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Extreme events in a random set of nonlinear elastic bending waves
No full textInternational audienceWe present an experimental setup designed to investigate the statistical properties of extreme events in random elastic bending waves induced by an electromagnetic shaker on a thin stainless steel plate. In this setup, the standard statistical criteria used to define extreme events, such as rogue waves in the sea, are not sufficiently restrictive. Therefore, we introduce a new, more restrictive criterion to quantify the occurrence of rare events, similar to those observed in wave tanks [G. Michel et al., J. Fluid Mech. 943, A26 (2022)]Using this refined criterion, we explore correlations between the amplitude of extreme events and other wave characteristics, such as slopes, energy, and periods of the waves. We find that extreme events in our setup are correlated to the longest wavelength of the plate, which corresponds to the plate's mode. We also observe that the steepness and kinetic energy of these events reach their time-averaged value, as expected for these slow-varying modes of the plate. The study raises questions about the purely statistical characterization of statistically rare events and rogue waves
Le renforcement morphologique dans l’histoire du démonstratif français : le cas des formes préfixées en i- (XIe – XVIe siècles)
No full textInternational audienceThis article deals with the evolution of the reinforced forms of the French demonstrative (icil, icele, icist, iceste, icelui, etc.) between the 11th and 16th centuries, revealing three diachronic phases in their frequency and context of use. During the 12th and 13th centuries, prefixed demonstratives duplicate simple forms, and are mainly used in Anglo-Norman texts. In Middle French, their frequency varies according to discourse domains and genres, and their paradigm is gradually limited to four forms (icelui, icele, iceux and iceles). After the end of the 1st third of the 16th century, their frequency becomes more stable in most of the texts, and their specialization in pronominal use is obvious. The final part of the study shows that they are used as autonomous pronouns, fulfilling a temporary function in the final phase of modern pronoun selection.L’article porte sur l’évolution des formes renforcées du démonstratif français (icil, icele, icist, iceste, icelui, etc.) entre le XIe et le XVIe siècle et fait apparaître trois phases diachroniques dans leur fréquence et leur contexte d’emploi. Aux XIIe et XIIIe siècles, les démonstratifs préfixés doublent les formes simples et sont surtout employés dans les textes anglo-normands. En moyen français, leur fréquence varie surtout en fonction du domaine et du genre discursif et leur paradigme se restreint à quatre formes (icelui, icele, iceux et iceles). À partir de la fin du 1er tiers du XVIe siècle, leur fréquence est plus stable dans la plupart des textes et ils se spécialisent nettement en fonction pronominale. La dernière partie de l’étude montre qu’ils servent de pronoms autonomes et remplissent une fonction temporaire lors de la phase terminale de sélection des pronoms démonstratifs modernes
Efficient Thermalization and Universal Quantum Computing with Quantum Gibbs Samplers
No full textInternational audienceThe preparation of quantum Gibbs states is a crucial task in quantum computing. In this work, we prove that a recently introduced, efficiently implementable dissipative evolution thermalizes to the Gibbs state in time scaling polynomially or even logarithmically with system size at high enough temperatures for any Hamiltonian that satisfies a Lieb-Robinson bound, such as local Hamiltonians on a lattice. Furthermore, we show the efficient adiabatic preparation of the associated purifications or "thermofield double" states. To the best of our knowledge, these are the first results rigorously establishing the efficient preparation of high-temperature Gibbs states and their purifications.In the low-temperature regime, we show that implementing this family of dissipative evolutions for inverse temperatures polynomial in the system's size is computationally equivalent to standard quantum computations. On a technical level, for high temperatures, our proof makes use of the mapping of the generator of the evolution into a Hamiltonian, and then connecting its convergence to that of the infinite temperature limit. We further present an alternative proof that is based on showing the exponential decay of the so-called oscillator norm, yielding convergence in logarithmic times. For low temperature, we instead perform a perturbation at zero temperature and resort to circuit-to-Hamiltonian mappings akin to the proof of universality of quantum adiabatic computing.Taken together, our results show that a family of quasi-local dissipative evolutions efficiently prepares a large class of quantum many-body states of interest, and has the potential to mirror the success of classical Monte Carlo methods for quantum many-body systems
Additivity and chain rules for quantum entropies via multi-index Schatten norms
No full textThe primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often plays a crucial role. A fundamental question in quantum information and cryptography is whether the minimum output entropy remains additive under the tensor product of channels. Here, we establish a general additivity statement for the optimized sandwiched Rényi entropy of quantum channels. For that, we generalize the results of [Devetak, Junge, King, Ruskai, CMP 2006] to multi-index Schatten norms. As an application, we strengthen the additivity statement of [Van Himbeeck and Brown, 2025] thus allowing the analysis of time-adaptive quantum cryptographic protocols. In addition, we establish chain rules for Rényi conditional entropies that are similar to the ones used for the generalized entropy accumulation theorem of [Metger, Fawzi, Sutter, Renner, CMP 2024]
Ground state energy of a dilute inhomogeneous Fermi gas
No full textWe study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the range of the interaction potential is much smaller than the typical inter-particle distance. We show that the energy per particle converges to the Thomas-Fermi energy of the system, with a perturbative term corresponding tot he interaction and exhibiting the scattering length of the potential. The proof is decomposed into two bounds. First, we construct an appropriate test-state to prove the upper bound. Then, we prove the lower bound by the Dyson lemma, which allows us to regularize the interaction potential, and several semi-classical tools
"Archimède : Que j'aime à faire apprendre ce nombre utile aux sages !", une conférence en référence au nombre Pi: Grenoble Pi Day 2025
No full textÀ l'occasion de la Journée internationale des mathématiques, l'Institut Fourier propose aux lycées de Grenoble et de la région Auvergne-Rhône-Alpes de venir s'immerger dans cette discipline scientifique, au cœur de la recherche !Sur le campus universitaire Grenoble Alpes et dans les laboratoires de recherche, venez assister à une conférence de maths d'Étienne Ghys, participer à des ateliers pour mieux comprendre la discipline et assister à des mini-exposés
Opéra de cour : une notion pertinente pour la France ? Analyse d’un système de production au service du prince
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