Centre de Physique Théorique


Janvier 2019

Mercredi 9 janvier 14:00-15:30, Amphi 5

Physics of active matter : A personal overview

Hugues Chaté (SPEC, CEA Saclay)

Active matter has come to refer to out-of-equilibrium systems where energy, either gathered from the environment, or stored internally, is spent by some local units to displace themselves or move other objects. Understandably, this includes most living systems from large animal groups to subcellular components, but also collections of man-made objects such as activated colloids and microswimmers.

While numerical approaches have often been at the leading edge of the field, progress has been slow regarding more fundamental theoretical understanding of the collective properties of active matter.

My talk will present a personal overview of this fast-growing part of statistical physics, with an emphasis on the minimal models at play and their continuous descriptions.

Mercredi 16 janvier 11:00-12:00, Amphi 5 du CPT

Semiclassical dynamics on singular spaces. Relation to the properties of geodesic flows and to certain problems of analytic number theory

Andrei Shafevich (Moscou)


We study propagation of quasi-particles (localized semi-classical solutions of the Schroedinger equation) on singular spaces. Such spaces can be obtained from metric graphs via replacing vertices by smooth Riemannian manifolds. We describe both local and global behaviour of quasi-particles. Local behaviour is governed by Maslov canonical operator modified near the points of gluing. The global large-time statistics is related to the properties of geodesics as well as to certain problems of Analytic Number Theory (the problem of distribution of abstract primes and the problem of counting the lattice points in growing polyhedra).

Mercredi 16 janvier 14:00-15:00, Amphi 5 du CPT

Kaluza-Klein and Nelson mechanisms reinterpreted on extended phase-space for reconciling General Relativity with Quantum Mechanics

Claudio Di Troia (ENEA, FSN dipartment)


Kaluza-Klein mechanism was rejected for inconsistencies due to the
Planck length scale.
Nelson derivation of Quantum Mechanics was rejected for having assumed,
without justification, a multivalued action and the presence of
universal fluctuations. Both the mechanisms can be reinterpreted without
problems at the light of the guiding center (for Kaluza-Klein) and
gyrocenter (for Nelson) transformations. It is demonstrated that with
the use of guiding center coordinates the fields follow an Einstein’s
equation on the phase-space extended to time and Gravitation includes
electromagnetism if considered on such extended phase space. Once
electromagnetic (now also gravitational) fluctuations are considered it
is shown that the gyrocenter follows the Schroedinger equation. It is
proposed to explaining the discrepancies between GR and QM in the
simplest way : they are describing different objects (guiding center and
gyrocenter, respectively) that are both representative of charges and/or
masses. In this way a unified theory is accessible and it can be
depicted without inconsistencies.

Mercredi 23 janvier 14:00-15:00, Amphi 5 du CPT

Spectral theory and limiting amplitude principle for Maxwell’s equations at the interface of a metamaterial

Maxence Cassier (Institut Fresnel, Université d'Aix-Marseille)


In this talk, we are interested in a transmission problem between a dielectric and a metamaterial. The question we consider is the following : does the limiting amplitude principle hold in such a medium ? This principle defines the stationary regime as the large time asymptotic behavior of a system subject to a periodic excitation. An answer is proposed here in the case of a plane interface between a metamaterial represented by the Drude model and the vacuum, which fill respectively complementary half-spaces. In this context, we reformulate the time-dependent Maxwell’s equations as a conservative Schr¨odinger equation and perform its complete spectral analysis. This permits a quasi-explicit representation of the solution via the ”generalized diagonalization” of the associated unbounded self-adjoint operator. As an application of this study, we show finally that the limiting amplitude principle holds except for a particular fequency characterized by a ratio of permittivities and permeabilities equal to −1 across the interface. This frequency is a resonance of the system and the response to this excitation blows up linearly in time. This is a common work with Christophe Hazard (Poems team) and Patrick Joly (Poems team).

Vendredi 25 janvier 14:00-15:00, Amphi 5 du CPT

Relativistic cosmological large scale structures at one-loop

Clément Stahl

In this talk, I will discuss some aspects of non-linear structure formation. The calculation of the bispectrum usually involves linear physics on large scales and non-linear (but Newtonian) physics on small scales. However, in the squeezed limit, the bispectrum (unlike the power spectrum) couples large scales with small scales. I calculated the non-linear relativistic corrections to the dynamics of dark matter perturbations. They are of the same order of magnitude, in the squeezed limit, than a primordial local non-Gaussianity signal. Such signal is expected to be within the accuracy of the next generation of LSS surveys.

Mercredi 30 janvier 11:00-12:00, Amphi 5 du CPT

Sur les propriétés spectrales d’opérateurs de Schrödinger discrets

Diomba Sambou (Université Pontificale Catholique de Santiago du Chili)


Dans cet exposé, nous considérerons l’opérateur de Schrödinger 1d discret perturbé par une perturbation V compacte non autoadjointe. Suivant différentes propriétés de régularité de V, nous analyserons le spectre discret et les valeurs propres plongées de l’opérateur perturbé. Nos résultats sont basés sur une combinaison adéquate des techniques de dilatation analytique et des méthodes de résonance.