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Quantum computing presents a promising alternative for the direct simulation of quantum systems with the potential to explore chemical problems beyond the capabilities of classical methods. However, current quantum algorithms are constrained by hardware limitations and the increased number of measurements required to achieve chemical accuracy. To address the measurement challenge, techniques for grouping commuting and anti-commuting terms, driven by heuristics, have been developed to reduce the number of measurements needed in quantum algorithms on near-term quantum devices. In this work, we propose a probabilistic framework using GFlowNets to group fully (FC) or qubit-wise commuting (QWC) terms within a given Hamiltonian. The significance of this approach is demonstrated by the reduced number of measurements for the found groupings; 51% and 67% reduction factors respectively for FC and QWC partitionings with respect to greedy coloring algorithms, highlighting the potential of GFlowNets for future applications in the measurement problem. Furthermore, the flexibility of our algorithm extends its applicability to other resource optimization problems in Hamiltonian simulation, such as circuit design., Comment: 8 pages, 2 figures. Accepted for Machine Learning and the Physical Sciences Workshop, NeurIPS 2024. Submission Number: 167

Managing complex disaster risks requires interdisciplinary efforts. Breaking down silos between law, social sciences, and natural sciences is critical for all processes of disaster risk reduction. This enables adaptive systems for the rapid evolution of AI technology, which has significantly impacted the intersection of law and natural environments. Exploring how AI influences legal frameworks and environmental management, while also examining how legal and environmental considerations can confine AI within the socioeconomic domain, is essential. From a co-production review perspective, drawing on insights from lawyers, social scientists, and environmental scientists, principles for responsible data mining are proposed based on safety, transparency, fairness, accountability, and contestability. This discussion offers a blueprint for interdisciplinary collaboration to create adaptive law systems based on AI integration of knowledge from environmental and social sciences. Discrepancies in the use of language between environmental scientists and decision-makers in terms of usefulness and accuracy hamper how AI can be used based on the principles of legal considerations for a safe, trustworthy, and contestable disaster management framework. When social networks are useful for mitigating disaster risks based on AI, the legal implications related to privacy and liability of the outcomes of disaster management must be considered. Fair and accountable principles emphasise environmental considerations and foster socioeconomic discussions related to public engagement. AI also has an important role to play in education, bringing together the next generations of law, social sciences, and natural sciences to work on interdisciplinary solutions in harmony., Comment: 20 pages, 2 figures

Controlled long-range transport of micro- and nano-scale objects is a key requirement in lab-on-a-chip and microfluidic applications, enabling the efficient capture, concentration, manipulation, and detection of analytes. Traditional methods such as microfluidic pumps and optical trapping face challenges including high power consumption and limited range of action. This study introduces a plasmonic Brownian ratchet designed for the directed transport of dielectric nanometer-sized particles at low optical powers. Through numerical simulations, the ratchet geometry was optimized to enhance electric fields, optical forces, and trapping potentials. Experimentally, the plasmonic ratchet demonstrated the ability to rectify random thermal motion of 40 nm polysterene spheres over extended distances in a specific direction, achieving velocities up to 2.4 $\mu$m/s at excitation powers as low as 0.785 kW/cm^2. This plasmonic ratchet offers a robust and efficient solution for the targeted delivery and concentration of nanoscale analytes on chips, with significant implications for advancing applications in the life sciences., Comment: to be submitted to ACS Nano

Artificial intelligence (AI) has become a commodity for people because of the advent of generative AI (GenAI) models that bridge the usability gap of AI by providing a natural language interface to interact with complex models. These GenAI models range from text generation - such as two-way chat systems - to the generation of image or video from textual descriptions input by a user. These advancements in AI have impacted Dentistry in multiple aspects. In dental education, the student now has the opportunity to solve a plethora of questions by only prompting a GenAI model and have the answer in a matter of seconds. GenAI models can help us deliver better patient healthcare by helping practitioners gather knowledge quickly and efficiently. Finally, GenAI can also be used in dental research, where the applications range from new drug discovery to assistance in academic writing. In this review, we first define GenAI models and describe their multiple generation modalities; then, we explain and discuss their current and potential applications in Dentistry; and finally, we describe the challenges these new technologies impose in our area.

