16th conference of the GDR DynQua "Quantum Dynamics"

31 janv. 2024, 08:30 → 2 févr. 2024, 14:40 Europe/Paris

CY Advanced Studies (Auditorium) (CY Cergy Paris Université • Neuville-sur-Oise)

Laurent Bruneau (CY Cergy Paris Université), Louis Garrigue (CY Cergy Paris Université), Constanza Rojas-Molina (CY Cergy Paris Université), Armen Shirikyan (CY Cergy Paris Université), Michal Wrochna (Utrecht University)

GDR DynQua "Dynamique Quantique' https://dynqua.math.cnrs.fr/

Coordinators:  N. Anantharaman, N. Berglund, J.M. Bouclet, B. Douçot

The GDR network DynQua promotes international exchanges and scientific collaborations around quantum dynamics problems at the interface of Mathematics and Physics. The GDR brings together 36 research units in Physics and Mathematics across France and aims to support young PhD students and Postdoctoral researchers in this active field. 

One of its main activities is the yearly conference, in 2024 held in Neuville-sur Oise and hosted by CY Cergy Paris Université. 

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List of senior speakers

Zied Ammari (Université de Rennes)

Janet Anders (University of Exeter / Universität Potsdam)

Margherita Disertori (University of Bonn)

Søren Fournais (University of Copenhagen)

Giambattista Giacomin (Université Paris Cité)

Stéphane Nonnenmacher (Université Paris-Saclay)

Annalisa Panati (Université de Toulon)

Claude-Alain Pillet (Université de Toulon)

Éric Séré (Université Paris Dauphine - PSL)

 

List of junior speakers

Rayan Fahs (Université Paul Sabatier, Toulouse)

Shahnaz Farhat (Constructor University, Bremen)

Rodrigue Lelotte (Ecole des Ponts)

Pascal Millet (Ecole Polytechnique)

Thomas Normand (Université de Nantes)

 

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Registration, financial support for young participants

Registration is open (we kindly ask all participants to register).

 

There is a limited budget for young participants: if you would like to apply for financial support, please write us an email to the following address before December 23, 2023, indicating your present situation (Phd student, post-doc) and details of the planned journey (dates and hours, preferred choice of train/plane/other). 

 

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Conference location

The conference is hosted by the CY Advanced Studies in Neuville-sur-Oise (1 rue Descartes, 95000 Neuville-sur-Oise), a 10 minutes walk from the RER A and Train L station Neuville-Université. Many hotels can be found along the RER A line, in Paris and near stations closer to Neuville. 

The talks and mini-lectures are held in the main auditorium.

 

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mercredi 31 janvier

12:15 Lunch break

IUT, site de Neuville
111 Rue d'Eragny, 95000 Neuville-sur-Oise

1 Mini-lecture 1: Entropic fluctuations in quantum two-time measurement framework

Non-equilibrium statistical mechanics has seen some impressive developments in the last three decades, since the ground-breaking formulation of the transient and steady entropic Fluctuation Relations (FR) in the early nineties.

The extension of these results to the quantum setting has turned out to be surprisingly challenging and it is still an ongoing effort. Kurchan’s seminal work (2000) showed quantum formulation of the transient version of FR is possible by introducing two time measurement framework.

In this mini course, we present some recent results where we attempt to introduce a quantum equivalent of steady entropic functional and compare it the transient version for open quantum system.

We consider both the case of idealised direct measurement on the reservoirs and experimentally accessible indirect measurement through coupling with an ancilla. We analyse in particular stability with respect to the initial state.

In order to deal with the thermodynamics limit and to have general results, we use methods of $C^*$- algebras and modular theory.

(Joint work with T. Benoist, L. Bruneau, V. Jakšić)

Orateurs: Annalisa Panati (Université de Toulon), Claude-Alain Pillet (Université de Toulon)

Panati.pdf

2 Strictly-Correlated Electrons systems and their dissociation at infinity

The Strictly-Correlated Electrons (SCE) is a formulation of density functional theory obtained in the semi-classical limit of the Levy-Lieb functional, which is used for strongly-correlated systems. I will present this problem, which arises as a multimarginal optimal transport of a special kind, and present a recent result on the dissociation at infinity of such systems.

Orateur: Rodrigue Lelotte (Ecole des Ponts)

Lelotte.pdf

15:30 Coffee break

3 On the energy of the dilute Bose gas

The ground state energy density $e(\rho)$ of a large system of interacting bosons in $3$ dimensions at density $\rho$ satisfies the formula
$$ e(\rho) = 4 \pi \rho^2 a \Big( 1 + \frac{15}{128 \sqrt{\pi}} \sqrt{\rho a^3} \Big) + \text{higher order terms}, $$ in the dilute limit $\rho a^3 \ll 1$. Here $a$ is the scattering length of the interaction potential. This is the celebrated Lee-Huang-Yang formula for the energy density. In this talk, I will review the proof of the lower bound in this formula. I will also comment on the harder $2$-dimensional case and how the proof can be modified to accommodate this case.

