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The scattering of wavepackets with arbitrary energy dispersion on surfaces has been analyzed. Expanding up to second order in scattering shifts, it is found that besides the known Goos-H\"anchen or Imbert-Fedorov spatial offset, as well as the Wigner delay time, new momentum and frequency shifts appear. Furthermore, the width of the scattered wave packet becomes modified as well, which can lead to a shrinking of pulses by multiple scattering. For a model of dielectric material characterized by a longitudinal and transverse dielectric function the shifts are calculated analytically. From the Goos-H\"anchen and Imbert-Fedorov shifts one can access the longitudinal and transversal dielectric function. Perfectly aligned crystal symmetry axes with respect to scattering beam shows no Imbert-Fedorov effect. It is found that the Goos-H\"anchen and Imbert-Fedorov effect are absent for homogeneous materials. Oppositely it is found that the Wigner delay time and the shrinking of the temporal pulse width allows to access the dielectric function independent on the beam geometry., Comment: errror corrected in application

Rydberg excitons in transition metal dichalcogenides (TMDs) have emerged as a promising platform for investigating the properties of open quantum systems, thanks to their large binding energies(hundreds of meV). However, the study of Rydberg excitons in TMDs has been hindered by sample quality limitations, strong background signals from ground excitons, and broadening at room temperature. In this work, we report the first observation of multiple Rydberg exciton states in monolayer MoS2 at room temperature using Imbert-Fedorov (IF) shift spectroscopy. By numerically solving the Schrodinger equation, we extracted the quasiparticle band gaps for A and B excitons, confirming the temperature-induced redshift of the band gap, in excellent agreement with previous results. Our findings establish IF shift spectroscopy as a powerful tool for characterizing Rydberg excitons in TMDs, paving the way for potential applications in quantum manipulation and control., Comment: 7 pages, 3 figures

Imbert-Fedorov (IF) shift, which refers to a tiny transverse splitting induced by spin-orbit interaction at a reflection/refraction interface, is sensitive to the refractive index of a medium and momentum state of incident light. Most of studies have focused on the shift for an incident light beam with a spin angular momentum (SAM) i.e., circular polarization. Compared to SAM, orbital angular momentum (OAM) has infinite dimensions in theory as a new degree of freedom of light and plays an important role in light-matter coupling. We demonstrate experimentally that the relative IF shifts of vortex beams with large opposite OAMs are highly enhanced in resonant structures when light refracts through a double-prism structure (DPS), in which the thickness and temperature of the air gap are precisely sensed via the observed relative IF shifts. The thickness and temperature sensitivities increase as the absolute value of opposite OAMs increases. Our results offer a technological and practical platform for applications in sensing of thickness and temperature, ingredients of environment gas, spatial displacement, chemical substances and deformation structure., Comment: 11pages, 6 figures

Backdoor attacks are an insidious security threat against machine learning models. Adversaries can manipulate the predictions of compromised models by inserting triggers into the training phase. Various backdoor attacks have been devised which can achieve nearly perfect attack success without affecting model predictions for clean inputs. Means of mitigating such vulnerabilities are underdeveloped, especially in natural language processing. To fill this gap, we introduce IMBERT, which uses either gradients or self-attention scores derived from victim models to self-defend against backdoor attacks at inference time. Our empirical studies demonstrate that IMBERT can effectively identify up to 98.5% of inserted triggers. Thus, it significantly reduces the attack success rate while attaining competitive accuracy on the clean dataset across widespread insertion-based attacks compared to two baselines. Finally, we show that our approach is model-agnostic, and can be easily ported to several pre-trained transformer models., Comment: accepted to Third Workshop on Trustworthy Natural Language Processing