Long-range interactions are a key resource in many quantum phenomena and technologies. Free-space photons mediate power-law interactions but lack tunability and suffer from decoherence processes due to their omnidirectional emission. Engineered dielectrics can yield tunable and coherent interactions, but typically at the expense of making them both shorter-ranged and sensitive to material disorder and photon loss. Here, we propose a platform that can circumvent all these limitations based on three-dimensional subwavelength atomic arrays subjected to magnetic fields. Our key result is to show how to design the polaritonic bands of these atomic metamaterials to feature a pair of frequency-isolated Weyl points. These Weyl excitations can thus mediate interactions that are simultaneously long-range, due to their gapless nature; robust, due to the topological protection of Weyl points; and decoherence-free, due to their subradiant character. We demonstrate the robustness of these isolated Weyl points for a large regime of interatomic distances and magnetic field values and characterize the emergence of their corresponding Fermi arcs surface states. The latter can as well lead to two-dimensional, non-reciprocal atomic interactions with no analogue in other chiral quantum optical setups., Comment: 15 pages, 6 figures

We show that coupling the $\textrm{SU}(2)$-valued Skyrme field to the $\rho$-meson solves the long-standing issue of (in)compressibility in the solitonic Skyrme model. Even by including only one $\rho\pi$ interaction term, motivated by a holographic-like reduction of Yang-Mills action by Sutcliffe, reduces the compression modulus from $K_0 \simeq 1080$ MeV, in the massive Skyrme model, to $K_0\simeq 351$ MeV., Comment: 20 pages, 5 figures

Time-varying media offer a platform to realize novel and exotic wave effects, including photonic time crystals characterized by momentum band gaps with exponential wave amplification. Here we focus on the quantum electrodynamical properties of time-varying media, in particular vacuum amplification and squeezing. For that purpose, we present a theory of photon pair generation in photonic time crystals that unveils the link between the classical and quantum electrodynamical properties of these systems, that is, a direct relation between reflectivity and pair generation through the squeezing parameter. By working within an Hermitian framework, we are able to characterize quantum pair generation processes in photonic time crystals, showing how momentum bandgaps result in a non-resonant exponential enhancement of dynamical Casimir processes.

Photonic systems with time-varying modulations have attracted considerable attention as they allow for the design of non-reciprocal devices without the need for an external magnetic bias. Unlike time-invariant systems, such modulations couple modes with different frequencies. Here, we discuss how this coupling and particle-hole symmetry may lead to the resonant interaction of positive and negative frequency oscillators. To illustrate this idea, we analyze a dispersive spacetime crystal described by a Drude-Lorentz model with a travelingwave modulation. Our findings demonstrate that the interaction between positive and negative frequency bands can induce parametric instabilities under certain conditions, stemming from the interplay between dispersion and spacetime modulations. In particular, we find that material dispersion creates the conditions for the formation of instabilities for arbitrarily small modulations speeds in the absence of dissipative channels., Comment: 15 pages, 4 figures

We compute the mass radius, scalar radius, tensor radius, baryon number radius and mechanical radius of nuclei with baryon number $B=1,2,3,4,5,6,7,8,32,108$ in the Skyrme model. The relations between these radii and the nuclear gravitational form factors are investigated. We also compute the `pressure' distribution and find that it is negative in the core region for all the nuclei with $B>1$. This suggests that the way mechanical stability is achieved in nuclei is qualitatively different than in the nucleon., Comment: 10 pages, 4 figures. 2 figures changed, 1 figure added for clarity. Other minor changes include an improved accuracy in numerical solutions, and addition of several references

In this article we study properties of isospin asymmetric nuclear matter in the generalized Skyrme model. This is achieved by canonically quantizing the isospin collective degrees of freedom of the recently found multi-wall skyrmion crystal. We obtain, for the first time, an equation of state from the Skyrme model which interpolates between infinite isospin asymmetric nuclear matter and finite isospin symmetric atomic nuclei. This enables us to describe neutron stars with crusts within the Skyrme framework. Furthermore, we observe that the symmetry energy tends to a constant value at zero density, which can be identified with the asymmetry coefficient in the semi-empirical mass formula for atomic nuclei. The symmetry energy also reveals a cusp in its structure below the nuclear saturation point $n_0$ at $n_*\sim 3n_0/4$. This cusp density point $n_*$ can be interpreted as the nuclear density whereby the infinite crystalline multi-wall configuration undergoes a phase transition to a finite isolated multi-wall configuration. Both of these observations are observed to be generic features of skyrmion crystals that tend asymptotically to somewhat isolated skyrmion configurations in the zero density limit. We find that the resulting neutron stars from our study agree quite well with recent NICER/LIGO observational data., Comment: 23 pages, 7 figures

The engineering of the spatial and temporal properties of both the electric permittivity and the refractive index of materials is at the core of photonics. When vanishing to zero, those two variables provide new knobs to control light-matter interactions. This perspective aims at providing an overview of the state of the art and the challenges in emerging research areas where the use of near-zero refractive index and hyperbolic metamaterials is pivotal, in particular light and thermal emission, nonlinear optics, sensing applications and time-varying photonics.

