Search

To a submodular function we define a class of preorders, conforming preorders. A submodular function $z$ corresponds to a generalized permutahedron $\Pi(z)$. We show the faces of $\Pi(z)$ are in bijection with the conforming preorders. The face poset structure of $\Pi(z)$ induces two order relations $\lhd$ and $\blacktriangleleft$ on conforming preorder, and we investigate their properties. Ardila and Aguiar introduced a Hopf monoid of submodular functions/generalized permutahedra. We show there is a cointeracting bimonoid of modular functions. By recent theory of L.Foissy this associates a canonical polynomial to any submodular function., Comment: 48 pages

We prove that certain specific sum of enhanced states produce torsion of order two in the Khovanov homology.

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

The ever-increasing demand for efficient data storage and processing has fueled the search for novel memory devices. Spintronics offers an alternative fast and efficient solution using spin-to-charge interconversion. In this work, we demonstrate a remarkable thirty-four-fold increase in spin-to-charge current conversion when incorporating a 2D epitaxial graphene monolayer between iron and platinum layers by exploring spin-pumping on-chip devices. Furthermore, we find that the spin conversion is also anisotropic. We attribute this enhancement and anisotropy to the asymmetric Rashba contributions driven by an unbalanced spin accumulation at the differently hybridized top and bottom graphene interfaces, as highlighted by ad-hoc first-principles theory. The improvement in spin-to-charge conversion as well as its anisotropy reveals the importance of interfaces in hybrid 2D-thin film systems opening up new possibilities for engineering spin conversion in 2D materials, leading to potential advances in memory, logic applications, or unconventional computing., Comment: 33 pages with double-spaced paragraphs. 23 pages without references. 4 figures and one extended figure. Supplementary information, not shown, contains 21 pages and 23 supplementary figures

We study the thermal properties of a bulk Ni55Fe19Ga26 Heusler alloy in a conduction calorimeter. At slow heating and cooling rates (1K/h), we compare as-cast and annealed samples. We report a smaller thermal hysteresis after the thermal treatment due to the stabilization of the 14M modulated structure in the martensite phase. In ultraslow experiments (40mK/h), we detect and analyze the calorimetric avalanches associated with the direct and reverse martensitic transformation from cubic to 14M phase. This reveals a distribution of events characterized by a power law with exponential cutoff $p(u) \propto u^{-\varepsilon}\exp(-u/\xi)$ where $\varepsilon\sim 2$ and damping energies $\xi=370$uJ (direct) and $\xi=27$uJ (reverse) that characterize the asymmetry of the transformation., Comment: 13 pages; 6 figures; 3 tables

We report a very large spin-orbit torque (SOT) capability of chromium-based transition metal dichalcogenides (TMD) in their Janus forms CrXTe, with X=S,Se. The structural inversion symmetry breaking, inherent to Janus structures is responsible for a large SOT response generated by giant Rashba splitting, equivalent to that obtained by applying a transverse electric field of $\sim 100 \,\text{V} \,\text{nm}^{-1}$ in non-Janus CrTe\textsubscript{2}, completely out of experimental reach. By performing transport simulations on custom-made Wannier tight-binding models, Janus systems are found to exhibit a SOT performance comparable to the most efficient two-dimensional materials, while allowing for field-free perpendicular magnetization switching owing to their reduced in-plane symmetry. Altogether, our findings evidence that magnetic Janus TMDs stand as suitable candidates for ultimate SOT-MRAM devices., Comment: 6 pages

We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multi-indices that recently appeared in the literature, which can be briefly described as the graded dual of the enveloping algebra of the free Novikov algebra generated by the set of decorations. Similarly to what happens for the Hopf algebra of rooted forests, the formula can be written in terms of admissible cuts. We also prove a combinatorial formula for the extraction-contraction coproduct for undecorated multi-indices, in terms of a suitable notion of covering subforest., Comment: 19 pages. Combinatorial formula for extraction-contraction coproduct added, one reference added

Diffusion models represent a new paradigm in text-to-image generation. Beyond generating high-quality images from text prompts, models such as Stable Diffusion have been successfully extended to the joint generation of semantic segmentation pseudo-masks. However, current extensions primarily rely on extracting attentions linked to prompt words used for image synthesis. This approach limits the generation of segmentation masks derived from word tokens not contained in the text prompt. In this work, we introduce Open-Vocabulary Attention Maps (OVAM)-a training-free method for text-to-image diffusion models that enables the generation of attention maps for any word. In addition, we propose a lightweight optimization process based on OVAM for finding tokens that generate accurate attention maps for an object class with a single annotation. We evaluate these tokens within existing state-of-the-art Stable Diffusion extensions. The best-performing model improves its mIoU from 52.1 to 86.6 for the synthetic images' pseudo-masks, demonstrating that our optimized tokens are an efficient way to improve the performance of existing methods without architectural changes or retraining.

