Category: Seminar UniMi

February 7, 2022, 14:00
Sala di Rappresentanza
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

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SPEAKER: Ngoc Nhi Nguyen (U Paris Saclay)

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Fermionic semiclassical L^p estimates

Spectral properties of Schrödinger operators are studied a lot in mathematical physics. They can give the description of trapped fermionic particles. Researches on the spatial concentration of semiclassical Schrödinger operators’ eigenfunctions are still carried out, whether in physics or in mathematics. There are very precise results in special cases like the harmonic oscillator. However, it is not always possible to obtain explicitly point wise information for more general potentials. We can measure the concentration by estimating these functions with L^p bounds.

December 20-22, 2021
Sala di Rappresentanza
Università degli Studi di Milano
Via Cesare Saldini 50, Milano, Italy

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Website: Quantum Before Christmas

This workshop will take place from Mon. 20 Dec. @14h, to Wed. 22 Dec. @13h.

Twelve speakers will present their current research, covering topics from many-body quantum mechanics to PDEs.

For more information, see the conference webpage above.

November 8, 2021, 14:00
"Aula di Rappresentanza"
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

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SPEAKER: Per Moosavi (ETH Zürich)

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Non-local Luttinger model out of equilibrium: Exact results and emergence of generalized hydrodynamics

The non-local Luttinger model is an exactly solvable 1+1D quantum field theory with finite-range interactions that lies somewhere between conformal and Bethe-ansatz integrable models. Using bosonization, I will show how exact analytical results can be computed for the time evolution of this model following an inhomogeneous quantum quench from initial states defined by smooth inverse-temperature and chemical-potential profiles. These results demonstrate that the finite-range interactions give rise to dispersive effects, not present in the conformal case of point-like interactions. Combining the same methods with the recent proposal of generalized hydrodynamics, one finds that this model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. These results are shown to emerge from the exact analytical ones at the relevant time and length scales. As such, the non-local Luttinger model provides a tractable example to analytically study the emergence of hydrodynamics in a quantum many-body system.