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Extreme mass ratio inspirals (EMRIs) are among the key sources of gravitational waves for the LISA space-based gravitational wave detector. Achieving sufficient accuracy in the gravitational wave template for these binaries requires modeling the effects of the spin of the comparably light secondary compact object. In this work, we employ the solution of the Hamilton-Jacobi equation for the motion of spinning bodies in Kerr space-time to obtain their generic orbits. Then, using the Teukolsky formalism we compute gravitational wave energy and angular momentum fluxes sourced by these orbits valid to linear order in secondary spin, and provide waveform snapshots corresponding to the motion. The solver we have developed substantially improves on previous studies in terms of speed and accuracy, and includes the case of a fully precessing secondary spin. As such, it provides a significant building block for the modelling of waveforms of precessing compact binaries at large mass ratios., Comment: 23 pages + appendices and references; 10 tables ; 10 figures. Supplemental Mathematica notebooks available at https://github.com/gabriel-andres-piovano/Spinning-Body-Hamilton-Jacobi

Quantum magnetic materials can provide explicit realizations of paradigm models in quantum many-body physics. In this context, SrCu$_2$(BO$_3$)$_2$ is a faithful realization of the Shastry-Sutherland model (SSM) for ideally frustrated spin dimers, even displaying several of its quantum magnetic phases as a function of pressure. We perform inelastic neutron scattering (INS) measurements on SrCu$_2$(BO$_3$)$_2$ at 5.5 GPa and 4.5 K, observing spin waves that characterize the high-pressure antiferromagnetic phase. The experimental spectra are well described by linear spin-wave calculations on a SSM with an inter-layer interaction, which is determined accurately as $J_c = 0.053(3)$ meV. The presence of $J_c$ indicates the need to account for the three-dimensional nature of SrCu$_2$(BO$_3$)$_2$ in theoretical models, also at lower pressures. We find that the ratio between in-plane interactions, $J'/J = 1.8(2)$, undergoes a dramatic change compared to lower pressures that we deduce is driven by a sharp drop in the dimer coupling, $J$. Our results underline the wide horizons opened by high-pressure INS experiments on quantum magnetic materials., Comment: Main text + supplemental material

In this paper we introduce a variational model for the study of multilayer films that allows for the treatment of both coherent and incoherent interfaces between layers. The model is designed in the framework of the theory of Stress Driven Rearrangement Instabilities, which are characterized by the competition between elastic and surface energy effects. The surface of each film layer is assumed to satisfy an ''exterior graph condition'', under which in particular bulk cracks are allowed to be of non-graph type. By applying the direct method of calculus of variations under a constraint on the number of connected components of the cracks not connected to the surface of the film layers the existence of energy minimizers is established in dimension 2. As a byproduct of the analysis the state of art on the variational modeling of single-layered films deposited on a fixed substrate is advanced by letting the substrate surface free, by addressing the presence of multiple layers of various materials, and by including the possibility of delamination between the various film layers., Comment: 27 pages, 2 figures

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

A variational model for describing the morphology of two-phase continua by allowing for the interplay between coherent and incoherent interfaces is introduced. Coherent interfaces are characterized by the microscopical arrangement of atoms of the two materials in a homogeneous lattice, with deformation being the solely stress relief mechanism, while at incoherent interfaces delamination between the two materials occurs. The model is designed in the framework of the theory of Stress Driven Rearrangement Instabilities, which are characterized by the competition between elastic and surface effects. The existence of energy minimizers is established in the plane by means of the direct method of the calculus of variations under a constraint on the number of boundary connected components of the underlying phase, whose exterior boundary is prescribed to satify a graph assumption, and of the two-phase composite region. Both the wetting and the dewetting regimes are included in the analysis., Comment: 62 pages, 6 figures

We investigate the impact of post-adiabatic (1PA) terms on parameter estimation for extreme and intermediate mass-ratio inspirals using state-of-the-art waveform models. Our analysis is the first to employ Bayesian inference to assess systematic errors for 1PA waveforms. We find that neglecting 1PA terms introduces significant biases for the (small) mass ratio $\epsilon \gtrsim 10^{-5}$ for quasi circular orbits in Schwarzschild spacetime, which can be mitigated with resummed 3PN expressions at 1PA order. Moreover, we show that the secondary spin is strongly correlated with the other intrinsic parameters, and it can not be constrained for $\epsilon \lesssim 10^{-5}$. Finally, we highlight the need for addressing eccentric waveform systematics in the small-mass-ratio regime, as they yield stronger biases than the circular limit in both intrinsic and extrinsic parameters., Comment: 25 + 11 pages, 10 figures, 5 tables, accepted for publication in PRD. Minor corrections to figures and new appendix on 1PA corrections to the EMRI waveform amplitudes

