Antsa Ratsimanetrimanana defenderá su tesis doctoral el miércoles 30 de octubre

  • La defensa tendrá lugar en la Sala Adela de Moyua de la Facultad de Ciencia y Tecnología de la UPV/EHU situada en Leioa, a las 12:00 pm 

Antsa Ratsimanetrimanana se licenció en Matemáticas por la Universidad de Burdeos (Francia) en 2013, y tiene un Master en Ingeniería Matemática, Modelización y Estadística obtenido en 2015 en la misma universidad.

Llegó al Basque Center for Applied Mathematics – BCAM en el verano de 2015 para realizar unas prácticas dentro de la línea de investigación de Mecánica Cuántica, a la que finalmente se incorporó en 2016 como estudiante de doctorado.

Su tesis doctoral, Equilibrium and Transport Properties of Quantum Manyy-Body systems, ha sido supervisada por Ikerbasque Research Proffessor Jean-Bernad Bru (BCAM-UPV/EHU).

En nombre de todos los miembros del centro queremos desear mucha suerte a Antsa en la defensa de su tesis.

 

PhD thesis Title: Equilibrium and Transport Properties of Quantum Many-Body systems

This thesis is a study of equilibrium and dynamical properties of macroscopic quantum many-body problems. An important part of the manuscript concerns the study of heat and charge transport properties of fermions on the lattice. This refers to the derivation, from first principles of quantum mechanics and thermodynamics, of the Ohm’s law, first published in 1827 by G. S. Ohm, and of the heat equation, the well-known (classical) equation introduced by J. Fourier in 1807. A complete derivation of the heat equation from quantum mechanics is still not achieved, but we prove here some preliminary results on this non-trivial issue. By contrast, the study of charge transport properties of fermion systems on the lattice is largely developed in this thesis. In particular, we give a mathematical justification, for non-interacting free-fermions, of recent experiments (in 2006 and 2012) which have shown that the classical Ohm’s law remains valid as atomic scales are reached even at very low temperature. Equilibrium state refers here to the notion of KMS state. We also set that the classical KMS condition can be derived from the (quantum) KMS condition for the so-called Bose-Hubbard model.