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Spring Semester 2021

Date / Time Speaker Title Location
4 March 2021
18:00-19:00 		Dario Feliciangeli
IST Austria
Event Details

PDE and Mathematical Physics

Title The strongly coupled polaron on a torus: quantum corrections to the Pekar asymptotics
Speaker, Affiliation Dario Feliciangeli, IST Austria
Date, Time 4 March 2021, 18:00-19:00
Location Y27 H 28
Abstract In this talk we discuss the Fröhlich Polaron model in the strong coupling regime, giving an overview of previously known results and presenting recent progress on it. In particular, we focus on quantum corrections to the Pekar asymptotics for the ground state energy of the system. Compared to previous works, the main novelty is that we are able to treat this problem in a translational invariant setting, namely a sufficiently large torus in R^3. This substantially complicates the discussion and calls for a precise study of the set of minimizers of the classical functional(s) corresponding to the Fröhlich Hamiltonian. We carry out this study by introducing an (almost) infinite dimensional diffeomorphism and formalizing some heuristic arguments contained in the physics literature
The strongly coupled polaron on a torus: quantum corrections to the Pekar asymptoticsread_more
Y27 H 28
11 March 2021
18:00-19:00 		Prof. Dr. Marjolaine Puel
Université Nice Sophia
Event Details

PDE and Mathematical Physics

Title Fractional diffusion approximation for 1d Fokker Planck equation.
Speaker, Affiliation Prof. Dr. Marjolaine Puel, Université Nice Sophia
Date, Time 11 March 2021, 18:00-19:00
Location Y27 H 28
Abstract Diffusion approximation is a well known process to approximate kinetic equations by macroscopic equations in order for examples to reduce the number of variables for numerical purpose. The goal of this talk is to give a overview of the recent progresses in diffusion approximation and to focus on the special case of the Fokker Planck equation with heavy tail equilibrium that model the cooling of atoms. In this particular case, the difficulty is due to the absence of a spectral gap for the collision operator. I'll present a joint work with Gilles Lebeau that cover the 1 dimensional case and discuss an extension of this method in the dimension d case.
Fractional diffusion approximation for 1d Fokker Planck equation.read_more
Y27 H 28
18 March 2021
18:00-19:00 		Prof. Dr. Guy David
Universite' Paris Sud
Event Details

PDE and Mathematical Physics

Title Estimates for the number of eigenvalues for a Schrödinger operator
Speaker, Affiliation Prof. Dr. Guy David, Universite' Paris Sud
Date, Time 18 March 2021, 18:00-19:00
Location Y27 H 28
Abstract Abstract Presentation of a joint result with M. Filoche and Svitlana Mayboroda. We estimate the number of eigenvalues (integrated density of states) for an operator $L =-\Delta + V$. Think of the Weyl formula, but we look for a uniform estimate, which is not asymptotic. The statement and proof use the so-called Landscape function(the solution of $Lu=1$). We should also mention rapidly a case of random potentials.
Estimates for the number of eigenvalues for a Schrödinger operatorread_more
Y27 H 28
25 March 2021
18:00-19:00 		Dr. Alessandro Olgiati
Universität Zürich
Event Details

PDE and Mathematical Physics

Title Bosons in a double well: two-mode approximation and fluctuations
Speaker, Affiliation Dr. Alessandro Olgiati, Universität Zürich
Date, Time 25 March 2021, 18:00-19:00
Location Y27 H 28
Abstract We study the ground state properties of a system of bosonic particles trapped by a double-well potential, in the limit of large inter-well separation and of high potential barrier. The N bosons also interact via a mean-field two-body potential, in the limit of large N. The leading-order physics is governed by a Bose-Hubbard Hamiltonian coupling two low-energy modes, each supported in the bottom of one well. Fluctuations beyond these two modes are ruled by two independent Bogoliubov Hamiltonians, one for each well. Our main result is that the variance of the number of particles in the low-energy modes is suppressed. This is a violation of the Central Limit Theorem which holds in the occurrence of Bose-Einstein condensation, and therefore it signals that particles develop correlations in the ground state. We achieve our result by proving a precise energy expansion in term of Bose-Hubbard and Bogoliubov energies. Joint work with Nicolas Rougerie (ENS Lyon) and Dominique Spehner (Universidad de Concepctión).
Bosons in a double well: two-mode approximation and fluctuationsread_more
Y27 H 28
15 April 2021
18:00-19:00 		Prof. Dr. Marcel Guardia
UPC
Event Details

PDE and Mathematical Physics

Title Breakdown of small amplitude breathers for the nonlinear Klein-Gordon equation
Speaker, Affiliation Prof. Dr. Marcel Guardia, UPC
Date, Time 15 April 2021, 18:00-19:00
Location Y27 H 28
Abstract Breathers are temporally periodic and spatially localized solutions of evolutionary PDEs. They are known to exist for integrable PDEs such as the sine-Gordon equation, but are believed to be rare for general nonlinear PDEs. When the spatial dimension is equal to one, exchanging the roles of time and space variables (in the so-called spatial dynamics framework), breathers can be interpreted as homoclinic solutions to steady solutions and thus arise from the intersections of the stable and unstable manifolds of the steady states. In this talk, we shall study the nonlinear Klein-Gordon equation and show that small amplitude breathers cannot exist (under certain conditions). We will also explain how to construct generalized breathers. These are solutions which are periodic in time and in space are localized up to exponentially small (with respect to the amplitude) tails. This is a joint work with O. Gomide and T. Seara.
Breakdown of small amplitude breathers for the nonlinear Klein-Gordon equationread_more
Y27 H 28
22 April 2021
18:00-19:00 		Dr. Robin Reuvers
University of Cambridge
Event Details

PDE and Mathematical Physics

Title Generalized Pauli constraints in large systems
Speaker, Affiliation Dr. Robin Reuvers, University of Cambridge
Date, Time 22 April 2021, 18:00-19:00
Location Y27 H 28
Abstract This talk is about fermionic quantum states. Such states are antisymmetric under permutation of the particles, and this implies the (much simpler) Pauli exclusion principle. Other simple consequences of the N-particle antisymmetry can be difficult to derive, but recently a class known as 'generalized Pauli constraints' received attention in the literature. I will provide an introduction to this concept, and present results about the large N limit, which had not been studied previously. Some physics motivation will be included.
Generalized Pauli constraints in large systemsread_more
Y27 H 28
29 April 2021
18:00-19:00 		Prof. Dr. Toan T Nguyen
Penn State University
Event Details

PDE and Mathematical Physics

Title Landau damping in the collisionless and weakly collisional regime
Speaker, Affiliation Prof. Dr. Toan T Nguyen, Penn State University
Date, Time 29 April 2021, 18:00-19:00
Location Y27 H 28
Abstract The talk is to give an overview of Landau damping, a fundamental mixing and relaxation of the electric field in a plasma modeled by the Vlasov-Poisson and Vlasov-Poisson-Landau system, including a resolvent analysis to linear Landau damping and a new elementary proof of the celebrated nonlinear Landau damping for analytic and Gevrey data in the collisionless case. The presentation then highlights a recent joint work with Jonathan Luk and Sanchit Chaturvedi for the weakly collisional plasma near global Maxwellians where uniform Landau damping and enhanced dissipation are obtained for Sobolev data at a certain stability threshold on size of initial perturbations.
Landau damping in the collisionless and weakly collisional regimeread_more
Y27 H 28

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