Weyl semimetals exhibit exotic transport responses, among which, recently Goos-Haenchen (GH) and Imbert-Fedorov (IF) effects have received a revived attention, which are, otherwise, well-studied phenomena in optical systems and certain electronic systems. Besides the usual parametric dependence of the shifts inherited from the underlying Hamiltonian to describe the Weyl system and/or that induced by external controls, the IF shift further carries a topological identity -- it depends on the chirality of the Weyl cones. A realistic system of Weyl semimetal naturally accommodates surface potentials induced by impurities present on its surface that could pose impediments to observe clean transport signatures predicted in theoretical models. Classifying these potentials, we study their effects on GH and IF shifts to provide useful guidance to future experiments that are tuned to the objective of characterizing Weyl semimetals and for a possible realisation of novel devices based on these phenomena. A transfer matrix-based approach is invoked to study the profile of Weyl wavefunctions across the interface which is hosting the impurity potentials, revealing that such potentials can lead to several discerning effects which, in certain cases, extend even to nullifying the IF shift completely and giving rise to phenomenon like valley inversion., Comment: 10 pages and 7 figures

We present a visual interpretation of fiber mode degeneracy lifting as SOI (Imbert-Fedorov shift) of OAM modes in a ray picture, and the analytical results are verified by comparing them with eigen equation solutions., Comment: Conference paper, 3 pages, 3 figures

We investigate the reflection of a Gaussian beam impinging upon the surface of an epsilon-near-zero (ENZ) medium. In particular, we discuss the occurrence of Goos-H\"anchen and Imbert-Fedorov shifts. Our calculations reveal that spatial shifts are significantly enhanced owing to the ENZ nature of the medium, and that their value and angular position can be tuned by tuning the plasma frequency of the medium.

The Imbert-Fedorov (IF) shift is the transverse shift of a beam at a surface or an interface. It is a manifestation of the three-component Berry curvature in three dimensions, and has been studied in optical systems and Weyl semimetals. Here we investigate the IF shift in two types of topological systems, topological semimetals with pseudospin-$N/2$ for an arbitrary integer $N$, and nodal-line semimetals (NLSMs). For the former, we find the IF shift depends on the components of the pseudospin, with the sign depending on the chirality. We term this phenomenon the pseudospin Hall effect of topological fermions. The shift can also be interpreted as a consequence of the conservation of the total angular momentum. For the latter, if the NLSM has both time-reversal and inversion symmetries, the IF shift is zero; otherwise it could be finite. We take the NLSM with a vortex ring, which breaks both symmetries, as an example, and show that the IF shift can be used to detect topological Lifshitz transitions. Finally, we propose experimental designs to detect the IF shift., Comment: 7 pages, 6 figures

In this work, I present a full analytical theory for the Goos-H\"anchen and Imbert-Fedorov shifts experienced by an Airy beam impinging on a dielectric surface. In particular, I will show how the decay parameter $\alpha$ associated with finite energy Airy beams is responsible for the occurence of giant angular shifts. A comparisons with the case of Gaussian beams is also discussed.

The Imbert-Fedorov (IF) shift in optics describes the transverse shift of light beams at the reflection interface. Recently, the IF shift of Weyl fermions at the interface between Weyl semimetals (WSMs) with single monopole charge has been studied. Here, we study the IF shift at the interface between two WSMs, each of which is carrying an arbitrary integer monopole charge. We find a general relation between the monopole charges of the two WSMs and the IF shift. In particular, the IF shift is proportional to the monopole charge if both WSMs have the same one. Our results can be used to infer the topology of the materials by experimentally measuring their IF shift. Furthermore, we consider the possibility that the Weyl fermions are scattered to other Weyl cones during the reflection, which results in qualitatively different behavior of the IF shift. While we use a quantum mechanical approach to solve the problem, semiclassical equations of motion and the conservation of total angular momentum can help us intuitively interpret our results in special cases., Comment: 7 pages, 3 figures, published version

Training task-oriented dialogue systems is both costly and time-consuming, due to the need for high-quality datasets encompassing diverse intents. Traditional methods depend on extensive human annotation, while recent advancements leverage large language models (LLMs) to generate synthetic data. However, these approaches often require custom prompts or code, limiting accessibility for non-technical users. We introduce GraphTOD, an end-to-end framework that simplifies the generation of task-oriented dialogues. Users can create dialogues by specifying transition graphs in JSON format. Our evaluation demonstrates that GraphTOD generates high-quality dialogues across various domains, significantly lowering the cost and complexity of dataset creation.

