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The growth of quantum technologies is attracting the interest of many students eager to learn concepts such as quantum entanglement or quantum superposition. However, the non-intuitive nature of these concepts poses a challenge to understanding them. Here, we present an entangled photon system which can perform a Bell test, i.e. the CHSH inequality, and can obtain the complete tomography of the two-photon state. The proposed setup is versatile, cost-effective and allows for multiple classroom operating modes. We present two variants, both facilitating the measurement of Bell inequalities and quantum state tomography. Experimental results showcase successful manipulation of the quantum state of the photons, achieving high-fidelity entangled states and significant violations of Bell's inequalities. Our setup's simplicity and affordability enhances accessibility for less specialized laboratories, allowing students to familiarize themselves with quantum physics concepts.

Quantum interactions exchanging different types of particles play a pivotal r\^{o}le in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspective. Here, we consider a system made of two fermions and one boson, in order to study the effect of such an off-diagonal interaction term, having in mind the physics of cuprate superconductors. Additionally, our model also includes a generalized Hubbard interaction (i.e., a general local repulsion term for the fermions). Regarding pairing, exponentially localized dressed bound fermion pairs are shown to exist and their effective dispersion relation is studied in detail. Scattering properties of the system are derived for two channels: the unbound and bound pair channels. We give particular attention to the regime of very large on-site (Hubbard) repulsions, because this situation is relevant for cuprate superconductors.

Intraventricular vector flow mapping (iVFM) seeks to enhance and quantify color Doppler in cardiac imaging. In this study, we propose novel alternatives to the traditional iVFM optimization scheme by utilizing physics-informed neural networks (PINNs) and a physics-guided nnU-Net-based supervised approach. When evaluated on simulated color Doppler images derived from a patient-specific computational fluid dynamics model and in vivo Doppler acquisitions, both approaches demonstrate comparable reconstruction performance to the original iVFM algorithm. The efficiency of PINNs is boosted through dual-stage optimization and pre-optimized weights. On the other hand, the nnU-Net method excels in generalizability and real-time capabilities. Notably, nnU-Net shows superior robustness on sparse and truncated Doppler data while maintaining independence from explicit boundary conditions. Overall, our results highlight the effectiveness of these methods in reconstructing intraventricular vector blood flow. The study also suggests potential applications of PINNs in ultrafast color Doppler imaging and the incorporation of fluid dynamics equations to derive biomarkers for cardiovascular diseases based on blood flow., Comment: 12 pages, accepted for publication in IEEE TUFFC; camera ready corrections, corrected acknowledgments

This work presents a simple power converter, without any high voltage transformer, able to supply and control a plasma jet based on dielectric barrier discharge. The converter, operating in pulsed current mode, requires a single power switch and is fed by a low voltage DC source. It can deliver very short duration pulses to the plasma jet with high current amplitude. The operating principle is explained by means of the state plane analysis and is validated with simulations and experimental results. The equations provided allow for the calculation during the design stage of important characteristics of the plasma jet as the peak voltage and the duration of the pulses. The power can be easily adjusted during experimentation to comply with the desired appearance of the plasma jet.

Accessibility in visualization is an important yet challenging topic. Sonification, in particular, is a valuable yet underutilized technique that can enhance accessibility for people with low vision. However, the lower bandwidth of the auditory channel makes it difficult to fully convey dense visualizations. For this reason, interactivity is key in making full use of its potential. In this paper, we present a novel approach for the sonification of dense line charts. We utilize the metaphor of a string instrument, where individual line segments can be "plucked". We propose an importance-driven approach which encodes the directionality of line segments using frequency and dynamically scales amplitude for improved density perception. We discuss the potential of our approach based on a set of examples., Comment: 5 pages, 6 figures; to be published in Proceedings of IEEE VIS 2023 (Short Papers)

The ASACUSA Cusp experiment requires the production of dense positron plasmas with a high repetition rate to produce a beam of antihydrogen. In this work, details of the positron production apparatus used for the first observation of the antihydrogen beam, and subsequent measurements are described in detail. This apparatus replaced the previous compact trap design resulting in an improvement in positron accumulation by a factor of ($52\pm3)$, Comment: 9 pages, 7 figures

Quadratic Hamiltonians are important in quantum field theory and quantum statistical mechanics. Their general studies, which go back to the sixties, are relatively incomplete for the fermionic case studied here. Following Berezin, they are quadratic in the fermionic field and in this way well-defined self-adjoint operators acting on the fermionic Fock space. We analyze their diagonalization by applying a novel elliptic operator-valued differential equations studied in a companion paper. This allows for their ($\mathrm{N}$-) diagonalization under much weaker assumptions than before. Last but not least, in 1994 Bach, Lieb and Solovej defined them to be generators of strongly continuous unitary groups of Bogoliubov transformations. This is shown to be an equivalent definition, as soon as the vacuum state belongs to the domain of definition of these Hamiltonians. This second outcome is demonstrated to be reminiscent to the celebrated Shale-Stinespring condition on Bogoliubov transformations.

Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all times, for instance in the operator or Hilbert-Schmidt norm topologies. This system presents remarkable ellipticity properties that turn out to be crucial for the study of the infinite-time limit of its solution, which is proven under relatively weak, albeit probably not necessary, hypotheses on the initial data. This system of differential equations is the elliptic counterpart of an hyperbolic flow applied to quantum field theory to diagonalize Hamiltonians that are quadratic in the bosonic field. In a similar way, this elliptic flow, in particular its asymptotics, has application in quantum field theory: it can be used to diagonalize Hamiltonians that are quadratic in the fermionic field while giving new explicit expressions and properties of these pivotal Hamiltonians of quantum field theory and quantum statistical mechanics., Comment: 42 pages, 1 figure

Recent experimental evidence shows that when a protein (or peptide) binds to its ligand pair, the protein effectively "switches on" enabling long-range charge transport within the protein. Astonishingly, the protein-ligand complex exhibits conductances in the order of nanosiemens over distances of many nanometers and macroscopic Ohm's law emerges. Here, we investigate this emergent phenomenon via the framework of many-body (fermionic) quantum statistical principles. We propose a simple model which gives rise to an Ohm's law with vanishing quantum effects in its thermodynamic limit (with respect to length scales). Specifically, we consider protein-ligand complexes as a two-band 1D lattice Hamiltonian system in which charge carriers (electrons or holes) are assumed to be quasi-free. We investigate theoretically and numerically the behavior of the microscopic current densities with respect to varying voltage, temperature and length within reasonable physiological parameter ranges. We compute the current observable at each site of the protein-ligand lattice and demonstrate how the local microscopic charge transport behavior generates the macroscopic current. The overall framework contributes to the search for unifying principles for long-range charge transport and associated emergent laws in protein complexes, which is crucial for bioelectronics., Comment: 29 pages, 10 figures

A two-dimensional optical-phased array is demonstrated by using a multiple-input star coupler, compatible with FMCW LiDAR. Previous approach using a single-input design achieves two-dimensional beam-steering by relying on a tunable laser source, taking advantage of grating coupler radiation angle wavelength dependance and variation of the waveguide refractive index. While implementing a convenient way to distribute power in a single step, star coupler architecture is inefficient in terms of employed waveguide length and thus, optical loss and footprint. Multi-input approach partially alleviates this by condensing several single-input devices into one, permitting to reduce the footprint proportionally to the employed number of inputs. We fabricated in silicon nitride technology a proof of concept steerer with beam waist 0.36 deg x 0.175 deg addressing a field of view of 15 deg x 2.8 deg. A new design iteration is also reported with and 0.24 deg x 0.16 deg beam waist and 15 deg x 11.2 deg field of view. Implications of this optical-phased array chips from a LiDAR system perspective are also presented., Comment: Accepted for publication in the IEEE Journal of Selected Topics in Quantum Electronics. Copyright 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses

Realistic effective interparticle interactions of quantum many-body systems are widely seen as being short-range. However, the rigorous mathematical analysis of this type of model turns out to be extremely difficult, in general, with many important fundamental questions remaining open still nowadays. By contrast, mean-field models come from different approximations or Ans\"{a}tze, and are thus less realistic, in a sense, but are technically advantageous, by allowing explicit computations while capturing surprisingly well many real physical phenomena. Here, we establish a precise mathematical relation between mean-field and short-range models, by using the long-range limit that is known in the literature as the Kac limit. If both attractive and repulsive long-range forces are present then it turns out that the limit mean-field model is not necessarily what one traditionally guesses. One important innovation of our study, in contrast with previous works on the subject, is the fact that we are able to show the convergence of equilibrium states, i.e., of all correlation functions. This paves the way for studying phase transitions, or at least important fingerprints of them like strong correlations at long distances, for models having interactions whose ranges are finite, but very large. It also sheds a new light on mean-field models. Even on the level of pressures, our results go considerably further than previous ones, by allowing, for instance, a continuum of long-range interaction components, as well as very general short-range Hamiltonians for the "free" part of the model.

