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Macroscopic Behavior of Many Body Quantum Systems

This project is devoted to the analysis of large quantum systems. It is divided in two parts: Part A focuses on the transport properties of interacting lattice models, while Part B concerns the derivation of effective evolution eq... ver más

31/01/2025

SISSA

983K€

Presupuesto del proyecto: 983K€

Líder del proyecto

SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVAN... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

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Ver 3 Participantes

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2025-01-31

ERC-2018-STG: ERC Starting Grant Scope:Objectives

I+D

Cerrada hace 7 años

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3 Participantes

SISSA

943.51K€ | Lider

CIFGA

195.43K€ | Participante

39.12K€ | Participante

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Duración del proyecto: 77 meses Fecha Inicio: 2018-08-06
Fecha Fin: 2025-01-31

Líder del proyecto

SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVAN... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 983K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto This project is devoted to the analysis of large quantum systems. It is divided in two parts: Part A focuses on the transport properties of interacting lattice models, while Part B concerns the derivation of effective evolution equations for many-body quantum systems. The common theme is the concept of emergent effective theory: simplified models capturing the macroscopic behavior of complex systems. Different systems might share the same effective theory, a phenomenon called universality. A central goal of mathematical physics is to validate these approximations, and to understand the emergence of universality from first principles. Part A: Transport in interacting condensed matter systems. I will study charge and spin transport in 2d systems, such as graphene and topological insulators. These materials attracted enormous interest, because of their remarkable conduction properties. Neglecting many-body interactions, some of these properties can be explained mathematically. In real samples, however, electrons do interact. In order to deal with such complex systems, physicists often rely on uncontrolled expansions, numerical methods, or formal mappings in exactly solvable models. The goal is to rigorously understand the effect of many-body interactions, and to explain the emergence of universality. Part B: Effective dynamics of interacting fermionic systems. I will work on the derivation of effective theories for interacting fermions, in suitable scaling regimes. In the last 18 years, there has been great progress on the rigorous validity of celebrated effective models, e.g. Hartree and Gross-Pitaevskii theory. A lot is known for interacting bosons, for the dynamics and for the equilibrium low energy properties. Much less is known for fermions. The goal is fill the gap by proving the validity of some well-known fermionic effective theories, such as Hartree-Fock and BCS theory in the mean-field scaling, and the quantum Boltzmann equation in the kinetic scaling.

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