This work is concerned with the appearance of decay bounds in the velocity variable for solutions of the space-inhomogeneous Boltzmann equation without cutoff posed in a domain in the case of hard and moderately soft potentials. Such bounds are derived for general non-negative suitable weak subsolutions. These estimates hold true as long as mass, energy and entropy density functions are under control. The following boundary conditions are treated: in-flow, bounce-back, specular reflection, diffuse reflection and Maxwell reflection. The proof relies on a family of Truncated Convex Inequalities that is inspired by the one recently introduced by F. Golse, L. Silvestre and the first author (2023). To the best of our knowledge, the generation of arbitrary polynomial decay in the velocity variable for the Boltzmann equation without cutoff is new in the case of soft potentials, even for classical solutions.

Silicon photonics is a leading platform for realizing the vast numbers of physical qubits needed for useful quantum information processing because it leverages mature complementary metal-oxide-semiconductor (CMOS) manufacturing to integrate on-chip thousands of optical devices for generating and manipulating quantum states of light. A challenge to the practical operation and scale-up of silicon quantum-photonic integrated circuits, however, is the need to control their extreme sensitivity to process and temperature variations, free-carrier and self-heating nonlinearities, and thermal crosstalk. To date these challenges have been partially addressed using bulky off-chip electronics, sacrificing many benefits of a chip-scale platform. Here, we demonstrate the first electronic-photonic quantum system-on-chip (EPQSoC) consisting of quantum-correlated photon-pair sources stabilized via on-chip feedback control circuits, all fabricated in a high-volume 45nm CMOS microelectronics foundry. We use non-invasive photocurrent sensing in a tunable microring cavity photon-pair source to actively lock it to a fixed pump laser while operating in the quantum regime, enabling large scale microring-based quantum systems. In this first demonstration of such a capability, we achieve a high CAR of 134 with an ultra-low g(2)(0) of 0.021 at 2.2 kHz off-chip detected pair rate and 3.3 MHz/mW2 on-chip pair generation efficiency, and over 100 kHz off-chip detected pair rate at higher pump powers (1.5 MHz on-chip). These sources maintain stable quantum properties in the presence of temperature variations, operating reliably in practical settings with many adjacent devices creating thermal disturbances on the same chip. Such dense electronic-photonic integration enables implementation and control of quantum-photonic systems at the scale required for useful quantum information processing with CMOS-fabricated chips.

Highly forbidden $\beta$ decays provide a sensitive test to nuclear models in a regime in which the decay goes through high spin-multipole states, similar to the neutrinoless double-$\beta$ decay process. There are only 3 nuclei ($^{50}$V, $^{113}$Cd, $^{115}$In) which undergo a $4^{\rm th}$ forbidden non-unique $\beta$ decay. In this work, we compare the experimental $^{113}$Cd spectrum to theoretical spectral shapes in the framework of the spectrum-shape method. We measured with high precision, with the lowest energy threshold and the best energy resolution ever, the $\beta$ spectrum of $^{113}$Cd embedded in a 0.43 kg CdWO$_4$ crystal, operated over 26 days as a bolometer at low temperature in the Canfranc underground laboratory (Spain). We performed a Bayesian fit of the experimental data to three nuclear models (IBFM-2, MQPM and NSM) allowing the reconstruction of the spectral shape as well as the half-life. The fit has two free parameters, one of which is the effective weak axial-vector coupling constant, $g_A^{\text{eff}}$, which resulted in $g_A^{\text{eff}}$ between 1.0 and 1.2, compatible with a possible quenching. Based on the fit, we measured the half-life of the $^{113}$Cd $\beta$ decay including systematic uncertainties as $7.73^{+0.60}_{-0.57} \times 10^{15}$ yr, in agreement with the previous experiments. These results represent a significant step towards a better understanding of low-energy nuclear processes., Comment: Accepted for publication by EPJC

The spatial and the angular variants of the Goos-H\"anchen (GH) and the Imbert-Federov (IF) beam shifts contribute in a complex interrelated way to the resultant beam shift in partial reflection at planar dielectric interfaces. Here, we show that the angular GH and the two variants of the IF effects can be decoupled, amplified and separately observed by weak value amplification and subsequent conversion of spatial$\leftrightarrow$angular nature of the beam shifts using appropriate pre and post selection of polarization states. We experimentally demonstrate such decoupling and illustrate various other intriguing manifestations of weak measurements by employing optimized pre and post selections (based on the eigen polarization states of the shifts) elliptical and / or linear polarization basis. The demonstrated ability to amplify, controllably decouple or combine the beam shifts via weak measurements may prove to be valuable for understanding the different physical contributions of the effects and for their applications in sensing and precision metrology, Comment: 10 pages,5 figures

We present a theoretical study of the Goos-H\"anchen and Imbert-Fedorov shifts for a fundamental Gaussian beam impinging on a surface coated with a single layer of graphene. We show that the graphene surface conductibility $\sigma(\omega)$ is responsible for the appearance of a giant and negative spatial Goos-H\"anchen shift.

