Descripción del proyecto
Mejora de los métodos para aproximar el comportamiento de sistemas cuánticos de muchos cuerpos
Las propiedades físicas de los sistemas cuánticos de muchos cuerpos se describen generalmente mediante el uso de ecuaciones de Schrödinger. Sin embargo, suele resultar imposible solucionar estas ecuaciones con las actuales técnicas numéricas. Por consiguiente, en la práctica, los físicos a menudo utilizan teorías de aproximación, las cuales se centran en tan solo unos pocos comportamientos colectivos de los sistemas descritos. Mediante análisis matemáticos, confirman si los modelos elegidos describen eficazmente el comportamiento de los sistemas. El objetivo general del proyecto RAMBAS, financiado con fondos europeos, es justificar determinadas aproximaciones eficaces que se utilizan en la física cuántica de muchos cuerpos. Al aprovechar nuevas técnicas de análisis funcional, la teoría espectral, el cálculo de variaciones y ecuaciones diferenciales parciales, el equipo de RAMBAS prevé llevar las aproximaciones normalizadas de los sistemas cuánticos al siguiente nivel y proporcionar así nuevas herramientas matemáticas a los físicos.
Objetivo
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.
Ámbito científico
- natural sciencesphysical sciencesquantum physics
- natural sciencesmathematicsapplied mathematicsmathematical physics
- natural sciencesmathematicspure mathematicsmathematical analysisfunctional analysis
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations
Palabras clave
Programa(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Régimen de financiación
HORIZON-ERC - HORIZON ERC GrantsInstitución de acogida
80539 MUNCHEN
Alemania