In many cases, the predictions of machine learning interatomic potentials (MLIPs) can be interpreted as a sum of body-ordered contributions, which is explicit when the model is directly built on neighbor density correlation descriptors, and implicit when the model captures the correlations through non-linear functions of low body-order terms. In both cases, the "effective body-orderedness" of MLIPs remains largely unexplained: how do the models decompose the total energy into body-ordered contributions, and how does their body-orderedness affect the accuracy and learning behavior? In answering these questions, we first discuss the complexities in imposing the many-body expansion on ab initio calculations at the atomic limit. Next, we train a curated set of MLIPs on datasets of hydrogen clusters and reveal the inherent tendency of the ML models to deduce their own, effective body-order trends, which are dependent on the model type and dataset makeup. Finally, we present different trends in the convergence of the body-orders and generalizability of the models, providing useful insights for the development of future MLIPs.

Electron-phonon coupling is at the origin of conventional superconductivity, enabling the pairing of electrons into Cooper pairs. The electron-phonon matrix elements depend on the electronic eigenstates and, in the standard linear approximation, on the first derivative of the potential felt by the electrons with respect to ionic perturbations. Here, we focus on the derivatives of the potential with a twofold aim: to assess their contribution to the overall coupling and to analyze the limitations of neglecting higher-order derivatives. Several real-space functions are proposed to do the analysis, and are computed for some well-known superconductors. Our results show that, in hydrides, the derivatives of the potential tend to be larger in regions of high electron localization, explaining the success of electronic descriptors previously described to correlate with the critical temperature. The new functions introduced here are able to tell apart structures with similar types of bonding but very different critical temperatures, such as H3S and H3Se Im-3m phases, where electronic descriptors alone fail. Interestingly, our descriptors are capable of easily estimating the impact of higher-order terms in the electron-phonon coupling. In fact, we capture the limitations of the linear approximation expected for PdH, and predict an even more important non-linear behavior in LaH10.

Cooperative behaviour has been extensively studied as a choice between cooperation and defection. However, the possibility to not participate is also frequently available. This type of problem can be studied through the optional public goods game. The introduction of the "Loner" strategy, allows players to withdraw from the game, which leads to a cooperator-defector-loner cycle. While prosocial punishment can help increase cooperation, anti-social punishment -- where defectors punish cooperators -- causes its downfall in both experimental and theoretical studies. In this paper, we introduce social norms that allow agents to condition their behaviour to the reputation of their peers. We benchmark this both with respect to the standard optional public goods game and to the variant where all types of punishment are allowed. We find that a social norm imposing a more moderate reputational penalty for opting out than for defecting, increases cooperation. When, besides reputation, punishment is also possible, the two mechanisms work synergically under all social norms that do not assign to loners a strictly worse reputation than to defectors. Under this latter setup, the high levels of cooperation are sustained by conditional strategies, which largely reduce the use of pro-social punishment and almost completely eliminate anti-social punishment.

Shaping the structure of light with flat optical devices has driven significant advancements in our fundamental understanding of light and light-matter interactions, and enabled a broad range of applications, from image processing and microscopy to optical communication, quantum information processing, and the manipulation of microparticles. Yet, pushing the boundaries of structured light beyond the linear optical regime remains an open challenge. Nonlinear optical interactions, such as wave mixing in nonlinear flat optics, offer a powerful platform to unlock new degrees of freedom and functionalities for generating and detecting structured light. In this study, we experimentally demonstrate the non-trivial structuring of third-harmonic light enabled by the addition of total angular momentum projection in a nonlinear, isotropic flat optics element -- a single thin film of amorphous silicon. We identify the total angular momentum projection and helicity as the most critical properties for analyzing the experimental results. The theoretical model we propose, supported by numerical simulations, offers quantitative predictions for light structuring through nonlinear wave mixing under various pumping conditions, including vectorial and non-paraxial pump light. Notably, we reveal that the shape of third-harmonic light is highly sensitive to the polarization state of the pump. Our findings demonstrate that harnessing the addition of total angular momentum projection in nonlinear wave mixing can be a powerful strategy for generating and detecting precisely controlled structured light.

The screening of Coulomb interaction controls many-body physics in carbon nanotubes, as it tunes the range and strength of the force that acts on charge carriers and binds electron-hole pairs into excitons. In doped tubes, the effective Coulomb interaction drives the competition between Luttinger liquid and Wigner crystal, whereas in undoped narrow-gap tubes it dictates the Mott or excitonic nature of the correlated insulator observed at low temperature. Here, by computing the dielectric function of selected narrow- and zero-gap tubes from first principles, we show that the standard effective-mass model of screening systematically underestimates the interaction strength at long wavelength, hence missing the binding of low-energy excitons. The reason is that the model critically lacks the full three-dimensional topology of the tube, being adapted from graphene theory. As ab inito calculations are limited to small tubes, we develop a two-band model dielectric function based on the plane-wave expansion of Bloch states and the exact truncated Coulomb cutoff technique. We demonstrate that our -- computationally cheap -- approach provides the correct screening for narrow-gap tubes of any size and chirality. A striking result is that the screened interaction remains long-ranged even in gapless tubes, as an effect of the microscopic local fields generated by the electrons moving on the curved tube surface. As an application, we show that the effective electron-electron force that is felt at distances relevant to quantum transport experiments is super Coulombic.