In this work we investigate the role of the beam astigmatism in the Goos-H\"anchen and Imbert-Fedorov shift. As a case study, we consider a Gaussian beam focused by an astigmatic lens and we calculate explicitly the corrections to the standard formulas for beam shifts due to the astigmatism induced by the lens. Our results show that astigmatism may enhance the angular part of the shift.

The Goos-H\"anchen (GH) shift and the Imbert-Fedorov (IF) shift are optical phenomena which describe the longitudinal and transverse lateral shifts at the reflection interface, respectively. Here, we report the GH and IF shifts in Weyl semimetals (WSMs) - a promising material harboring low energy Weyl fermions, a massless fermionic cousin of photons. Our results show that GH shift in WSMs is valley-independent which is analogous to that discovered in a 2D relativistic material - graphene. However, the IF shift has never been explored in non-optical systems, and here we show that it is valley-dependent. Furthermore, we find that the IF shift actually originates from the topological effect of the system. Experimentally, the topological IF shift can be utilized to characterize the Weyl semimetals, design valleytronic devices of high efficiency, and measure the Berry curvature.

The optical analogue of quantum weak measurements have shown considerable promise for the amplification and observation of tiny optical beam shifts, namely, the Goos-H\"anchen (GH) and the Imbert-Fedorov (IF) shifts. Here, we demonstrate simultaneous weak value amplification of both the angular GH and the IF shifts in partial reflection of fundamental Gaussian beam at planar dielectric interfaces. We employ pre- and post selection schemes with appropriate linear polarization basis states for simultaneous weak measurements and amplification of both these shifts. The experimentally observed enhancement of the beam shifts and their dependence on the angle of incidence are analyzed / interpreted via quantum mechanical treatment of weak measurements., Comment: 4 pages, 4 figures

Weak measurements have recently allowed for the observation of the spin-Hall effect of light in reflection or transmission, which is a spin-dependent light beam shift orthogonal to the plane of incidence. We report here the observation of the Imbert-Fedorov shift via a weak value amplification scheme. The Imbert-Fedorov effect does not depend on the spin of the incident photon only, but it has richer polarization dependence. We prove that weak measurements allow for a complete experimental characterization of the polarization properties of this tiny optical effect.

In this article, we establish a "Gehring lemma" for a real function satisfying a reverse H\"older inequality on all "kinetic cylinders" contained in a large one: it asserts that the integrability degree of the function improves under such an assumption. The kinetic cylinders are derived from the non-commutative group of invariances of the Kolmogorov equation. Our contributions here are (1) the extension of Gehring's Lemma to this kinetic (hypoelliptic) scaling used to generate the cylinders, (2) the localisation of the lemma in this hypoelliptic context (using ideas from the elliptic theory), (3) the streamlining of a short and quantitative proof. We then use this lemma to establish that the velocity gradient of weak solutions to linear kinetic equations of Fokker-Planck type with rough coefficients have Lebesgue integrability strictly greater than two, while the natural energy estimate merely ensures that it is square integrable. Our argument here is new but relies on Poincar\'e-type inequalities established in previous works.

