H2020Индивидуална стипендия2015–2017

DEDMEE · Derivation of Effective Dynamics from Microscopic Evolution Equations

„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“

Период: 2015-06-01 → 2017-05-31
Финансиране от ЕС: 158 122 €
Участници: 1
Схема: MSCA-IF-EF-ST

Линиите свързват координатора с партньорите.

Накратко на български

Математическите модели на квантовите системи помагат да се разбере как микроскопичните взаимодействия се превръщат в макроскопични свойства, например при Бозе-Айнщайн кондензатите. Това позволява по-точно описание на поведението на частиците и тяхната стабилност при различни температури.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Derivation of Effective Dynamics from Microscopic Evolution Equations

Problem: We are interested in the derivation of effective equations from microscopic considerations. The particular interest of our approach relies on the combination of rigorous methods of Quantum Field Theory and Quantum Statistical Mechanics, which is both innovative and creative. We paid particular attention to the macroscopic properties of interacting quantum systems governed by a microscopic dynamics. The research project yielded significant outcomes in this field, while developing important knowledge transfers, locally between Breteaux, Bru, and Ratsimanetrimanana, and globally between BCAM and the TU Braunschweig, University of Paris Nord, ETH Zurich and university of São Paulo, Université de Rennes 1, LMU Münich, and université de Metz. For interacting systems such issues are notoriously difficult problems at the interface between Mathematics and Physics and we focus on the mathematical derivation of two types of effective (macroscopic) theories: I. Hartree-type equations II. Kinetic equations Importance for Society: We disseminate the knowledge gained by our research - in Scientific Journals indexed related to Mathematics, - by the organization of workshops and seminars, - through courses, workshops, our website. Objectives : I.a Derive the Hartree-Fock equation from first principle of Quantum Mechanics for fermionic systems with Coulomb two body interaction potential in the semiclassical scaling. I.b Derive the Hartree-Fock-Bogoliubov equation, and use it to study the thermal effects in a Bose-Einstein condensate, and their effects on the stability of such a condensate. II.a Prove that the Wigner measure associated with a family of states satisfies the linear Boltzmann equation, for general initial data and a poissonian random field. II.b Clarify the relation between kinetic equations and transport property for interacting systems.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

The derivation of macroscopic (effective) equations from microscopic considerations is a long-standing challenge of the mathematical analysis of many-body problems. In this research proposal, we focus on the derivation of (linear or non-linear) kinetic and Hartree-type equations from microscopic quantum models. The innovative and creative potential of the project relies on the combination of rigorous methods of Quantum Field Theory (QFT) and Quantum Statistical Mechanics (QSM).Particular attention will indeed be paid to the macroscopic properties of interacting quantum systems governed by a microscopic dynamics. The latter is a notoriously difficult mathematical problem for which only few rigorous results exist. The proposed research will yield significant outcomes in this field, while developing important knowledge transfers, locally between the researchers Sébastien Breteaux, Jean-Bernard Bru and Miguel Escobedo, and globally between BCAM and TU Braunschweig, the University of Paris Nord, ETH Zürich and the University of São Paulo

Оригинален текст от CORDIS (на английски).

Участници

BCAM - BASQUE CENTER FOR APPLIED MATHEMATICS · BilbaoКоординаторИспания