A general review of the crystalline solutions of the generalized Skyrme model and their application to the study of cold nuclear matter at finite density and the Equation of State (EOS) of neutron stars is presented. For the relevant range of densities, the ground state of the Skyrme model in the three torus is shown to correspond to configurations with different symmetries, with a sequence of phase transitions between such configurations. The effects of nonzero finite isospin asymmetry are taken into account by the canonical quantization of isospin collective coordinates, and some thermodynamical and nuclear observables (such as the symmetry energy) are computed as a function of the density. We also explore the extension of the model to accommodate strange degrees of freedom, and find a first order transition for the condensation of kaons in the Skyrme crystal background in a thermodynamically consistent, non-perturbative way. Finally, an approximate EOS of dense matter is constructed by fitting the free parameters of the model to some nuclear observables close to saturation density, which are particularly relevant for the description of nuclear matter. The resulting neutron star mass-radius curves already reasonably satisfy current astrophysical constraints., Comment: 54 pages, 28 figures, review

Boson Stars are, at present, hypothetical compact stellar objects whose existence, however, could resolve several enigmas of current astrophysics. If they exist, either as independent astrophysical entities or as a matter admixture of more standard compact stars, then their imprints can probably be observed in the not-too-distant future from the gravitational signal of coalescing binaries in current and future GW detectors. Here we show that the multipole moments of rotating boson stars obey certain universal relations, valid for a broad set of models and various states in terms of the \textit{harmonic indices}. These universal relations are equivalent to a kind of no-hair theorem for this exotic matter, allowing to map these universal (i.e. model independent) multipoles to an equally universal gravitational field around the stellar object. Further, the multipole moments can be related to observable astrophysical quantities., Comment: 17 pages, 21 figures. We have added some references

We compute the gravitational form factor $D(t)$ of various nuclei in the generalized Skyrme model where nuclei are described as solitonic field configurations each with a definite baryon number $B$. We separately discuss the cases $B=1$ (nucleons), $B=2$ (deuteron), $B=3$ (helium-3 and tritium) and extrapolate to larger $B$-values. Configurations with $B>1$ are in general not spherically symmetric, and we demonstrate how group theory helps to extract the form factor. Numerical results are presented for the configurations with $B=1,2,3,4,5,6,7,8,32,108$. We find that the $B$-dependence is consistent with a power-law $D(0)\propto B^{\beta}$ with $\beta=1.7\sim 1.8$. Other gravitational form factors can be calculated in the same framework, and we show the result for the $J(t)$ form factor associated with angular momentum for the $B=3$ solution., Comment: Version accepted in PRD. Minor typos corrected, new references and table 1 with values of D terms added. 15 pages, 7 figures

In recent years there has been a great interest in topological photonics and protected edge states. Here, we present a first principles method to compute topological invariants of three-dimensional gapless phases. Our approach allows to calculate the topological charges of Weyl points through the efficient numerical computation of gap Chern numbers, which relies solely on the photonic Green's function of the system. We particularize the framework to the Weyl points that are found to emerge in a magnetized plasma due to the breaking of time reversal symmetry. We discuss the relevance of modelling nonlocality when considering the topological properties of continuous media such as the magnetized plasma. We find that for some of the considered material models the charge of the Weyl point can be expressed in terms of a difference of the gap Chern numbers of two-dimensional material subcomponents. Our theory may be extended to other three-dimensional topological phases, or to Floquet systems., Comment: 13 pages, 11 figures

Pairs of entangled photons -- biphotons -- are indispensable in quantum applications. However, some important spectral ranges, like ultraviolet, have been inaccessible to them so far. Here, we use four-wave mixing in a xenon-filled single-ring photonic crystal fiber to generate biphotons with one of the photons in the ultraviolet and its entangled partner in the infrared spectral range. We tune the biphotons in frequency by varying the gas pressure inside the fiber and thus tailoring the fiber dispersion landscape. The ultraviolet photons are tunable from 271 nm to 235 nm and their entangled partners, from 764 nm to 1342 nm, respectively. The tunability up to 170 THz is achieved by adjusting the gas pressure by only 0.57 bar. At 1.32 bar, the photons of a pair are separated by more than 2 octaves. The access to ultraviolet wavelengths opens the possibility for spectroscopy and sensing with undetected photons in this spectral range., Comment: 6 pages, 6 figures

