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Probing the magnetic origin of the pseudogap using a Fermi-Hubbard quantum simulator
No full textInternational audienceIn strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual ``pseudogap'' metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associated with strong electron correlations, still offers major computational challenges despite its simple formulation. In this context, ultracold atoms quantum simulators have provided invaluable insights into the microscopic nature of correlated quantum states. Here, we use a quantum gas microscope Fermi-Hubbard simulator to explore a wide range of doping levels and temperatures in a regime where a pseudogap is known to develop. By measuring multi-point correlation functions up to fifth order, we uncover a novel universal behaviour in magnetic and higher-order spin-charge correlations. This behaviour is characterized by a doping-dependent energy scale that governs the exponential growth of the magnetic correlation length upon cooling. Accurate comparisons with determinant Quantum Monte Carlo and Minimally Entangled Typical Thermal States simulations confirm that this energy scale agrees well with the pseudogap temperature . Our findings establish a qualitative and quantitative understanding of the magnetic origin and physical nature of the pseudogap and pave the way towards the exploration of pairing and collective phenomena among charge carriers expected to emerge at lower temperatures
Brochette first-passage percolation
No full textWe investigate a novel first-passage percolation model, referred to as the Brochette first-passage percolation model, where the passage times associated with edges lying on the same line are equal. First, we establish a point-to-point convergence theorem, identifying the time constant. In particular, we explore the case where the time constant vanishes and demonstrate the existence of a wide range of possible behaviours. Next, we prove a shape theorem, showing that the limiting shape is the diamond. Finally, we extend the analysis by proving a point-to-point convergence theorem in the setting where passage times are allowed to be infinite
The geometry of intersecting codes and applications to additive combinatorics and factorization theory
No full textInternational audienceIntersecting codes are linear codes where every two nonzero codewords have nontrivially intersecting support. In this article we expand on the theory of this family of codes, by showing that nondegenerate intersecting codes correspond to sets of points (with multiplicities) in a projective space that are not contained in two hyperplanes. This correspondence allows the use of geometric arguments to demonstrate properties and provide constructions of intersecting codes. We improve on existing bounds on their length and provide explicit constructions of short intersecting codes. Finally, generalizing a link between coding theory and the theory of the Davenport constant (a combinatorial invariant of finite abelian groups), we provide new asymptotic bounds on the weighted 2-wise Davenport constant. These bounds then yield results on factorizations in rings of algebraic integers and related structures
On the structure of the Schur squares of Twisted Generalized Reed-Solomon codes and application to cryptanalysis
No full textInternational audienceTwisted generalized Reed-Solomon (TGRS) codes constitute an interesting family of evaluation codes, containing a large class of maximum distance separable codes non-equivalent to generalized Reed-Solomon (GRS) ones. Moreover, the Schur squares of TGRS codes may be much larger than those of GRS codes with same dimension. Exploiting these structural differences, in 2018, Beelen, Bossert, Puchinger and Rosenkilde proposed a subfamily of Maximum Distance Separable (MDS) Twisted Reed-Solomon (TRS) codes over with twists for McEliece encryption, claiming their resistance to both Sidelnikov Shestakov attack and Schur products--based attacks. In short, they claimed these codes to resist to classical key recovery attacks on McEliece encryption scheme instantiated with Reed-Solomon (RS) or GRS codes. In 2020, Lavauzelle and Renner presented an original attack on this system based on the computation of the subfield subcode of the public TRS code. In this paper, we show that the original claim on the resistance of TRS and TGRS codes to Schur products based--attacks is wrong. We identify a broad class of codes including TRS and TGRS ones that is distinguishable from random by computing the Schur square of some shortening of the code. Then, we focus on the case of single twist (i.e., ), which is the most efficient one in terms of decryption complexity, to derive an attack. The technique is similar to the distinguisher-based attacks of RS code-based systems given by Couvreur, Gaborit, Gauthier-Uma\~na, Otmani, Tillich in 2014
Contactless defects detection using modulated photoluminescence technique: model for a single Shockley-Read-Hall trap in a semiconductor thin layer
No full textInternational audienceStudying defects in semiconductors is, in practice, a very important topic for opto-electronic applications. It involves advanced characterization tools able to quantify and qualify the defect densities present in the materials. In the present article we focus on the use of a contactless frequency domain technique: modulated photoluminescence (MPL), and show its potential to detect defects. MPL has been used for the measurement of differential lifetime for several decades in silicon wafers. By extending it to low lifetime/highly defective materials we discovered its potential to become a defect spectroscopy method, measuring time constants close to the ones governing impedance spectroscopy measurements. Proofs of concept and an analytical model for doped materials have been presented already. Here, we reformulate the analytical model more explicitly and check its applicability by extensive numerical simulations for the case of a low illumination for a thin layer with a single defect. We present a parametric numerical study simulating the response of a single Shockley-Read-Hall center, showing the appearance of so-called V-Shapes in the MPL phase patterns as predicted by the analytical model, and valid beyond small-signal approximation. We discuss the difference between these two approaches and extend the analytical model and numerical investigations to intrinsic materials
Approximating Queries on Probabilistic Graphs