We prove that the Fisher information is monotone decreasing in time along solutions of the space-homogeneous Boltzmann equation for a large class of collision kernels covering all classical interactions derived from systems of particles. For general collision kernels, a sufficient condition for the monotonicity of the Fisher information along the flow is related to the best constant for an integro-differential inequality for functions on the sphere, which belongs in the family of the Log-Sobolev inequalities. As a consequence, we establish the existence of global smooth solutions to the space-homogeneous Boltzmann equation in the main situation of interest where this was not known, namely the regime of very soft potentials. This is opening the path to the completion of both the classical program of qualitative study of space-homogeneous Boltzmann equation, initiated by Carleman, and the program of using the Fisher information in the study of the Boltzmann equation, initiated by McKean. From the proofs and discussion emerges a strengthened picture of the links between kinetic theory, information theory and log-Sobolev inequalities., Comment: 35 pages

Trefftz schemes are high-order Galerkin methods whose discrete spaces are made of elementwise exact solutions of the underlying PDE. Trefftz basis functions can be easily computed for many PDEs that are linear, homogeneous, and have piecewise-constant coefficients. However, if the equation has variable coefficients, exact solutions are generally unavailable. Quasi-Trefftz methods overcome this limitation relying on elementwise "approximate solutions" of the PDE, in the sense of Taylor polynomials. We define polynomial quasi-Trefftz spaces for general linear PDEs with smooth coefficients and source term, describe their approximation properties and, under a non-degeneracy condition, provide a simple algorithm to compute a basis. We then focus on a quasi-Trefftz DG method for variable-coefficient elliptic diffusion-advection-reaction problems, showing stability and high-order convergence of the scheme. The main advantage over standard DG schemes is the higher accuracy for comparable numbers of degrees of freedom. For non-homogeneous problems with piecewise-smooth source term we propose to construct a local quasi-Trefftz particular solution and then solve for the difference. Numerical experiments in 2 and 3 space dimensions show the excellent properties of the method both in diffusion-dominated and advection-dominated problems., Comment: 26 pages, 6 figures, 2 tables, added some remarks and one figure

We present a theoretical analysis for the \GH and \IF shifts experienced by an X-wave upon reflection from a dielectric interface. We show that the temporal chirp, as well as the bandwidth of the X-wave directly affect the spatial shifts in a way that can be experimentally observed, while the angular shifts do not depend on the spectral features of the X-Wave. A dependence of the spatial shifts on the spatial structure of the X-wave is also discussed.

We consider reflection and transmission of polarized paraxial light beams at a plane dielectric interface. The field transformations taking into account a finite beam width are described based on the plane-wave representation and geometric rotations. Using geometrical-optics coordinate frames accompanying the beams, we construct an effective Jones matrix characterizing spatial-dispersion properties of the interface. This results in a unified self-consistent description of the Goos-H\"anchen and Imbert-Fedorov shifts (the latter being also known as spin-Hall effect of light). Our description reveals intimate relation of the transverse Imbert-Fedorov shift to the geometric phases between constituent waves in the beam spectrum and to the angular momentum conservation for the whole beam. Both spatial and angular shifts are considered as well as their analogues for the higher-order vortex beams carrying intrinsic orbital angular momentum. We also give a brief overview of various extensions and generalizations of the basic beam-shift phenomena and related effects., Comment: 24 pages, 6 figure, to appear in J. Opt. (special issue "Beam shifts")

We study the classical optics effects known as Goos-H\"anchen (GH) and Imbert-Fedorov (IF) shifts, occurring when reflecting a bounded light beam from a planar surface, by using a quantum-mechanical formalism. This new approach allows us to naturally separate the spatial shift into two parts, one independent on orbital angular momentum (OAM) and the other one showing OAM-induced spatial-vs-angular shift mixing. In addition, within this quantum-mechanical-like formalism, it becomes apparent that the angular shift is proportional to the beams angular spread, namely to the variance of the transverse components of the wave vector. Moreover, we extent our treatment to the enhancement of beam shifts via weak measurements and relate our results to recent experiments., Comment: 16 pages, 1 figure

Goos-Haenchen and Imbert-Fedorov shifts are diffractive corrections to geometrical optics that have been extensively studied for a Gaussian beam that is reflected or transmitted by a dielectric interface. Propagating in free space before and after reflection or transmission, such a Gaussian beam spreads due to diffraction. We address here the question how the Goos-Haenchen and Imbert-Fedorov shifts behave for a ``nondiffracting'' Bessel beam., Comment: 3 pages, 1 figure

We present precise expressions of the spatial and angular Goos-Haenchen and Imbert-Fedorov shifts experienced by a longitudinally and transversally limited beam of light (wave packet) upon reflection from a dielectric interface, as opposed to the well-known case of a monochromatic beam which is bounded in transverse directions but infinitely extended along the direction of propagation. This is done under the assumption that the detector time is longer than the temporal length of the wave packet (wave packet regime). Our results will be applied to the case of a Gaussian wave packet and show that, at the leading order in the Taylor expansion of reflected-field amplitudes, the results are the same of the monochromatic case.