Ordered lattices of emitters with subwavelength periodicities support unconventional forms of light-matter interactions arising from collective effects. Here, we propose the realization and control of subradiant optical states within the radiation continuum in two-dimensional lattices. We show how bound states in the continuum (BICs) which are completely decoupled from radiative states emerge in non-Bravais lattices of emitters. Symmetry breaking results in quasi-BICs with greatly extended lifetimes, which can be exploited for quantum information storage. The analytical derivation of a generalized effective polarizability tensor allows us to study the optical response of these arrays. We discuss how thanks to the quasi-BICs, a rich phenomenology takes place in the reflectivity spectrum, with asymmetric Fano resonances and an electromagnetically induced transparency window. Finally, we exploit these lattices as quantum metasurfaces acting as efficient light polarizers.

We investigate the monotonicity of the minimal period of the periodic solutions of some quasilinear differential equations involving the $p$-Laplace operator. The monotonicity is obtained as a function of a Hamiltonian energy in two cases. We first extend to the case $p\ge2$ classical results for $p=2$ due to Chow and Wang, and Chicone. Then we consider a differential equation associated with a fundamental interpolation inequality in Sobolev spaces. In that case, we generalize to $p\ge2$ a recent result due to Benguria, Depassier and~Loss when $p=2$.

We show that constrained $CP^1$ instantons, combined with the Relativistic Moduli Space approach, can accurately describe kink-antikink collisions in the $\phi^4$ model., Comment: 8 pages, 5 figures

We address the possibility of the appearance of a charged kaon condensate in neutron star cores described within a generalized Skyrme model. Our treatment of strange degrees of freedom is based on the Bound State Approach by Callan and Klebanov, which allows to obtain an in-medium effective potential for the $s$-wave kaon condensate. We predict the onset of kaon condensation at a certain threshold density - whose value depends on the parameters of the model, and ranges between 1.5 and 2.5 times saturation density -, and obtain both the particle fractions and equation of state for dense matter in the kaon condensed phase. Finally, we discuss the effect of such condensates on the mass-radius curves and other observable properties of neutron stars with kaon condensed cores., Comment: 17 pages, 8 figures

Given $k\in\mathbb N$, we define a class of continuous piecewise functions $f$ having abrupt but controlled magnitude changes so that the problem $$\Delta u +f(u)=0,\quad x\in \mathbb R^N, N> 2, $$ has at least $k$ radially symmetric ground state solutions., Comment: 29 pages, 8 figures

Here we study the solutions of any sign of the system --$\Delta$u 1 = |$\nabla$u 2 | p , --$\Delta$u 2 = |$\nabla$u 1 | q , in a domain of R N , N 3 and p, q > 0, pq > 1.. We show their relation with Lane-Emden Hardy-H{\'e}non equations --$\Delta$ N p w= $\epsilon$r $\sigma$ w q , $\epsilon$ = $\pm$1, where u $\rightarrow$ $\Delta$ N p u (p > 1) is the p-Laplacian in dimension N, q > p -- 1 and $\sigma$ $\in$ R. This leads us to explore these equations in not often tackled ranges of the parameters N, p, $\sigma$. We make a complete description of the radial solutions of the system and of the Hardy-Henon equations and give nonradial a priori estimates and Liouville type results.

Antikink-kink ( $\bar{\rm K} $$ {\rm K}$) collisions in the $\phi^6$ model exhibit resonant scattering although the $\phi^6$ kinks do not support any bound states to which energy could be transferred. In Phys. Rev. Lett. 107 (2011) 091602 it was conjectured that, instead, energy is transferred to a collective bound mode of the full $\bar{\rm K} $$ {\rm K}$ configuration. Here we present further strong evidence for this conjecture. Further, we construct a collective coordinate model (CCM) for $\bar{\rm K} $$ {\rm K}$ scattering based on this collective bound mode trapped between the $\bar{\rm K} $$ {\rm K}$ pair which allows us to reproduce the full dynamics of $\bar{\rm K} $$ {\rm K}$ scattering with striking accuracy. We also study kink-antikink (${\rm K} $$ \bar{\rm K}$) scattering and its description by a CCM. In this case a significant role of radiation is discovered., Comment: 17 pages, 17 figures