Orateur: Søren Fournais (University of Copenhagen)

Fournais.pdf

4 The ground state of the Dirac-Fock model: a new approach

I will present a new approach to the ground state of the relativistic Dirac-Fock energy inspired of Lieb’s relaxed variational principle for Hartree-Fock. This approach seems simpler and more suitable for theoretical and numerical investigations than previous ones. Based on this approach, I will present existence results for the ground state of molecules and crystals. The existence proof for this ground state suggests an algorithm for its computation, that generalizes the ODA algorithm of Cances-Lebris. The existence result for crystals is joint work with Isabelle Catto, Long Meng and Eric Paturel. The theoretical study and implementation of the algorithm is work in progress with Maxime Chupin, Guillaume Legendre and Long Meng.

Orateur: Eric Séré (Université Paris Dauphine - PSL)

Sere.pdf

GDR scientific committee meeting

jeudi 1 février

08:30 Welcome coffee

5 Mini-lecture 2: Entropic fluctuations in quantum two-time measurement framework

Orateurs: Annalisa Panati (Université de Toulon), Claude-Alain Pillet (Université de Toulon)

Panati.pdf

6 Leading-order term expansion for the Teukolsky equation on subextremal Kerr black holes

The study of wave propagation on black hole spacetimes has been an intense field of research in the past decades. This interest has been driven by the stability problem for black holes and by questions related to scattering theory. In the analysis of Maxwell's equations and the equations of linearized gravity, the focus often shifts to the study of the Teukolsky equation, which offers the advantage of being scalar in nature. I will present a result providing the large time leading-order term for initially localized and regular solutions and valid for the full subextremal range of black hole parameters. I will also discuss some aspects of the proof which relies on recent advances in spectral and microlocal analysis.

Orateur: Pascal Millet (Ecole Polytechnique)

Millet.pdf

10:40 Coffee break

7 Recovery of qubit state after noisy leakage in high-dimensional space

Experiments often encode qubit states in physical systems that have many more physical dimensions. Unfortunately, environmental noise can cause the logical qubit to leak into these dimensions, compromising the qubit nature of the state. This causes unwanted artefacts, such as increased entropies. I will describe a new mathematical method to recover a meaningful qubit state from a known noisy high-dimensional state [1]. This method is valid for many physical situations where noise acts separately on two subspaces. As an example, we apply the method to the tomographically obtained states of a microwave cavity, which was used in a Maxwell demon experiment [2]. We find excellent recovery of the encoded state and a massive reduction in entropy. The new recovery method paves the way for quantum experiments and technologies to extract meaningful qubit information from a jungle of noise.

[1] J. Anders, S. Sevitz, et al, in preparation.
[2] N. Cottet, et al., “Observing a quantum Maxwell demon at work”, PNAS 114, 7561 (2017).

Orateur: Janet Anders (University of Exeter)

Anders.pdf

12:10 Lunch break

IUT, site de Neuville
111 Rue d'Eragny, 95000 Neuville-sur-Oise

8 Gibbs measures for Hamiltonian PDEs: KMS property and completeness

During the past few decades, Gibbs measures have been used in nonlinear PDEs to establish various remarkable results related to almost sure well-posedness and flow properties. The main ingredients are Fourier analysis, the Hamiltonian structure and the measure invariance. In this talk I will report on some recent contributions obtained in collaboration with Shahnaz Farhat and Vedran Sohinger. In particular, the following aspects will be discussed:
(i) The Kubo-Martin-Schwinger (KMS) property: I will define the KMS equilibrium states for Hamiltonian PDEs and show under certain hypotheses that there exists a unique KMS equilibrium state for such system given by the Gibbs measure.
(ii) Completeness: I will underline a general principle proving that if a (Hamiltonian) PDE admits a stationary probability measure then the PDE admits almost surely global solutions.

Orateur: Zied Ammari (Université de Rennes)

Ammari.pdf

9 Quantum-classical motion of charged particles interacting with scalar fields

The goal of this talk is to investigate the dynamics of semi-relativistic or non-relativistic charged particles in interaction with a scalar meson field. Our main contribution is the derivation of the classical dynamics of a particle-field system as an effective equation of the quantum microscopic Nelson model, in the classical limit where the value of the Planck constant approaches zero ($\hbar \rightarrow 0$). Thus, we prove the validity of Bohr’s correspondence principle, that is to establish the transition from quantum to classical dynamics. We use a Wigner measure approach to study such transition. Then, as a consequence of this interplay between classical and quantum dynamics, we establish the global well-posedness of the classical particle-field interacting system, despite the low regularity of the related vector field, which prevents the use of a fixed point argument.