In this paper, we present a systematic study of beam shifts and angular momenta of paraxial vortex beams at air-left-handed material (LHM) interfaces. It is shown that, compared to their counterparts at air-right-handed material (RHM) interfaces, the spatial Goos-H\"{a}nchen (GH) and Imbert-Fedorov (IF) shifts remains the same, while the angular GH and IF shifts are reversed, at air-LHM interfaces. The spatial and angular shifts of paraxial vortex beams have their respective origins in transverse angular momenta and transverse linear momenta. The spatial GH and IF shifts remain unreversed as a result of the both reversions of transverse angular momenta and z-component linear momentum, while the angular GH and IF shifts are reversed due to that the z-component linear momentum is reversed and the transverse linear momenta are unreversed, at air-LHM interfaces. In addition, we perform a quantitative analysis on spin-orbit angular momentum conversion and orbit-orbit angular momentum conversion, which further helps us understand the essence of vortex beam shifts at air-LHM interfaces and their fundamental distinctions with those at air-RHM interfaces., Comment: 11 pages, 6 figures, accepted for publication in Physical Review A

We study, analytically and numerically, reflection and transmission of an arbitrarily polarized vortex beam on an interface separating two dielectric media and derive general expressions for linear and angular Goos-Hanchen and Imbert-Fedorov shifts. We predict a novel vortex-induced Goos-Hanchen shift, and also reveal direct connection between the spin-induced angular shifts and the vortex-induced linear shifts., Comment: 4 pages, 2 figures, to appear in Optics Letters

We derive the polarization-dependent displacements parallel and perpendicular to the plane of incidence, for a Gaussian light beam reflected from a planar interface, taking into account the propagation of the beam. Using a classical-optics formalism we show that beam propagation may greatly affect both Goos-H\"{a}nchen and Imbert-Fedorov shifts when the incident beam is focussed., Comment: 3 pages, 1 figure, submitted to Opt. Lett

It is shown that the spatial Goos-H\"anchen shift is greatly affected by spatial coherence. A typical example is given., Comment: 1page, 1 figure

A unified theory is advanced to describe both the lateral Goos-H\"{a}nchen (GH) effect and the transverse Imbert-Fedorov (IF) effect, through representing the vector angular spectrum of a 3-dimensional light beam in terms of a 2-form angular spectrum consisting of its 2 orthogonal polarized components. From this theory, the quantization characteristics of the GH and IF displacements are obtained, and the Artmann formula for the GH displacement is derived. It is found that the eigenstates of the GH displacement are the 2 orthogonal linear polarizations in this 2-form representation, and the eigenstates of the IF displacement are the 2 orthogonal circular polarizations. The theoretical predictions are found to be in agreement with recent experimental results., Comment: 15 pages, 3 figures

We prove that the entropy solution to a scalar conservation law posed on the real line with a flux that is discontinuous at one point (in the space variable) coincides with the derivative of the solution to a Hamilton-Jacobi (HJ) equation whose Hamiltonian is discontinuous. Flux functions (Hamiltonians) are not assumed to be convex in the state (gradient) variable. The proof consists in proving the convergence of two numerical schemes. We rely on the theory developed by B.~Andreianov, K.~H.~Karlsen and N.~H.~Risebro (\textit{Arch. Ration. Mech. Anal.}, 2011) for such scalar conservation laws and on the viscosity solution theory developed by the authors (\textit{arxiv}, 2023) for the corresponding HJ equation. This study allows us to characterise certain germs introduced in the AKR theory (namely maximal and complete ones) and relaxation operators introduced in the viscosity solution framework.

