Séminaires du LPTMC

Quantum to classical computability transition via negative Markov chains formalism

In this talk I will present a recently introduced representation of quantum dynamics based on negative Markov chain processes. By introducing particles and antiparticles, this formalism enables the mapping of generic quantum dynamics onto a Markov process defined over an exponentially large configuration space. Within this framework, quantum complexity arises from the proliferation of stochastic particles, which ultimately renders classical simulation intractable beyond a certain timescale. In the presence of noise, we demonstrate that for any unitary evolution generated by a linear combination of local or pairwise interactions, there exists at least one noise channel that effectively classicalizes the system by suppressing the growth of stochastic particles. As a corollary, we show that for this class of unitaries, the dynamics of an open quantum spin chain subject to depolarizing noise undergoes an exact transition to classical simulability once the noise strength exceeds a critical threshold.

Majorana or not? A closer look at Fe(Se,Te)

The search for Majorana fermions in condensed matter systems has
resulted in a number of putative claims of their discovery. If true,
these exotic particles that are their own anti-particle could be
exploited for error-free quantum computing, turning a fundamental
curiosity into a billion dollar business. Unambiguous proof, however,
is thus far lacking and challenging to provide. A recently proposed
method to distinguish Majorana bound states from more conventional
Andreev-, and Yu-Shiba-Rusinov states is to measure their shot noise
[1]. Using our MHz enabled scanning tunnelling microscope [2], we set
out to investigate three possible Majorana sightings in Fe(Se,Te):
zero energy bound states at single Fe impurities [3] and other native
impurities, linear sub-gap density of states at 1D defects [4] and
vortex cores. In this talk I will discuss our findings.

[1] Phys. Rev. B 104, L121406 (2021)
[2] Rev. Sci. Instrum. 89, 093708 (2018)
[3] Nature Communications 15, 8526 (2024)
[4] Nature Communications 15, 3774 (2024)

Bath-Induced Phase Transitions in the XXZ Chain in a Magnetic Field

I present a study of a one-dimensional XXZ spin chain in an external magnetic field, coupled to a bath of harmonic oscillators. Using bosonization techniques, we map this dissipative quantum system onto an effective classical problem describing the thermal fluctuations of a two-dimensional interface. Within this framework, the coupling to Caldeira–Leggett baths generates effective long-range interactions in the interface representation, profoundly modifying the system’s critical properties. Using methods from statistical physics, we determine the resulting phase diagram, highlighting the competition between interactions, external magnetic field and dissipation. In particular, we show how dissipation can give rise to new phases absent in the corresponding closed system.

in collaboration with Oscar Bouverot-Dupuis and Laura Foini

Separation of timescales controls feature learning and overfitting in large neural networks

To understand the inductive bias and generalization capabilities of large, overparameterized machine learning models, it is essential to analyze the out-of-equilibrium dynamics of their training algorithms. Using dynamical mean field theory we investigate the learning dynamics of large two-layer neural networks. Our findings reveal that, for networks with a large width, the training process exhibits a separation of timescales phenomenon. This leads to several key observations: 1. The emergence of a slow timescale linked to the growth of a carefully defined complexity measure of the network; 2. An inductive bias favoring low complexity when the initial model complexity is sufficiently small; 3. A dynamical decoupling between feature learning and overfitting phases; 4. A non-monotonic trend in test error, characterized by a "feature unlearning" regime at later stages of training.

Making Sense of Electrical Noise by Simulating Electrolyte Solutions

Seemingly unrelated experiments such as electrolyte transport through nanotubes, nano-scale electrochemistry, NMR relaxometry and Surface Force Balance measurements, all probe electrical fluctuations: of the electric current, the charge and polarization, the field gradient (for quadrupolar nuclei) and the coupled mass/charge densities. By combining Statistical Mechanics with molecular and mesoscopic simulations, it is possible to predict the fluctuations of these observables from the dynamics of ions and solvent molecules, thereby enabling experimentalists to decipher the microscopic properties encoded in the measured electrical noise. In this presentation, I will illustrate this idea, focusing on the link between the electrode charge fluctuations in nanocapacitors, the electrochemical response, and the properties of the interfacial electrolyte. 

References

https://benrotenberg.github.io/erc-senses/

How Pauli's principle becomes a theorem in relativity

The Pauli principle ceases to be a principle and becomes a theorem when we move from Galilean quantum mechanics to Lorentz-invariant quantum theory, i.e. quantum field theory. The fascinating aspect of this transition is that even though this principle/theorem plays a major role in the Galilean limit (its consequences do not become smaller and smaller as we consider speeds that are small compared to the speed of light), no one has ever been able to prove it by restricting themselves to Galilean invariance.
Much to the chagrin of some, this seminar will only address historical and conceptual aspects of the problem. The Pauli principle will be explained and its demonstration in the context of quantum field theory will be sketched. Some of its most striking consequences will also be reviewed. The role of the four-dimensional space-time will be briefly discussed.

Non-thermal fixed points in far-from-equilibrium 3D Bose gases

Résumé: 

Following a quantum quench, local observables in many-body systems typically thermal-
ize. In certain cases, however, this thermalization occurs via a two-stage process: the system
first exhibits universal dynamical scaling laws with strongly non-thermal properties, before
eventually reaching thermal equilibrium on a longer time scale. This phenomenon is referred
to as a non-thermal fixed point.
In this talk, I will discuss the non-thermal fixed point that emerges when a 3D Bose gas is
quenched across the condensation transition. I will show that it generally involves a transient
"weak turbulence" regime, followed at later times by a coarsening dynamics associated with
the slow recombination of vortex lines. Quenches performed exactly at the critical point, in
contrast, display a distinct coarsening dynamics, presumably without vortices but involving
the diffusion of critical fluctuations. If time permits, I will also discuss the robustness of
this universal dynamics against external perturbations, typically disorder and drive.

The Nobel Prize in Physics 2025: Quantum physics with electrical circuits

The Nobel Prize in Physics 2025 was awarded to John Clarke, Michel Devoret and John Martinis “for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit”. I will describe their experiments, which gave birth to the now flourishing domain of quantum electronics.

Vers une phyllotaxie tridimensionnelle

Résumé : Inspirés par l'observation de certaines croissances spirales de plantes, les arrangements phyllotactiques bidimensionnels sont des exemples très intéressants de structures homogènes non périodiques engendrées par des règles simples. En séparant les parties radiales et angulaires , ils peuvent par ailleurs être généralisés à des surfaces de courbure positive ou négative. Nous décrirons ici plusieurs essais de généralisation à trois dimensions de ce type d'arrangements. Un premier exemple  reprend la modalité de construction des réseaux périodiques compacts à 3D par empilement itérés de réseaux triangulaires sur les espaces interstitiels des couches précédentes. Une seconde approche procède différemment,  par croissance radiale, soit de façon automatique en suivant une règle simple, ou bien de façon numérique en minimisant un potentiel d'interaction. Deux autres modèles, pouvant également donner lieu à des structures intéressantes dans R3 seront présentés : un ensemble phyllotactique sur la sphere S3 construit autour d'une fibration de Hopf discrète, et un autre à 4 dimensions obtenu comme produit de deux structures phyllotactiques 2d.

Reference : Some attempts toward 3-dimensional phyllotaxy, Rémy Mosseri and Jean-François Sadoc, Structural chemistry, vol 36, pages 1963–1972 (2025)