Month: November 2021

7/2/2022: Ngoc Nhi Nguyen @ UniMi

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

SPEAKER: Ngoc Nhi Nguyen (U Paris Saclay)

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.

20-22/12/2021: Quantum Before Christmas @ UniMi

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

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.

13/12/2021: Riccardo Adami @ PoliMi

quantumseminarSeminar PoliMi 
December 13, 2021, 14:00
Sala Consiglio - VII Piano
Politecnico di Milano
Building 14 (Nave), Campus Leonardo
P.zza da Vinci 32, Milano, Italy

SPEAKER: Riccardo Adami (Politecnico di Torino)

Ground states for the two-dimensional NLS in the presence of point interactions

We prove the existence of ground states, i.e. minimizers of the energy at fixed mass, for the focusing, subcritical Nonlinear Schroedinger equation in two dimensions, with a linear point interaction, or defect. Ground states turn out to be positive up to a phase, and to show a logaritmico singularity at the defect. The analogous problem has been widely treated in the one dimensional setting, including the case of graphs. The two dimensional version is more complicated because of the structure of the energy space, that is larger than the standard one. This result opens the way to the study of nonlinear hybrids. This is a joint work with Filippo Boni, Raffaele Carlone, and Lorenzo Tentarelli.

Important Notice: To access the seminar room, please wait at the entrance of the Mathematics Department, Building 14. One of the organizers will let you in using the dedicated elevator for staff. As per internal regulations of Politecnico, the COVID19 green certificate will be checked before entering the room.

29/11/2021: Marcello Porta @ PoliMi

quantumseminarSeminar PoliMi 
November 29, 2021, 14:00
Aula Seminario III Piano
Politecnico di Milano
Building 14 (Nave), Campus Leonardo
P.zza da Vinci 32, Milano, Italy

SPEAKER: Marcello Porta (SISSA Trieste)

Correlation energy of mean-field Fermi gases

In this talk I will discuss the ground state properties of homogeneous, interacting Fermi gases, in the mean-field scaling. In this regime, Hartree-Fock theory provides a good approximation for the ground state energy of the system; this approximation is based on the replacement of the space of fermionic wave functions with the smaller set of Slater determinants, where the only correlations among the particles are those induced by the Pauli principle. I will discuss a rigorous approach that allows to go beyond the Hartree-Fock approximation, and that in particular allows to compute the leading order of the correlation energy, defined as the difference between the many-body and Hartree-Fock ground state energies. The expression we obtain reproduces the ground state energy of a non-interacting Bose gas, and agrees with the prediction of the random-phase approximation. The proof is based on a rigorous bosonization method, that allows to describe the particle-hole excitations around the Fermi surface in terms of a quasi-free Bose gas. Joint work with N. Benedikter, P. T. Nam, B. Schlein and R. Seiringer.

Slides Marcello Porta 29/11/2021Download

8/11/2021: Per Moosavi @ UniMi

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

SPEAKER: Per Moosavi (ETH Zürich)

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.

Slides Per Moosavi 8/11/2021Download