Séminaires du LPTMC

Superconducting dome and incipient modulate phase in SrTiO3

SrTiO₃ is a “quantum paraelectric” in which dipolar fluctuations grow upon cooling, yet long-range ferroelectric order never develops. In this seminar, I will discuss the evolution of these dipolar fluctuations, as measured by inelastic neutron scattering, as the system is tuned toward superconducting and ferroelectric phases.

First, I will show that the superconducting dome of SrTiO₃ is driven by the competition between the increase in the density of states and the inevitable collapse of the quantum paraelectric phase under electron doping. Second, I will demonstrate that these dipolar fluctuations couple to a transverse acoustic mode (elastic constant c₄₄), with this coupling being most pronounced at small q-vectors. I will further show that SrTiO₃ lies near a modulated phase, as evidenced by significant softening of its transverse acoustic branch.

Both the amplitude of the coupling and the modulation vector are strongly influenced by the enhancement of the ferroelectric and antiferrodistortive (AFD) phase transitions. These findings suggest that SrTiO₃ is not only an incipient ferroelectric but also an incipient modulated material, with the modulated phase cooperating, rather than competing, with ferroelectricity and the AFD transition.

If time permits, I will also present the electric-field dependence of the thermal conductivity—another probe of acoustic phonons—in SrTiO₃. This will provide further evidence of TO–TA hybridization in SrTiO₃.

Rare events and single big jump effects in stochastic processes

Rare events in stochastic processes are typically described within large deviation theory (LDT), where atypical fluctuations arise from the accumulation of many small contributions. In systems with sub-exponential statistics, however, rare events can instead be dominated by a single large fluctuation, as prescribed by the big jump principle (BJP). In this talk, I will discuss this alternative mechanism and its interplay with standard large deviation behavior across different classes of stochastic processes. I will first focus on power-law dynamics, such as Lévy processes, where single big jump effects control extreme value statistics and first-passage properties, including the behavior of the fastest trajectories in multi-particle settings, in particular their mean exit time from a bounded domain. I will then turn to processes with stretched-exponential statistics, with particular emphasis on the Ornstein–Uhlenbeck process. Using a renewal representation, one can identify a crossover between a regime of typical fluctuations described by LDT and a rare-event regime governed by the BJP, providing a physical interpretation of previously observed anomalous solutions in terms of single big jump effects. Finally, I will briefly discuss a perturbative approach that allows one to access intermediate regimes of moderate deviations, interpolating between these two limits.

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.