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24-27 Jun 2024 Metz (France)
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Program
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Monday, June 24, 2024 › |
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09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
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9:00 - 10:00 (1h)
M. Ballesteros
 Amphi
Miguel Ballesteros
10:00 - 10:30 (30min)
Coffee break
Coffee Room
10:30 - 11:30 (1h)
M. Grillakis
Amphi
Manoussos Grillakis
›11:30 (1h)
S. Cenatiempo: Quantum Mechanics at our scale: a mathematical challenge
While the theory of quantum mechanics describes interactions between constituents of matter at the microscopic scale, the effects of these interactions may lead to fascinating quantum mechanics phenomena at a macroscopic scale. The discovery of such phenomena, including superfluidity and superconductivity as two pioneering examples, has led to extraordinary developments in realizing new materials that exploit the principles of quantum mechanics to exhibit innovative behaviours. In these lectures, we will discuss the challenge of developing mathematical models that rigorously describe how these macroscopic effects emerge from the microscopic scale, focusing on the paradigmatic example of the interacting Bose gas. › Amphi
11:30 - 12:30 (1h)
S. Cenatiempo: Quantum Mechanics at our scale: a mathematical challenge
Amphi
While the theory of quantum mechanics describes interactions between constituents of matter at the microscopic scale, the effects of these interactions may lead to fascinating quantum mechanics phenomena at a macroscopic scale. The discovery of such phenomena, including superfluidity and superconductivity as two pioneering examples, has led to extraordinary developments in realizing new materials that exploit the principles of quantum mechanics to exhibit innovative behaviours. In these lectures, we will discuss the challenge of developing mathematical models that rigorously describe how these macroscopic effects emerge from the microscopic scale, focusing on the paradigmatic example of the interacting Bose gas.
12:30 - 14:30 (2h)
Lunch
Restaurant Universitaire
›14:30 (1h)
M. Falconi: Scaling limits in quantum models of particle-field interaction
In these lectures I will review a series of recent results on the interaction between quantum particles and fields, in different scaling regimes (all somewhat related to Bohr's correspondence principle). From a mathematical perspective, infinite dimensional semiclassical analysis lies at the backbone of our results; we will review its main developments and connect them with the study of systems of quantum particles in interaction with a semiclassical field, as well as with the equations of classical electrodynamics. › Amphi
14:30 - 15:30 (1h)
M. Falconi: Scaling limits in quantum models of particle-field interaction
Amphi
In these lectures I will review a series of recent results on the interaction between quantum particles and fields, in different scaling regimes (all somewhat related to Bohr's correspondence principle). From a mathematical perspective, infinite dimensional semiclassical analysis lies at the backbone of our results; we will review its main developments and connect them with the study of systems of quantum particles in interaction with a semiclassical field, as well as with the equations of classical electrodynamics.
›15:30 (1h)
I. M. Sigal: Gross-Pitaevski equation
The Gross-Pitaevski equation describes superfluids and Bose-Einstein condensates (Nobel prizes 1996 and 2001) in ``macroscopic'' regime. Exactly the same equation appeared in theories of plasma and surface waves where it is called the nonlinear Schr\"odinger equation (NLS). Mathematically, it is a key nonlinear Hamiltonian partial differential equation (PDE) and it has led to rich mathematics. In this lecture, I will give an introduction into the theory of the GPE, proceeding quickly to recent results and exciting open problems. › Amphi
15:30 - 16:30 (1h)
I. M. Sigal: Gross-Pitaevski equation
Amphi
The Gross-Pitaevski equation describes superfluids and Bose-Einstein condensates (Nobel prizes 1996 and 2001) in ``macroscopic'' regime. Exactly the same equation appeared in theories of plasma and surface waves where it is called the nonlinear Schr\"odinger equation (NLS). Mathematically, it is a key nonlinear Hamiltonian partial differential equation (PDE) and it has led to rich mathematics. In this lecture, I will give an introduction into the theory of the GPE, proceeding quickly to recent results and exciting open problems.
16:30 - 17:00 (30min)
Coffee break
Coffee Room
17:00 - 18:00 (1h)
J. Fröhlich: Why text-book Quantum Mechanics calls for a completion, and why the "ETH - Approach to Quantum Mechanics" may provide an adequate one.
Amphi
Jürg Fröhlich
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