No full text29 pages. Extended version of the ICDT'24 articleInternational audienceQuery evaluation over probabilistic databases is notoriously intractable -- not only in combined complexity, but often in data complexity as well. This motivates the study of approximation algorithms, and particularly of combined FPRASes, with runtime polynomial in both the query and instance size. In this paper, we focus on tuple-independent probabilistic databases over binary signatures, i.e., probabilistic graphs, and study when we can devise combined FPRASes for probabilistic query evaluation. We settle the complexity of this problem for a variety of query and instance classes, by proving both approximability results and (conditional) inapproximability results doubled with (unconditional) DNNF provenance circuit size lower bounds. This allows us to deduce many corollaries of possible independent interest. For example, we show how the results of Arenas et al. on counting fixed-length strings accepted by an NFA imply the existence of an FPRAS for the two-terminal network reliability problem on directed acyclic graphs: this was an open problem until now. We also show that one cannot extend a recent result of van Bremen and Meel that gives a combined FPRAS for self-join-free conjunctive queries of bounded hypertree width on probabilistic databases: neither the bounded-hypertree-width condition nor the self-join-freeness hypothesis can be relaxed. We last show how our methods can give insights on the evaluation and approximability of regular path queries (RPQs) on probabilistic graphs in the data complexity perspective, showing in particular that some of them are (conditionally) inapproximable
Stationary regimes of piecewise linear dynamical systems with priorities
No full textInternational audienceDynamical systems governed by priority rules appear in the modeling of emergency organizations and road traffic. These systems can be modeled by piecewise linear time-delay dynamics, specifically using Petri nets with priority rules. A central question is to show the existence of stationary regimes (i.e., steady state solutions) -- taking the form of invariant half-lines -- from which essential performance indicators like the throughput and congestion phases can be derived. Our primary result proves the existence of stationary solutions under structural conditions involving the spectrum of the linear parts within the piecewise linear dynamics. This extends to a broader class of systems a fundamental theorem of Kohlberg (1980) dealing with nonexpansive dynamics. The proof of our result relies on topological degree theory and the notion of ``Blackwell optimality'' from the theory of Markov decision processes. Finally, we validate our findings by demonstrating that these structural conditions hold for a wide range of dynamics, especially those stemming from Petri nets with priority rules. This is illustrated on real-world examples from road traffic management and emergency call center operations
Measurement of asymmetries in decays
No full textInternational audienceA search for violation in and decays is presented using the full Run 1 and Run 2 data samples of collisions collected with the LHCb detector, corresponding to an integrated luminosity of 9 at center-of-mass energies of 7, 8, and 13 TeV. For the Run 2 data sample, the -violating asymmetries are measured to be and , where the first uncertainty is statistical and the second is systematic. Following significant improvements in the evaluation of systematic uncertainties compared to the previous LHCb measurement, the Run 1 dataset is reanalyzed to update the corresponding results. When combining the Run 2 and updated Run 1 measurements, the final results are found to be and , constituting the most precise measurements of these asymmetries to date
Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEs
No full textInternational audienceWe present the Finite Element Neural Network Interpolation (FENNI) framework, a sparse neural network architecture extending previous work on Embedded Finite Element Neural Networks (EFENN) introduced with the Hierarchical Deep-learning Neural Networks (HiDeNN). Due to their mesh-based structure, EFENN requires significantly fewer trainable parameters than fully connected neural networks, with individual weights and biases having a clear interpretation. Our FENNI framework, within the EFENN framework, brings improvements to the HiDeNN approach. First, we propose a reference element-based architecture where shape functions are defined on a reference element, enabling variability in interpolation functions and straightforward use of Gaussian quadrature rules for evaluating the loss function. Second, we propose a pragmatic multigrid training strategy based on the framework's interpretability. Third, HiDeNN's combined rh-adaptivity is extended from 1D to 2D, with a new Jacobian-based criterion for adding nodes combining h- and r-adaptivity. From a deep learning perspective, adaptive mesh behavior through rh-adaptivity and the multigrid approach correspond to transfer learning, enabling FENNI to optimize the network's architecture dynamically during training. The framework's capabilities are demonstrated on 1D and 2D test cases, where its accuracy and computational cost are compared against an analytical solution and a classical FEM solver. On these cases, the multigrid training strategy drastically improves the training stage's efficiency and robustness. Finally, we introduce a variational loss within the EFENN framework, showing that it performs as well as energy-based losses and outperforms residual-based losses. This framework is extended to surrogate modeling over the parametric space in Part II
Inverse scattering for the multipoint potentials of Bethe-Peierls-Thomas-Fermi type
No full textInternational audienceWe consider the Schrödinger equation with a multipoint potential of the Bethe-Peierls-Thomas-Fermi type. We show that such a potential in dimension d = 2 or d = 3 is uniquely determined by its scattering amplitude at a fixed positive energy. Moreover, we show that there is no non-zero potential of this type with zero scattering amplitude at a fixed positive energy and a fixed incident direction. Nevertheless, we also show that a multipoint potential of this type is not uniquely determined by its scattering amplitude at a positive energy E and a fixed incident direction. Our proofs also contribute to the theory of inverse source problem for the Helmholtz equation with multipoint source.</div