Rapidly rotating bodies moving in curved space-time experience the so-called spin-curvature force, which becomes important for the motion of compact objects in gravitational-wave inspirals. As a first approximation, this effect is captured in the motion of a spinning test particle. We solve the equations motion of a spinning particle to leading order in spin in arbitrary static and spherically symmetric space-times in terms of one-dimensional closed-form integrals. This solves the problem and proves its integrability in a wide range of modified gravities and near exotic compact objects. Then, by specializing to the case of bound orbits in Schwarzschild space-time, we demonstrate how to express the solution in the form of Jacobi elliptic functions., Comment: The notebooks and machine-readable formulas can be found in the repo https://github.com/VojtechW/Analytical-Solution-Spinning-particle-Spherical

In metal-organic-framework (MOF) perovskites, both magnetic and ferroelectric orderings can be readily realized by compounding spin and charge degrees of freedom. The hydrogen bonds that bridge the magnetic framework and organic molecules have long been thought of as a key in generating multiferroic properties. However, the underlying physical mechanisms remain unclear. Here, we combine neutron diffraction, quasielastic and inelastic neutron scattering, and THz spectroscopy techniques to thoroughly investigate the dynamical properties of the multiferroic MOF candidate [CH$_3$NH$_3$][Co(HCOO)$_3$] through its multiple phase transitions. The wide range of energy resolutions reachable by these techniques enables us to scrutinize the coupling between the molecules and the framework throughout the phase transitions and interrogate a possible magnetoelectric coupling. Our results also reveal a structural change around 220 K which may be associated with the activation of a nodding donkey mode of the methylammonium molecule due to the ordering of the CH$_3$ groups. Upon the occurrence of the modulated phase transition around 130 K, the methylammonium molecules undergo a freezing of its reorientational motions which is concomitant with a change of the lattice parameters and anomalies of collective lattice vibrations. No significant change has been however observed in the lattice dynamics around the magnetic ordering, which therefore indicates the absence of a substantial magneto-electric coupling in zero-field.

The morphology of crystalline thin films evolving on flat rigid substrates by condensation of extra film atoms or by evaporation of their own atoms in the surrounding vapor is studied in the framework of the theory of Stress Driven Rearrangement Instabilities (SDRI). By following the literature both the elastic contributions due to the mismatch between the film and the substrate lattices at their theoretical (free-standing) elastic equilibrium, and a curvature perturbative regularization preventing the problem to be ill-posed due to the otherwise exhibited backward parabolicity, are added in the evolution equation. The resulting Cauchy problem under investigation consists in an anisotropic mean-curvature type flow of the fourth order on the film profiles, which are assumed to be parametrizable as graphs of functions measuring the film thicknesses, coupled with a quasistatic elastic problem in the film bulks. The existence of a regular solution for a finite period of time is established under periodic boundary conditions by means of employing minimizing movements to exploit the gradient-flow structure of the evolution equation., Comment: 23 pages, 0 figures

The existence and the regularity results obtained in [37] for the variational model introduced in [36] to study the optimal shape of crystalline materials in the setting of stress-driven rearrangement instabilities (SDRI) are extended from two dimensions to any dimensions $n\geq2$. The energy is the sum of the elastic and the surface energy contributions, which cannot be decoupled, and depend on configurational pairs consisting of a set and a function that model the region occupied by the crystal and the bulk displacement field, respectively. By following the physical literature, the ``driving stress'' due to the mismatch between the ideal free-standing equilibrium lattice of the crystal with respect to adjacent materials is included in the model by considering a discontinuous mismatch strain in the elastic energy. Since two-dimensional methods and the methods used in the previous literature where Dirichlet boundary conditions instead of the mismatch strain and only the wetting regime were considered, cannot be employed in this setting, we proceed differently, by including in the analysis the dewetting regime and carefully analyzing the fine properties of energy-equibounded sequences. This analysis allows to establish both a compactness property in the family of admissible configurations and the lower-semicontinuity of the energy with respect to the topology induced by the $L^1$-convergence of sets and a.e.\ convergence of displacement fields, so that the direct method can be applied. We also prove that our arguments work as well in the setting with Dirichlet boundary conditions., Comment: 69 pages, 5 figures