The thermal transport of magnons has attracted substantial attention as an energy-efficient alternative to the transport of electrons. Most theoretical studies so far have been carried out within the frame of the linear spin-wave theory, which dramatically fails upon increasing the temperature and in the presence of competing interactions. In this work, we consider the impact of three- and four-magnon interactions in a honeycomb antiferromagnet, where such interactions are remarkably strong even at zero temperature. Using a combination of quantum field theory and mean-field theory, we compute the band structure of the interacting magnons and investigate the spin Nernst effect. We find that in the presence of in-plane Dzyaloshinskii-Moriya Interaction, the three-magnon interaction induces a non-reciprocal band splitting, even at zero temperature, leading to an enhancement of the spin Nernst conductivity. In contrast, the four-magnon interaction renormalizes the magnon spectrum at high temperatures, leading to a reduction of the overall magnon spin Nernst effect. These results suggest that interactions can massively influence the transport properties of magnons in antiferromagnets, even at zero temperature, and should be taken into account for predictive modeling., Comment: 15 pages, 8 figures

We establish a comprehensive theoretical framework for systems subjected to a static uniform temperature gradient, employing the non-equilibrium Keldysh-Dyson formalism. This framework interprets the statistical force due to the temperature gradient as a mechanical force, utilizing both Luttinger's scalar and Moreno-Coleman-Tatara's vector potentials, which collectively emulate the gauge invariance stemming from the conservation of energy. Our approach has the ability to treat heat current and heat magnetization on an equal footing, thereby extending and generalizing previous formalisms. The derived result for the thermal conductivity is applied to investigate the thermal characteristics of Weyl magnons in a stacked honeycomb ferromagnet featuring a trivial insulator phase, a magnon Chern insulator phase, and three Weyl magnon phases. Against the expectation from the Berry curvature, the magnon Chern insulator phase exhibits the highest transverse thermal conductivity., Comment: 15 pages, 8 figures

The role of spin fluctuations near magnetic phase transitions is crucial for generating various exotic phenomena, including anomalies in the extraordinary Hall effect, excess spin-current generation through the spin-Hall effect (SHE), and enhanced spin-pumping, amongst others. In this study, we experimentally investigate the temperature dependence of spin-orbit torques (SOTs) generated by Mn3Ni0.35Cu0.65N (MNCN), a member of the noncollinear antiferromagnetic family that exhibits unconventional magnetotransport properties. Our work uncovers a strong and nontrivial temperature dependence of SOTs, peaking near the N\'eel temperature of MNCN, which cannot be explained by conventional intrinsic and extrinsic scattering mechanisms of the SHE. Notably, we measure a maximum SOT efficiency of 30%, which is substantially larger than that of commonly studied nonmagnetic materials such as Pt. Theoretical calculations confirm a negligible SHE and a strong orbital Hall effect that can explain the observed SOTs. We propose a previously unidentified mechanism wherein fluctuating antiferromagnetic moments trigger the generation of substantial orbital currents near the N\'eel temperature due to the emergence of scalar spin chirality. Our findings present an approach for enhancing SOTs, which holds promise for magnetic memory applications by leveraging antiferromagnetic spin fluctuations to amplify both orbital and spin currents.