We report on the development of thermal detectors based on large-size tellurium dioxide crystals (45x45x45 mm), containing tellurium enriched in $^{130}$Te to about 91%, for the CROSS double-beta decay experiment. A powder used for the crystals growth was additionally purified by the directional solidification method, resulting in the reduction of the concentration of impurities by a factor 10, to a few ppm of the total concentration of residual elements (the main impurity is Fe). The purest part of the ingot (the first ~200 mm, about 80% of the total length of the cylindrical part of the ingot) was determined by scanning segregation profiles of impurities and used for the $^{130}$TeO$_2$ powder production with no evidence of re-contamination. The crystal growth was verified with precursors produced from powder with natural Te isotopic composition, and two small-size (20x20x10 mm) samples were tested at a sea-level laboratory showing high bolometric and spectrometric performance together with acceptable $^{210}$Po content (below 10 mBq/kg). This growth method was then applied for the production of six large cubic $^{130}$TeO$_2$ crystals and 4 of them were taken randomly to be characterized at the Canfranc underground laboratory, in the CROSS-dedicated low-background cryogenic facility. Two $^{130}$TeO$_2$ samples were coated with a thin, $O$(100 nm), metal film in form of Al layer (on 4 sides) or AlPd grid (on a single side) to investigate the possibility to tag surface events by pulse-shape discrimination. Similarly to the small natural precursors, large-volume $^{130}$TeO$_2$ bolometers show high performance and even better internal purity ($^{210}$Po activity $\sim$ 1 mBq/kg, while activities of $^{228}$Th and $^{226}$Ra are below 0.01 mBq/kg), satisfying requirements for the CROSS and, potentially, next-generation experiments., Comment: Submitted to JINST; 22 pages, 11 figures, 4 tables

The CROSS experiment will search for neutrinoless double-beta decay using a specific mechanical structure to hold thermal detectors. The design of the structure was tuned to minimize the background contribution, keeping an optimal detector performance. A single module of the structure holds two scintillating bolometers (with a crystal size of 45x45x45 mm and a Ge slab facing the crystal's upper side) in the Cu frame, allowing for a modular construction of a large-scale array. Two designs are released: the initial $Thick$ version contains around 15% of Cu over the crystal mass (lithium molybdate, LMO), while this ratio is reduced to ~6% in a finer ($Slim$) design. Both designs were tested extensively at aboveground (IJCLab, France) and underground (LSC, Spain) laboratories. In particular, at LSC we used a pulse-tube-based CROSS facility to operate a 6-crystal array of LMOs enriched/depleted in $^{100}$Mo. The tested LMOs show high spectrometric performance in both designs; notably, the measured energy resolution is 5--7 keV FWHM at 2615 keV $\gamma$s, nearby the Q-value of $^{100}$Mo (3034 keV). Due to the absence of a reflective cavity around LMOs, a low scintillation signal is detected by Ge bolometers: ~0.3 keV (150 photons) for 1-MeV $\gamma$($\beta$) LMO-event. Despite that, an acceptable separation between $\alpha$ and $\gamma$($\beta$) events is achieved with most devices. The highest efficiency is reached with light detectors in the $Thick$ design thanks to a lower baseline noise width (0.05--0.09 keV RMS) when compared to that obtained in the $Slim$ version (0.10--0.35 keV RMS). Given the pivotal role of bolometric photodetectors for particle identification and random coincidences rejection, we will use the structure here described with upgraded light detectors, featuring thermal signal amplification via the Neganov-Trofimov-Luke effect, as also demonstrated in the present work., Comment: Submitted to JINST; 31 pages, 16 figures, 5 tables

This paper presents an energy resolution study of the JUNO experiment, incorporating the latest knowledge acquired during the detector construction phase. The determination of neutrino mass ordering in JUNO requires an exceptional energy resolution better than 3\% at 1~MeV. To achieve this ambitious goal, significant efforts have been undertaken in the design and production of the key components of the JUNO detector. Various factors affecting the detection of inverse beta decay signals have an impact on the energy resolution, extending beyond the statistical fluctuations of the detected number of photons, such as the properties of the liquid scintillator, performance of photomultiplier tubes, and the energy reconstruction algorithm. To account for these effects, a full JUNO simulation and reconstruction approach is employed. This enables the modeling of all relevant effects and the evaluation of associated inputs to accurately estimate the energy resolution. The results of study reveal an energy resolution of 2.95\% at 1~MeV. Furthermore, this study assesses the contribution of major effects to the overall energy resolution budget. This analysis serves as a reference for interpreting future measurements of energy resolution during JUNO data collection. Moreover, it provides a guideline for comprehending the energy resolution characteristics of liquid scintillator-based detectors.