Barium zirconate (BaZrO$_3$) is one of the very few perovskites that is claimed to retain an average cubic structure down to \SI{0}{\K}, while being energetically very close to an antiferrodistortive phase obtained by condensation of a soft phonon mode at the R point of the Brillouin zone boundary. In this work, we report a combined experimental and theoretical study of the temperature dependence of this soft phonon mode. Inelastic neutron and x-ray scattering measurements on single crystals show that it softens substantially from \SI{9.4}{\meV} at room temperature to \SI{5.6}{\meV} at \SI{2}{\K}. In contrast, the acoustic mode at the same R point is nearly temperature independent. The effect of the anharmonicity on the lattice dynamics is investigated non-perturbatively using direct dynamic simulations as well as a first-principles based self-consistent phonon theory, including quantum fluctuations of the atomic motion. By adding cubic and quartic anharmonic force constants, quantitative agreement with the neutron data for the temperature dependence of the antiferrodistortive mode is obtained. The quantum fluctuations of the atomic motion are found to be important to obtain the proper temperature dependence at low temperatures. The mean squared displacements of the different atoms are determined as function of temperature and are shown to be consistent with available experimental data. Adding anharmonicity to the computed fluctuations of the Ba-O distances also improves the comparison with available EXAFS data at \SI{300}{\K}.

We report neutron scattering measurements on YbMnSb$_2$ which shed new light on the nature of the magnetic moments and their interaction with Dirac fermions. Using half-polarized neutron diffraction we measured the field-induced magnetization distribution in the paramagnetic phase and found that the magnetic moments are well localised on the Mn atoms. Using triple-axis neutron scattering we measured the magnon spectrum throughout the Brillouin zone in the antiferromagnetically ordered phase, and we determined the dominant exchange interactions from linear spin-wave theory. The analysis shows that the interlayer exchange is five times larger than in several related compounds containing Bi instead of Sb. We argue that the coupling between the Mn local magnetic moments and the topological band states is more important in YbMnSb$_2$ than in the Bi compounds., Comment: 8 pages, 8 figures. Submitted to Physical Review B

We present triple-axis neutron scattering studies of low-energy magnetic fluctuations in strongly underdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x=0.05$, $0.06$ and $0.07$, providing quantitative evidence for a direct competition between these fluctuations and superconductivity. At dopings $x=0.06$ and $x=0.07$, three-dimensional superconductivity is found, while only a very weak signature of two-dimensional superconductivity residing in the CuO$_2$ planes is detectable for $x=0.05$. We find a surprising suppression of the low-energy fluctuations by an external magnetic field at all three dopings. This implies that the response of two-dimensional superconductivity to a magnetic field is similar to that of a bulk superconductor. Our results provide direct evidence of a very gradual onset of superconductivity in cuprates., Comment: 5 pages, 4 figures, and supplementary material

The low-temperature state of the quantum spin liquid candidate $\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$ emerges via an anomaly at $T^{*}\sim6$ K. Although signatures of this anomaly have been revealed in various quantities, its origin has remained unclear. Here we report inelastic neutron scattering measurements on single crystals of $\kappa$-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$, aiming at studying phonon renormalization effects at $T^{*}$. A drastic change was observed in the phonon damping across $T^{*}$ for a breathing mode of BEDT-TTF dimers at $E=4.7$ meV. The abrupt change in the phonon damping is attributed to a phase transition into a valence bond solid state based on an effective model describing the spin-charge coupling in this dimer-Mott system., Comment: 5 pages, 3 figures, supplemental materials (8 pages, 6 figures)

We estimate the accuracy in the measurement of the tidal Love number of a supermassive compact object through the detection of an extreme mass ratio inspiral~(EMRI) by the future LISA mission. A nonzero Love number would be a smoking gun for departures from the classical black hole prediction of General Relativity. We find that an EMRI detection by LISA could set constraints on the tidal Love number of a spinning central object with dimensionless spin $\hat a=0.9$ ($\hat a=0.99$) which are approximately four (six) orders of magnitude more stringent than what achievable with current ground-based detectors for stellar-mass binaries. Our approach is based on the stationary phase approximation to obtain approximate but accurate semi-analytical EMRI waveforms in the frequency-domain, which greatly speeds up high-precision Fisher-information matrix computations. This approach can be easily extended to several other tests of gravity with EMRIs and to efficiently account for multiple deviations in the waveform at the same time., Comment: 8 pages + appendices and references; 2 tables and 1 figure