We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in divergence form. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C^1 boundary, the other stated for sets with finite perimeter.

We develop and analyze an inexact regularized alternating projection method for nonconvex feasibility problems. Such a method employs inexact projections on one of the two sets, according to a set of well-defined conditions. We prove the global convergence of the algorithm, provided that a certain merit function satisfies the Kurdyka-Lojasiewicz property on its domain. The method is then specialized to the class of affine rank minimization problems, which includes matrix completion as a special case. We approximate the truncated Singular Value Decomposition of the matrix that has to be projected by means of a Krylov solver, and provide suitable stopping criteria for the Krylov method complying with the theoretical inexactness conditions. The information needed to implement such stopping criteria do not require an extra computational effort as they are a by-product of the Krylov method itself and avoid the so called oversolving phenomena. Results of the numerical validation of the algorithm on matrix completion problems are presented.

We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the particle action. The emerging linear sigma model contains a scalar effective potential that reproduces the effects of the curvature. We present here further details on the construction, and extend its perturbative evaluation to orders high enough to read off the type-A trace anomalies of a conformal scalar in dimensions d = 14 and d = 16.

We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on the strong convexity assumption of the gradient part of the energy, which excludes relevant cases. In this work, we remove the convexity condition and establish new qualitative properties of solutions under general assumptions on the diffusion and mobility functions. In two spatial dimensions, we prove uniqueness of weak solutions, their smoothing effect for positive times, and convergence to equilibrium as time tends to infinity. In three dimensions, we show local well-posedness of strong solutions for arbitrary initial data and global existence for data close to energy minimizers, yielding a Lyapunov stability principle. A key ingredient of our analysis is a Lojasiewicz-Simon inequality tailored to the nonlinear diffusion case, which enables us to characterize the longtime dynamics.

Fifty years ago Walter Kohn speculated that a zero-gap semiconductor might be unstable against the spontaneous generation of excitons---electron-hole pairs bound together by Coulomb attraction. The reconstructed ground state would then open a gap breaking the symmetry of the underlying lattice, a genuine consequence of electronic correlations. Here we show that this excitonic insulator is realized in zero-gap carbon nanotubes by performing first-principles calculations through many-body perturbation theory as well as quantum Monte Carlo. The excitonic order modulates the charge between the two carbon sublattices opening an experimentally observable gap, which scales as the inverse of the tube radius and weakly depends on the axial magnetic field. Our findings call into question the Luttinger liquid paradigm for nanotubes and provide tests to experimentally discriminate between excitonic and Mott insulator.

Ultraclean, undoped carbon nanotubes are observed to be always insulating, even when the gap predicted by band theory is zero: the residual band gap is then thought to have a many-body origin. Here we theoretically show that the correlated insulator is excitonic in $all stable$ narrow-gap tubes irrespective of their size, thus extending our previous claim, limited to gapless (armchair) tubes [D.~Varsano, S.~Sorella, D.~Sangalli, M.~Barborini, S.~Corni, E.~Molinari, M.~Rontani, Nature Communications $\mathbf{8}$, 1461 (2017)]. We derive the scaling law of the exciton binding energy with the tube radius and chirality, and compute self-consistently the fundamental transport gap of the excitonic insulator, by enhancing the two-band model with an accurate treatment of screening validated from first principles. Our findings point to the broader connection between the exciton length scale, dictated by structure, and the stability of the excitonic phase.

This work elaborates on the TRust-region-ish (TRish) algorithm, a stochastic optimization method for finite-sum minimization problems proposed by Curtis et al. in [Curtis2019, Curtis2022]. A theoretical analysis that complements the results in the literature is presented, and the issue of tuning the involved hyper-parameters is investigated. Our study also focuses on a practical version of the method, which computes the stochastic gradient by means of the inner product test and the orthogonality test proposed by Bollapragada et al. in [Bollapragada2018]. It is shown experimentally that this implementation improves the performance of TRish and reduces its sensitivity to the choice of the hyper-parameters.