We explore the bound neutrons decay into invisible particles (e.g., $n\rightarrow 3 \nu$ or $nn \rightarrow 2 \nu$) in the JUNO liquid scintillator detector. The invisible decay includes two decay modes: $ n \rightarrow { inv} $ and $ nn \rightarrow { inv} $. The invisible decays of $s$-shell neutrons in $^{12}{\rm C}$ will leave a highly excited residual nucleus. Subsequently, some de-excitation modes of the excited residual nuclei can produce a time- and space-correlated triple coincidence signal in the JUNO detector. Based on a full Monte Carlo simulation informed with the latest available data, we estimate all backgrounds, including inverse beta decay events of the reactor antineutrino $\bar{\nu}_e$, natural radioactivity, cosmogenic isotopes and neutral current interactions of atmospheric neutrinos. Pulse shape discrimination and multivariate analysis techniques are employed to further suppress backgrounds. With two years of exposure, JUNO is expected to give an order of magnitude improvement compared to the current best limits. After 10 years of data taking, the JUNO expected sensitivities at a 90% confidence level are $\tau/B( n \rightarrow { inv} ) > 5.0 \times 10^{31} \, {\rm yr}$ and $\tau/B( nn \rightarrow { inv} ) > 1.4 \times 10^{32} \, {\rm yr}$., Comment: 28 pages, 7 figures, 4 tables

The current experiments searching for neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay also collect large statistics of Standard Model allowed two-neutrino double-$\beta$ ($2\nu\beta\beta$) decay events. These can be used to search for Beyond Standard Model (BSM) physics via $2\nu\beta\beta$ decay spectral distortions. $^{100}$Mo has a natural advantage due to its relatively short half-life, allowing higher $2\nu\beta\beta$ decay statistics at equal exposures compared to the other isotopes. We demonstrate the potential of the dual read-out bolometric technique exploiting a $^{100}$Mo exposure of 1.47 kg $\times$ y, acquired in the CUPID-Mo experiment at the Modane underground laboratory (France). We set limits on $0\nu\beta\beta$ decays with the emission of one or more Majorons, on $2\nu\beta\beta$ decay with Lorentz violation, and $2\nu\beta\beta$ decay with a sterile neutrino emission. In this analysis, we investigate the systematic uncertainty induced by modeling the $2\nu\beta\beta$ decay spectral shape parameterized through an improved model, an effect never considered before. This work motivates searches for BSM processes in the upcoming CUPID experiment, which will collect the largest amount of $2\nu\beta\beta$ decay events among the next-generation experiments.

We show the existence and uniqueness of fundamental solution operators to Kolmo\-gorov-Fokker-Planck equations with rough (measurable) coefficients and local or integral diffusion on finite and infinite time strips. In the local case, that is to say when the diffusion operator is of differential type, we prove $\L^2$ decay using Davies' method and the conservation property. We also prove that the existence of a generalized fundamental solution with the expected pointwise Gaussian upper bound is equivalent to Moser's $\L^2-\L^\infty$ estimates for local weak solutions to the equation and its adjoint. When coefficients are real, this gives the existence and uniqueness of such a generalized fundamental solution and a new and natural way to obtain pointwise decay., Comment: Revision following the referee's suggestion. Edition of the presentation of the homogeneous Sobolev norms for clarity. Most changes are in Section 2

In this article, we establish embeddings {\`a} la Lions and transfer of regularity {\`a} la Bouchut for a large scale of kinetic spaces. We use them to identify a notion of weak solutions to Kolmogorov-Fokker-Planck equations with (local or integral) diffusion and rough (measurable) coefficients under minimal requirements. We prove their existence and uniqueness for a large class of source terms, first in full space for the time, position and velocity variables and then for the kinetic Cauchy problem on infinite and finite time intervals., Comment: 40 pages, submitted. A correction to the argument in Theorem 6.7 and the corresponding argument in Section 7. Statements unchanged. Some typos eliminated