We consider the discrete atomistic setting introduced in \cite{PiVe1} to microscopically justify the continuum model related to the \emph{Winterbottom problem}, i.e., the problem of determining the equilibrium shape of crystalline film drops resting on a substrate, and relax the rigidity assumption considered in \cite{PiVe1} to characterize the \emph{wetting} and \emph{dewetting regimes} and to perform the \emph{discrete to continuum passage}. In particular, all results of \cite{PiVe1} are extended to the setting where the distance between the reference lattices for the film and the substrate is not smaller than the optimal bond length between a film and a substrate atom. Such optimal film-substrate bonding distance is prescribed together with the optimal film-film distance by means of two-body atomistic interaction potentials of Heitmann-Radin type, which are both taken into account in the discrete energy, and in terms of which the wetting-regime threshold and the effective expression for the wetting parameter in the continuum energy are determined., Comment: arXiv admin note: substantial text overlap with arXiv:2010.08787

Extreme mass-ratio inspirals~(EMRIs) detectable by the Laser Inteferometric Space Antenna~(LISA) are unique probes of astrophysics and fundamental physics. Parameter estimation for these sources is challenging, especially because the waveforms are long, complicated, known only numerically, and slow to compute in the most relevant regime, where the dynamics is relativistic. We perform a time-consuming Fisher-matrix error analysis of the EMRI parameters using fully-relativistic numerical waveforms to leading order in an adiabatic expansion on a Kerr background, taking into account the motion of the LISA constellation, higher harmonics, and also including the leading correction from the spin of the secondary in the post-adiabatic approximation. We pay particular attention to the convergence of the numerical derivatives in the Fisher matrix and to the numerical stability of the covariance matrix, which for some systems requires computing the numerical waveforms with approximately $90$-digit precision. Our analysis confirms previous results (obtained with approximated but much more computationally efficient waveforms) for the measurement errors on the binary's parameters. We also show that the inclusion of higher harmonics improves the errors on the luminosity distance and on the orbital angular momentum angles by one order and two orders of magnitude, respectively, which might be useful to identify the environments where EMRIs live. We particularly focus on the measurability of the spin of the secondary, confirming that it cannot be measured with sufficient accuracy. However, due to correlations, its inclusion in the waveform model can deteriorate the accuracy on the measurements of other parameters by orders of magnitude, unless a physically-motivated prior on the secondary spin is imposed., Comment: 11 pages + appendices and references; 4 tables. Supplemental Mathematica notebooks available at https://web.uniroma1.it/gmunu/resources

The continuum model related to the Winterbottom problem, i.e., the problem of determining the equilibrium shape of crystalline drops resting on a substrate, is derived in dimension two by means of a rigorous discrete-to-continuum passage by $\Gamma$-convergence of atomistic models taking into consideration the atomic interactions of the drop particles both among themselves and with the fixed substrate atoms. As a byproduct of the analysis effective expressions for the drop surface anisotropy and the drop/substrate adhesion parameter appearing in the continuum model are characterized in terms of the atomistic potentials, which are chosen of Heitmann-Radin sticky-disc type. Furthermore, a threshold condition only depending on such potentials is determined distinguishing the wetting regime, where discrete minimizers are explicitly characterized as configurations contained in a layer with a one-atom thickness, i.e., the wetting layer, on the substrate, from the dewetting regime. In the latter regime, also in view of a proven conservation of mass in the limit as the number of atoms tends to infinity, proper scalings of the minimizers of the atomistic models converge (up to extracting a subsequence and performing translations on the substrate surface) to a bounded minimizer of the Winterbottom continuum model satisfying the volume constraint.

In the near future, it is envisioned that cellular networks will have to cope with extensive Internet of Things (IoT) devices. Therefore, a required feature of cellular IoT will be the capability to serve simultaneously a large number of devices with heterogeneous demands and qualities of Channel State Information at the Transmitter (CSIT). In this paper, we focus on an overloaded Multiple-Input Single-Output (MISO) Broadcast Channel (BC) with two groups of CSIT qualities, namely one group of users (representative of high-end devices) for which the transmitter has partial knowledge of the CSI, the other group of users (representative of IoT devices) for which the transmitter only has knowledge of the statistical CSI. We introduce Rate-Splitting Multiple Access (RSMA), a new multiple access based on multi-antenna Rate-Splitting (RS) for cellular IoT. Two strategies are proposed, namely, Time Partitioning-RSMA (TP-RSMA) and Power Partitioning-RSMA (PP-RSMA). The former independently serves the two groups of users over orthogonal time slots while the latter jointly serves the two groups of users within the same time slot in a non-orthogonal manner. We first show at high Signal-to-Noise Ratio (SNR) that PP-RSMA achieves the optimum Degrees-of-Freedom (DoF) in an overloaded MISO BC with heterogeneous CSIT qualities and then show at finite SNR that, by marrying the benefits of PP and RSMA, PP-RSMA achieves explicit sum rate gain over TP-RSMA and all baseline schemes. Furthermore, PP-RSMA is robust to CSIT inaccuracy and flexible to cope with Quality of Service (QoS) rate constraints of all users. The DoF and rate analysis helps us draw the conclusion that PP-RSMA is a powerful framework for cellular IoT with a large number of devices., Comment: 30 pages, 10 figures, submitted to the potential transaction for publication