In this work we study self-consistent solutions in one-dimensional lattice models obtained via many-body perturbation theory. The Dyson equation is solved in a fully self-consistent manner via the algorithmic-inversion method based on the sum-over-poles representation (AIM-SOP) of dynamical operators. In particular, we focus on the GW approximation, analyzing the spectral properties and the emergence of possible magnetic- or charge-density-wave broken symmetry solutions. We start by validating our self-consistent AIM-SOP implementation by taking as test case the one-dimensional Hubbard model. We then move to the study of antiferromagnetic and charge density wave solutions in one-dimensional lattice models, taking into account a long-range Coulomb interaction between the electrons. We show that moving from local to non-local electronic interactions leads to a competition between antiferromagnetic and charge-density-wave broken symmetry solutions. Complementary, by solving the Sham-Schl\"uter equation, we can compute the non-interacting Green's function reproducing the same charge density of the interacting system. In turn, this allows for the evaluation of the derivative discontinuity of the Kohn-Sham (KS) potential, showing that its contribution to the fundamental gap can become dominating in some of the studied cases.

In 2016 Tafazolian et al. introduced new families of $\mathbb{F}_{q^{2n}}$-maximal function fields $\mathcal{Y}_{n,s}$ and $\mathcal{X}_{n,s,a,b}$ arising as subfields of the first generalized GK function field (GGS). In this way the authors found new examples of maximal function fields that are not isomorphic to subfields of the Hermitian function field. In this paper we construct analogous function fields $\tilde{\mathcal{Y}}_{n,s}$ and $\tilde{\mathcal{X}}_{n,s,a,b}$ as subfields of the second generalized GK function field (BM) and determine their automorphism groups. Using that the automorphism group is an invariant under isomorphism, we show that the function fields $\tilde{\mathcal{Y}}_{n,s}$ and ${\mathcal{Y}}_{n,s}$, as well as $\tilde{\mathcal{X}}_{n,s,a,b}$ and $\mathcal{X}_{n,s,a,b}$, are not isomorphic unless $m/s$ divides $q^2-q+1$ and $3$ divides $n$. In other words, the difference between the BM and GGS function fields can be found again at the level of the subfields that we consider.

We compute tree-level gluon amplitudes as worldline correlators of vertex operators in a bosonic spinning particle model. In this framework, the particle's position degrees of freedom are extended by complex bosonic variables that encode its spin. In the free theory, the model exhibits a first-class constraint algebra whose gauging ensures the unitarity of the quantum theory. This algebra is a contraction of the $sl(2,\mathbb{R})$ algebra, which is by itself a subalgebra of the Virasoro algebra. In string theory, gauging the Virasoro algebra plays a similar role. Our model admits a consistent truncation to describe a pure spin-1 particle. Non-abelian interactions are introduced by using BRST techniques, which allow us to extract the vertex operators of the theory as suitable deformations of the BRST charge. BRST invariance is central to ensuring the consistency of the tree-level amplitudes analyzed in this work. We discuss connections with similar worldline constructions and comment on the potential relevance of this framework for uncovering the structures underlying the double-copy program in gauge and gravitational theories.

Internet users generate content at unprecedented rates. Building intelligent systems capable of discriminating useful content within this ocean of information is thus becoming a urgent need. In this paper, we aim to predict the usefulness of Amazon reviews, and to do this we exploit features coming from an off-the-shelf argumentation mining system. We argue that the usefulness of a review, in fact, is strictly related to its argumentative content, whereas the use of an already trained system avoids the costly need of relabeling a novel dataset. Results obtained on a large publicly available corpus support this hypothesis.

We construct an effective field theory for complex Stueckelberg dark photon dark matter. Such an effective construction can be realized by writing down a complete set of operators up to dimension six built with the complex dark photon and Standard Model fields. Classifying the effective operators, we find that in order to properly take into account the non-renormalizable nature of an interacting massive vector, the size of the Wilson coefficients should be naturally smaller than naively expected. This can be consistently taken into account by a proper power counting, that we suggest. First we apply this to collider bounds on light dark matter, then to direct detection searches by extending the list of non-relativistic operators to include the case of complex vectors. In the former we correctly find scaling limits for small masses, while in the latter we mostly focus on electric dipole interactions, that are the smoking gun of this type of dark matter. Simple UV completions that effectively realize the above scenarios are also outlined.

Molecular spins offer a promising platform for quantum sensing, particularly in organic, supramolecular or biological environments. Detection of periodic magnetic fields has been demonstrated with molecular spins ($S$ = 1/2) using manipulation protocols synchronized with the probed field. In this work, we develop two quantum sensing protocols that enable discrimination between different time-dependent magnetic field signals, without synchronization. These are based on the Hahn echo sequence and have been tested on VO(TPP) and $\text{VOPt(SCOPh)}_4$ molecular spins embedded in a superconducting YBCO microwave resonator. We report a magnetic field sensitivity up to a few $10^{-7} T \text{Hz}^{-\frac{1}{2}}$ (with lower bounds approaching $10^{-8} T \text{Hz}^{-\frac{1}{2}}$) for signals with duration of a few microseconds. Under the given conditions, the minimum signal area that can be measured is in the $10^{-10}$ T s range, suggesting a potential trade-off between minimum measurable field and the required signal duration and memory time.