Reference: PID2024-156184NB-I00
Coordinator: BCAM - Basque Center for Applied Mathematics
Duration: -
BCAM budget: 48,750.00
Funding agency: AEI
Type: National Project
BCAM research line(s) involved:
MP
BCAM research area(s) involved:
MP

Objective:

Since its inception almost a century ago, quantum physics has brought us many innovations, such as the transistor and the laser. In recent years, its impact has accelerated considerably, leading to a global race for the quantum advantage. The research proposal does not aim to produce technological spin-offs, but to deepen our understanding of the quantum world through purely mathematical work. We are talking here about "quantum mathematics", an intrinsically interdisciplinary field of Mathematics. The scientific proposal is oriented in three interdependent directions: (a) Mathematical development of Quantum Many-Body Theory. For example, mathematical study of Bose systems and Bose-Einstein condensation phenomena in the presence of interactions; analysis of universality properties in Condensed Matter Physics and Statistical Mechanics. (b) Application of new mathematical developments of Quantum Many-Body Theory to concrete physical systems: quantum transport in fermionic systems in the presence of interactions, mathematical study of models associated with high-temperature superconductivity, etc. (c) Mathematics inspired by Quantum Many-Body Theory: Differential equations on operators and nonlinear thermodynamic formalism.

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