The modeling of convection is a long standing problem in stellar physics. Up-to-now, all ad hoc models rely on a free parameter alpha (among others) which has no real physical justification and is therefore poorly constrained. However, a link exists between this free parameter and the entropy of the stellar adiabat. Prescriptions, derived from 3D stellar atmospheric models, are available that provide entropy as a function of stellar atmospheric parameters (effective temperature, surface gravity, chemical composition). This can provide constraints on alpha through the development of entropy-calibrated models. Several questions arise as these models are increasingly used. Which prescription should be used? How do uncertainties impact entropy-calibrated models? We aim to study the three existing prescriptions and determine which one should be used, and how. We implemented the entropy-calibration method into the stellar evolution code Cesam2k20 and performed comparisons with the Sun and the alpha Cen system. In addition, we used data from the CIFIST grid of 3D atmosphere models to evaluate the accuracy of the prescriptions. Of the three entropy prescriptions available, we determine which one best reproduces the entropies of the 3D models. We also demonstrate that the entropy obtained from this prescription should be corrected for the evolving chemical composition and for an entropy offset different between various EoS tables, following a precise procedure, otherwise classical parameters obtained from the models will be strongly biased. Finally, we also provide table with entropy of the adiabat of the CIFIST grid, as well as fits of these entropies. We performed a precise examination of entropy-calibrated modelling, and gave recommendations on which adiabatic entropy prescription to use, how to correct it and to implement the method into a stellar evolution code., Comment: 18 pages, 11 figures. Submitted to Astronomy and Astrophysics, recommended for publication with minor revisions

Experimental investigations of spin-charge interconversion in magnetic bilayers comprising a ferromagnet adjacent to a topological insulator have reported scattered results on the spin-charge and charge-spin conversion efficiency. Attempting to reconcile these contradicting experimental results, we develop a phenomenological theory of spin-charge interconversion accounting for both interfacial interconversion through the spin galvanic effect, also called the Rashba-Edelstein effect, as well as bulk interconversion via the spin Hall effect. We find that the spin current leakage into the nonmagnetic metal plays a central role during the spin-to-charge and charge-to-spin conversion, leading to dissymmetric interconversion processes. In particular, spin-to-charge conversion is much less sensitive to the spin current absorption in the nonmagnetic metal than charge-to-spin conversion. This suggests that spin pumping is a more trustable technique to extract the interfacial Rashba parameter than spin-orbit torque., Comment: 4 figures, 9 pages

We investigate the optical response induced by a d.c. current flowing in a nonmagnetic material that lacks inversion symmetry. In this class of materials, the flowing current experiences a nonlinear Hall effect and induces a nonequilibrium orbital magnetization, even in the absence of spin-orbit coupling. As a result, an orbital-driven Kerr effect arises that can be used to probe not only the orbital magnetization but also the nonlinear Hall effect. In addition, in the long wavelength limit, the nonlinear Hall effect leads to a rectification current that can be used to detect terahertz radiation. We apply the theory to selected model systems, such as WTe$_2$ bilayer and metallic superlattices. The nonequilibrium orbital Kerr efficiencies obtained in these systems are comparable to the largest values reported experimentally in GaAs and MoS$_2$, exceeding the values reported in metals and suggesting a large terahertz current responsivity., Comment: 11 pages, 8 figures

We give the explicit description of the NPL-operad structure on the free commutative monoid $\mathbf E\circ \mathbf q$ generated by a given positive operad $\mathbf q$. We propose to name NPL-operad a weak form of operad in which the nested associativity axiom is weakened down to a nested pre-Lie condition. This structure is new up to our knowledge., Comment: Major correction of the previous (withdrawn) version

This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure to match the double twisted bialgebra axioms is explicitly described.

The extremely high pseudo-magnetic field emerging in strained graphene suggests that an oscillating nano-deformation will induce a very high current even without electric bias. In this paper, we demonstrate the sub-terahertz (THz) dynamics of a valley-current and the corresponding charge pumping with a periodically excited nano-bubble. We discuss the amplitude of the pseudo-electric field and investigate the dependence of the pumped valley current on the different parameters of the system. Finally, we report the signature of extra-harmonics generation in the valley current that might lead to potential modern devices development operating in the nonlinear regime, Comment: 7 pages

The Edelstein effect is the origin of the spin-orbit torque: a current-induced torque that is used for the electrical control of ferromagnetic and antiferromagnetic materials. This effect originates from the relativistic spin-orbit coupling, which necessitates utilizing materials with heavy elements. Here we show that in magnetic materials with non-collinear magnetic order, the Edelstein effect and consequently also a current-induced torque can exist even in the absence of the spin-orbit coupling. Using group symmetry analysis, model calculations, and realistic simulations on selected compounds, we identify large classes of non-collinear magnet candidates and demonstrate that the current-driven torque is of similar magnitude as the celebrated spin-orbit torque in conventional transition metal structures. We also show that this torque can exist in an insulating material, which could allow for highly efficient electrical control of magnetic order., Comment: 11 pages, 5 figues