Structures which appear to move at or near the velocity of light contain singular points. Energy generated by the motion accumulates at these points into ever-narrowing peaks. In this paper we show that energy is generated by a curious process that conserves the number of photons, adding energy by forcing photons already present to climb a ladder of increasing frequency. We present both a classical proof based on conservation of lines of force, and a more formal QED proof demonstrating the absence of unpaired creation and annihilation operators. Exceptions to this rule are found when negative frequencies make an appearance. Finally we make a connection to laboratory-based models of black holes and Hawking radiation., Comment: 13 pages, 4 figures

Boson stars represent a hypothetical exotic type of compact stellar object that may be observed from the gravitational signal of coalescing binaries in current and future GW detectors. In this work we show that the moment of inertia $I$, the (dimensionless) angular momentum $\chi$ and the quadrupole moment $Q$ of rotating boson stars obey a universal relation, valid for a wide set of boson star models. Further, the obtained $I-\chi-Q~$ relation clearly differs from its famous neutron star counterpart, providing us with an unequivocal diagnostic tool to distinguish boson stars from ordinary compact stars or other celestial bodies in GW observations. Such universal (i.e. model-independent) relations also provide a useful tool to probe the strong gravity regime of general relativity and to constrain the equation of state of matter inside compact stars., Comment: 12 pages, 20 figures. In this current version, we have changed the format and the Appendix

We discuss the emergence and manipulation of generalised Dirac cones in the subradiant collective modes of quantum metasurfaces. We consider a collection of single quantum emitters arranged in a honeycomb lattice with subwavelength periodicity. While conventional honeycomb quantum metasurfaces host bound modes that display Dirac cones at the K and K' points, we show that introducing uniaxial anisotropy in the lattice results in modified dispersion relations. These include the tilting of Dirac cones, which changes the local density of states at the Dirac point from vanishing (type I) to diverging (types II and III), the emergence of semi-Dirac points, with linear and quadratic dispersions in orthogonal directions, and the anisotropic movement of Dirac cones away from the K and K' points. Such energy dispersions can modify substantially the dynamics of local probes, such as quantum emitters, to which they have been shown to induce anisotropic, power-law interactions

Topological Quantum Chemistry (TQC) has recently emerged as a instrumental tool to characterize the topological nature of both fermionic and bosonic band structures. TQC is based on the study of band representations and the localization of maximally localized Wannier functions. In this article, we study various two-dimensional photonic crystal structures analyzing their topological character through a combined study of TQC, their Wilson-loop spectra and the electromagnetic energy density. Our study demonstrates that the analysis of the spatial localization of the energy density complements the study of the topological properties in terms of the spectrum of the Wilson-loop operator and TQC.

We report a switchable time-varying mirror, composed of an ITO-Au stack, which can be efficiently modulated in time with over a ten-fold increase in reflectivity, with a change of 0.6. Upon interacting with the time-varying mirror, the frequency content of a reflected pulse is extended to 31 THz. This originates from the shortening of the response time of the mirror beyond saturation, as confirmed by a time-varying model and by further four-wave mixing experiments. A temporal response unbounded by the pump bandwidth opens new avenues for spectral manipulation from time-varying systems with impact for communication networks, optical switching and computing. We report a switchable time-varying mirror, composed of an ITO-Au bilayer, displaying a ten-fold modulation of reflectivity ($\Delta R \approx 0.6$), which saturates for a driving pump intensity $I_{\mathrm{pump}}\approx 100$~GW/cm$^2$. Upon interacting with the saturated time-varying mirror, the frequency content of a reflected pulse is extended up to 31 THz, well beyond the pump spectral content (2.8 THz). We interpret the spectral broadening as a progressive shortening of the mirror rise time from 110 fs to sub 30 fs with increasing pump power, which is confirmed by four-wave mixing experiments and partially captured by a linear time-varying model of the mirror. A temporal response unbounded by the pump bandwidth opens new avenues for spectral manipulation from time-varying systems with impact for communication networks, optical switching and computing., Comment: 6 pages, 4 figures Supplemental: 7 pages, 5 figures update: resubmitted version following referee feedback - removed red-colored sentences

The canonical quantization method for collective coordinates in crystalline configurations of the generalized Skyrme model is applied in order to find the quantum ground state of Skyrmion crystals and study the quantum corrections to the binding energy resulting from the isospin degrees of freedom. This leads to a consistent description of asymmetric nuclear matter within the Skyrme framework and allows us to compute the symmetry energy of the Skyrmionic crystal as a function of the baryon density, and to compare with recent observational constraints., Comment: V3: 16 pages, 4 figures. Some typos corrected. Minor changes in figures 1, 3 and 4. References added