectroscopy, and thermal transport"**

**Syllabus:**

1. Mathematical prelude: functionals and functional derivatives.

2. The (generalized) Helmann-Feynman theorem; perturbation theory; response versus fluctuations in classical and quantum mechanics.

3. Density functional theory.

4. Density functional perturbation theory: static response functions and lattice dynamics.

5. Mathematical interlude:Fourier transforms, signal analysis, and the Shannon-Nyquist thorem.

6. Physical interlude: the Schroedinger and Liouville equations; propagators in classical and quantum mechanics.

7. Time-dependent density-functional theory.

8. Dynamical linear response in density-functional theory: optical spectroscopy.

9. Rydberg states, excitons, charge-transfer excitations: what is wrong (if anything) with TDDFT and the fixes that have been proposed.

10. Other spectroscopies: charge and spin fluctuations in extended systems. Plasmons and magnons.

11. Back to classical mechanics: the Green-Kubo theory of linear response and the fluctuation-dissipation theorem. Correlation and response functions.

12. Hydrodynamic fluctuations in extended systems: the linearised Navier-Stokes equations and the linear-response theory of heat conduction.

13. Atomic heat transport from density-functional theory.

14. Transport coefficients from equilibrium molecular dynamics.

15. Mathematical postlude: the statistical theory of time series, or how to squeeze all the juice from a molecular dynamics trajectory.

**Tentative schedule (to be confirmed)**:

April 28 (Fri) 14:00 – 15.30, 16.00 – 17:30 (3 hrs)

May 5 (Fri) 14:00 – 15.30, 16.00 – 17:30 (3 hrs)

May 18 (Th) 11:15 – 12.00 12.15 – 13:00 (1.5 hrs)

May 19 (Fri) 14:00 – 15.30, 16.00 – 17:30 (3 hrs)

May 25 (Th) 11:15 – 12.00 12.15 – 13:00 (1.5 hrs)

May 26 (Fri) 14:00 – 15.30, 16.00 – 17:30 (3 hrs)

**Audience**: The course is open to all those who are interested. It has been designed for PhD and Master students, both oriented to theory and to experiments, and should contain all the background information that is required.

**Short bio**:

Stefano Baroni is Professor of Condensed Matter Theory at SISSA in Trieste. His research over the years has led to new theoretical ideas and numerical tools for the study of properties and processes otherwise inaccessible to quantitative theoretical investigation. He has touched on diverse applications, including: semiconductor interfaces and alloys, the chemical reactivity of metal surfaces and catalysis, lattice dynamics and related materials properties (incl. those occurring at extreme pressure and temperature conditions), the dynamics of quantum systems, the excitations of complex molecular and nanostructured systems. Professor Baroni is also known for pioneering different quantum simulation methods, among which density-functional perturbation theory, as well as the development of the open-source package Quantum ESPRESSO for ab-initio electronic structure calculations and materials modeling. Quantum ESPRESSO is one of the flagship codes of the MaX European Centre of Excellence devoted to 'Materials at the eXascale'.

**Info** elisa.molinari@unimore.it