Innovating Works

RAMBAS

Financiado
Rigorous Approximations for Many-Body Quantum Systems
From first principles of quantum mechanics, physical properties of many-body quantum systems are usually encoded into Schroedinger equations. However, since the complexity of the Schroedinger equations grows so fast with the numbe... From first principles of quantum mechanics, physical properties of many-body quantum systems are usually encoded into Schroedinger equations. However, since the complexity of the Schroedinger equations grows so fast with the number of particles, it is generally impossible to solve them by current numerical techniques. Therefore, in practice approximate theories are often applied, which focus only on some collective behaviors of the systems in question. The corroboration of such effective models largely depends on mathematical methods. The overall goal of RAMBAS is to justify key effective approximations used in many-body quantum physics, including the mean-field, quasi-free, and random-phase approximations, as well as to derive subtle corrections in critical regimes. Building on my unique expertise in mathematical physics, I will 1) develop general techniques to understand corrections to the mean-field and Bogoliubov approximations for dilute Bose gases, 2) introduce rigorous bosonization methods and combine them with existing techniques from the theory of Bose gases to understand Fermi gases, and 3) employ the bosonization structure of Fermi gases to study the many-body quantum dynamics in long time scales, thus deriving quantum kinetic equations. By applying and suitably inventing mathematical techniques from functional analysis, spectral theory, calculus of variations and partial differential equations, RAMBAS will take standard approximations of quantum systems to the next level, with special focus on those particularly challenging situations where the particle correlation plays a central role but is yet not adequately addressed. RAMBAS will thereby provide the physics community with crucial mathematical tools, which are at the same time rigorous and applicable. ver más
30/09/2027
LMU MUENCHEN
2M€
Perfil tecnológico estimado
Duración del proyecto: 65 meses Fecha Inicio: 2022-04-06
Fecha Fin: 2027-09-30

Línea de financiación: concedida

El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2022-04-06
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-2021-COG: ERC CONSOLIDATOR GRANTS
Cerrada hace 3 años
Presupuesto El presupuesto total del proyecto asciende a 2M€
Líder del proyecto
LUDWIGMAXIMILIANSUNIVERSITAET MUENCHEN No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5