Orateur: Shahnaz Farhat (Jacobs University Bremen)

Farhat.pdf

15:30 Coffee break

10 Delocalization of the Laplace eigenmodes on Anosov surfaces

The eigenmodes of the Laplace-Beltrami operator on a smooth compact Riemannian
manifold $(M,g)$ can exhibit various localization properties in the high frequency regime, which strongly depend on the properties of the geodesic flow. We will focus on situations where this flow is strongly chaotic (Anosov), e.g. if the sectional curvature of $(M,g)$ is negative. The Quantum Ergodicity theorem then states that almost all the eigenmodes become equidistributed on $M$, in the the high frequency limit. The Quantum Unique Ergodicity conjecture claims that this behaviour admits no exception. What can be said about possible "exceptional" eigenstates?

In the case of compact surfaces with Anosov geodesic flow, we prove that all eigenmodes fully delocalize across $M$: for any open set $\Omega$ on $M$, the $L^2$ mass on $\Omega$ of any eigenstate is uniformly bounded from below. This is in contrast with, e.g., the case of eigenstates on the round sphere, which may be strongly concentrated along a closed geodesic.

The proof uses various methods of semiclassical analysis, the structure of stable and unstable manifolds of the Anosov flow, and a Fractal Uncertainty Principle due to Bourgain-Dyatlov.

Joint work with S.Dyatlov and L.Jin.

Orateur: Stéphane Nonnenmacher (Université Paris-Saclay)

Nonnenmacher.pdf

11 Disorder relevance for the random field Ising chain in the large interaction limit

I will present results that describe the domain-wall structure appearing in the large interaction limit for the one dimensional Ising model with centered random external field. These results match with the D. Fisher infinite disorder fixed point prediction (developed for this model in [D. Fisher, P. Le Doussand, C. Monthus, Phys. Rev. E 2001]) and represent a case in which a very strong form of disorder relevance is present. The aim is to present the results along with some ideas from the proof. Hopefully I will be able to discuss also the delicate (and widely open) issue of understanding the universality class to which Fisher’s idea should apply. The talk will be mostly based on joint work with Orphée Collin and Yueyun Hu.

Orateur: Giambattista Giacomin (Université Paris Cité)

Q&A session: Quantum Mechanics

Président de session: Louis Garrigue (CY Cergy Paris Université)

Q&A session: Statistical Physics

Président de session: Vojkan Jakšić (McGill University)

19:00 Conference dinner

Restaurant M. Orbicole
4 Rue Joseph Cornudet, 95000 Neuville-sur-Oise

vendredi 2 février

08:30 Welcome coffee

12 Mini-lecture 3: Entropic fluctuations in quantum two-time measurement framework

Orateurs: Annalisa Panati (Université de Toulon), Claude-Alain Pillet (Université de Toulon)

Panati2.pdf

13 Boundary states of the magnetic Robin Laplacian

In this talk, we will discuss the spectral analysis of the Robin Laplacian on a smooth bounded two-dimensional domain in the presence of a constant magnetic field. In the semi-classical limit, I will explain how to get a uniform description of the spectrum located between the Landau levels. The corresponding eigenfunctions, called edge states, are exponentially localized near the boundary. By means of a microlocal
dimensional reduction, I will explain how to derive a very precise Weyl law, and also how to simultaneously refine old results about the low-lying eigenvalues in the Robin case and recent ones about edge states in the Dirichlet case.

Orateur: Rayan Fahs (Université Toulouse III - Paul Sabatier)

Fahs.pdf

10:40 Coffee break

14 Small eigenvalues and metastability for semiclassical Boltzmann operators

We consider some inhomogeneous linear Boltzmann equations in a low temperature
regime and in the presence of an external force deriving from a potential. We provide a sharp description of the spectrum near 0 of the associated operators. It enables us to obtain some precise information on the long time behavior of the solutions with
in particular some quantitative results of return to equilibrium and metastability.
This type of work usually requires two steps.
First, we establish some resolvent estimates thanks to hypocoercive methods.
We can then use and adapt some constructions of ‘gaussian quasimodes’ (approximated eigenfunctions) involving some tools from semiclassical microlocal analysis which will provide the desired sharp localization of the small eigenvalues.

Orateur: Thomas Normand (Université de Nantes)

Normand.pdf

15 Phase transition in the Integrated Density of States of the Anderson model arising from a supersymmetric sigma model

Localization/delocalization transition in random Schrödinger operators cannot in general be seen from the behavior of the corresponding Integrated Density of States (IDS). Here we consider a random Schrödinger operator appearing in the study of certain reinforced random processes in connection with a supersymmetric sigma-model, and show that the IDS undergoes a phase transition between weak and strong disorder regime in dimension larger or equal to three. This transition follows from a phase transition in the corresponding random process and supersymmetric sigma-model. This is joint work with V. Rapenne, C. Rojas-Molina and X. Zeng.

Orateur: Margherita Disertori (University of Bonn)

Disertori.pdf

12:40 Lunch

IUT, site de Neuville
111 Rue d'Eragny, 95000 Neuville-sur-Oise