Gender-based crime is one of the most concerning scourges of contemporary society. Governments worldwide have invested lots of economic and human resources to radically eliminate this threat. Despite these efforts, providing accurate predictions of the risk that a victim of gender violence has of being attacked again is still a very hard open problem. The development of new methods for issuing accurate, fair and quick predictions would allow police forces to select the most appropriate measures to prevent recidivism. In this work, we propose to apply Machine Learning (ML) techniques to create models that accurately predict the recidivism risk of a gender-violence offender. The relevance of the contribution of this work is threefold: (i) the proposed ML method outperforms the preexisting risk assessment algorithm based on classical statistical techniques, (ii) the study has been conducted through an official specific-purpose database with more than 40,000 reports of gender violence, and (iii) two new quality measures are proposed for assessing the effective police protection that a model supplies and the overload in the invested resources that it generates. Additionally, we propose a hybrid model that combines the statistical prediction methods with the ML method, permitting authorities to implement a smooth transition from the preexisting model to the ML-based model. This hybrid nature enables a decision-making process to optimally balance between the efficiency of the police system and aggressiveness of the protection measures taken., Comment: 17 pages, 5 figures, 4 tables. This work has been submitted to the IEEE for possible publication

We prove that the G\"{a}rtner--Ellis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the limit of logarithms of Gaussian Berezin integrals. The covariances of the Gaussian integrals are shown to have a uniform Pfaffian bound and to be summable in general cases of interest, including systems that are not translation invariant. The Berezin integral representation can thus be used to obtain convergent expansions of the generating function in terms of powers of its parameter. The derivation and analysis of the expansions of logarithms of Berezin integrals are the subject of the second part of the present work. Such technical results are also useful, for instance, in the context of quantum information theory, in the computation of relative entropy densities associated with fermionic Gibbs states, and in the theory of quantum normal fluctuations for weakly interacting fermion systems., Comment: Reviews in Mathematical Physics, 2021/2022

We propose a new class of hypertopologies, called here weak$^{\ast }$ hypertopologies, on the dual space $\mathcal{X}^{\ast }$ of a real or complex topological vector space $\mathcal{X}$. The most well-studied and well-known hypertopology is the one associated with the Hausdorff metric for closed sets in a complete metric space. Therefore, we study in detail its corresponding weak$^{\ast }$ hypertopology, constructed from the Hausdorff distance on the field (i.e. $\mathbb{R}$ or $\mathbb{C}$) of the vector space $\mathcal{X}$ and named here the weak$^{\ast }$-Hausdorff hypertopology. It has not been considered so far and we show that it can have very interesting mathematical connections with other mathematical fields, in particular with mathematical logics. We explicitly demonstrate that weak$^{\ast }$ hypertopologies are very useful and natural structures\ by using again the weak$^{\ast }$-Hausdorff hypertopology in order to study generic convex weak$^{\ast }$-compact sets in great generality. We show that convex weak$^{\ast }$-compact sets have generically weak$^{\ast }$-dense set of extreme points in infinite dimensions. An extension of the well-known Straszewicz theorem to Gateaux-differentiability (non necessarily Banach) spaces is also proven in the scope of this application., Comment: In press. arXiv admin note: text overlap with arXiv:2009.04969

The relationship between classical and quantum mechanics is usually understood via the limit $\hbar \rightarrow 0$. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity with quantum mechanics and quantum field theory has challenged for many decades this basic idea. We recently showed the emergence of classical dynamics for very general quantum lattice systems with mean-field interactions, without (complete) supression of its quantum features, in the infinite volume limit. This leads to a theoretical framework in which the classical and quantum worlds are entangled. Such an entanglement is noteworthy and is a consequence of the highly non-local character of mean-field interactions. Therefore, this phenomenon should not be restricted to systems with mean-field interactions only, but should also appear in presence of interactions that are sufficiently long-range, yielding effective, classical background fields, in the spirit of the Higgs mechanism of quantum field theory. In order to present the result in a less abstract way than in its original version, here we apply it to a concrete, physically relevant, example and discuss, by this means, various important aspects of our general approach. The model we consider is not exactly solvable and the particular results obtained are new.

We extend Araki's well-known results on the equivalence of the KMS condition and the variational principle for equilibrium states of quantum lattice systems with short-range interactions, to a large class of models possibly containing mean-field interactions (representing an extreme form of long-range interactions). This result is reminiscent of van Hemmen's work on equilibrium states for mean-field models. The extension was made possible by our recent outcomes on states minimizing the free energy density of mean-field models on the lattice, as well as on the infinite volume dynamics for such models.

The aim of the current paper is to illustrate, in a simple example, our recent, very general, rigorous results [Bru J.-B., de Siqueira Pedra W., J. Math. Anal. Appl. (2020), doi.org: 10.1016/j.jmaa.2020.124434 and 10.1016/j.jmaa.2020.124517] on the dynamical properties of fermions and quantum-spin systems with long-range, or mean-field, interactions, in infinite volume. We consider here the strong-coupling BCS-Hubbard model, because this example is very pedagogical and, at the same time, physically relevant for it highlights the impact of the (screened) Coulomb repulsion on ($s$-wave) superconductivity.