We have successfully grown centimeter-sized layered $R$SrNiO$_4$ single crystals under high oxygen pressures of 120 bar by the floating zone technique. This enabled us to perform neutron scattering experiments where we observe close to quarter-integer magnetic peaks below $\sim$77 K that are accompanied by steep upwards dispersing spin excitations. Within the high-frequency Ni-O bond stretching phonon dispersion, a softening at the propagation vector for a checkerboard modulation can be observed. Together with our spin wave simulations these observations reveal that this Ni$^{3+}$ system exhibits charge disproportionation with charges segregating into a checkerboard pattern within a nano phase separation scenario rather than showing a Jahn-Teller effect.

The model introduced in [Kholmatov-Piovano 2020] in the framework of the theory on Stress-Driven Rearrangement Instabilities (SDRI) [Asaro-Tiller 1972; Grinfeld 1993} for the morphology of crystalline materials under stress is considered. As in [Kholmatov-Piovano 2020] and in agreement with the models in [Lowengrub et al. 2009; Spencer 1999], a mismatch strain, rather than a Dirichlet condition as in [Crismale-Friedrich 2020], is considered to include into the analysis the lattice mismatch between the crystal and possible adjacent (supporting) materials. The existence of solutions is established in dimension two in the absence of graph-like assumptions and of the restriction to a finite number $m$ of connected components for the free boundary of the region occupied by the crystalline material, thus extending previous results for epitaxially strained thin films and material cavities. Due to the lack of compactness and lower semicontinuity for the sequences of $m$-minimizers, i.e., minimizers among configurations with at most $m$ connected boundary components, a minimizing candidate is directly constructed, and then shown to be a minimizer by means of uniform density estimates and the convergence of $m$-minimizers' energies to the energy infimum as $m\to\infty$. Finally, regularity properties for the morphology satisfied by every minimizer are established., Comment: 52 pages, 1 figures

Extreme mass-ratio inspirals detectable by the future Laser Interferometer Space Antenna provide a unique way to test general relativity and fundamental physics. Motivated by this possibility, here we study in detail the EMRI dynamics in the presence of a spinning secondary, collecting and extending various results that appeared in previous work and also providing useful intermediate steps and new relations for the first time. We present the results of a frequency-domain code that computes gravitational-wave fluxes and the adiabatic orbital evolution for the case of circular, equatorial orbits with (anti)aligned spins. The spin of the secondary starts affecting the gravitational-wave phase at the same post-adiabatic order as the leading-order self-force terms and introduces a detectable dephasing, which can be used to measure it at $5-25\%$ level, depending on individual spins. In a companion paper we discuss the implication of this effect for tests of the Kerr bound., Comment: Improvements in response to referee reports. Typos corrected. Longer companion paper of arXiv:2003.08448. Data and code available at the website https://web.uniroma1.it/gmunu

An outstanding prediction of general relativity is the fact that the angular momentum $S$ of an isolated black hole with mass $\mu$ is limited by the Kerr bound, $S\leq G\mu^2/c$. Testing this cornerstone is challenging due to the difficulty in modelling spinning compact objects that violate this bound. We argue that precise, model-independent tests can be achieved by measuring gravitational waves from an extreme mass ratio inspiral around a supermassive object, one of the main targets of the future LISA mission. In the extreme mass ratio limit, the dynamics of the small compact object depends only on its multipole moments, which are free parameters. At variance with the comparable-mass case, accurate waveforms are valid also when the spin of the small object greatly exceeds the Kerr bound. By computing the orbital dephasing and the gravitational-wave signal emitted by a spinning point particle in circular, nonprecessing, equatorial motion around a Kerr black hole, we estimate that LISA will be able to measure the spin of the small compact object at the level of $10\%$. Together with mass measurements, this will allow for theory-agnostic, unprecedented constraints on string-theory inspired objects such as "superspinars", almost in their entire parameter space., Comment: Improvements in response to referee reports. Typos corrected. Data and code available at https://web.uniroma1.it/gmunu

Starting from the three-dimensional setting, we derive a limit model of a thin magnetoelastic film by means of {\Gamma}-convergence techniques. As magnetization vectors are defined on the elastically deformed configuration, our model features both Lagrangian and Eulerian terms. This calls for qualifying admissible three-dimensional deformations of planar domains in terms of injectivity. In addition, a careful treatment of the Maxwell system in the deformed film is required.