We propose a general theory of charge, spin, and orbital diffusion based on Keldysh formalism. Our findings indicate that the diffusivity of orbital angular momentum in metals is much lower than that of spin or charge due to the strong orbital intermixing in crystals. Furthermore, our theory introduces the concept of spin-orbit polarization by which a pure orbital (spin) current induces a longitudinal spin (orbital) current, a process as efficient as spin polarization in ferromagnets. Finally, we find that orbital currents undergo momentum swapping, even in the absence of spin-orbit coupling. This theory establishes several key parameters for orbital transport of direct importance to experiments.

We show that dynamics of the magnetization in ferromagnets can pump the orbital angular momentum, which we denote by orbital pumping. This is the reciprocal phenomenon to the orbital torque that induces magnetization dynamics by the orbital angular momentum in non-equilibrium. The orbital pumping is analogous to the spin pumping established in spintronics but requires the spin-orbit coupling for the orbital angular momentum to interact with the magnetization. We develop a formalism that describes the generation of the orbital angular momentum by magnetization dynamics within the adiabatic perturbation theory. Based on this, we perform first-principles calculation of the orbital pumping in prototypical $3d$ ferromagnets, Fe, Co, and Ni. The results show that the ratio between the orbital pumping and the spin pumping ranges from 5 to 15 percents, being smallest in Fe and largest in Ni. This implies that ferromagnetic Ni is a good candidate for measuring the orbital pumping. Implications of our results on experiments are also discussed.

Spin and charge pumping induced by a precessing magnetization has been instrumental to the development of spintronics. Nonetheless, most theoretical studies so far treat the spin-orbit coupling as a perturbation, which disregards the competition between exchange and spin-orbit fields. In this work, based on Keldysh formalism and Wigner expansion, we develop an adiabatic theory of spin and charge pumping adapted to systems with arbitrary spin-orbit coupling. We apply this theory to the magnetic Rashba gas and magnetic graphene cases and discuss the pumped ac and dc current. We show that the pumped current possesses both intrinsic (Berry curvature-driven) and extrinsic (Fermi surface breathing-driven) contributions, akin to magnetic damping. In addition, we find that higher harmonics can be generated under large-angle precession and we propose a couple of experimental setups where such an effect can be experimentally observed., Comment: 9 pages, 10 figures

In wireless communication systems, mmWave beam tracking is a critical task that affects both sensing and communications, as it is related to the knowledge of the wireless channel. We consider a setup in which a Base Station (BS) needs to dynamically choose whether the resource will be allocated for one of the three operations: sensing (beam tracking), downlink, or uplink transmission. We devise an approach based on the Proximal Policy Optimization (PPO) algorithm for choosing the resource allocation and beam tracking at a given time slot. The proposed framework takes into account the variable quality of the wireless channel and optimizes the decisions in a coordinated manner. Simulation results demonstrate that the proposed method achieves significant performance improvements in terms of average packet error rate (PER) compared to the baseline methods while providing a significant reduction in beam tracking overhead. We also show that our proposed PPO-based framework provides an effective solution to the resource allocation problem in beam tracking and communication, exhibiting a great generalization performance regardless of the stochastic behavior of the system.

After providing a short review on the recently introduced notion of post-group by Bai, Guo, Sheng and Tang, we exhibit post-group counterparts of important post-Lie algebras in the literature, including the infinite-dimensional post-Lie algebra of Lie group integrators. The notion of free post-group is examined, and a group isomorphism between the two group structures associated to a free post-group is explicitly constructed., Comment: Inaccurracy corrected by considering weak post-groups (recently introduced by S. Wang, arXiv:2307.10535)

Magnonics or magnon spintronics is an emerging field focusing on generating, detecting, and manipulating magnons. As charge-neutral quasi-particles, magnons are promising information carriers because of their low energy dissipation and long coherence length. In the past decade, topological phases in magnonics have attracted intensive attention due to their fundamental importance in condensed-matter physics and potential applications of spintronic devices. In this review, we mainly focus on recent progress in topological magnonics, such as the Hall effect of magnons, magnon Chern insulators, topological magnon semimetals, etc. In addition, the evidence supporting topological phases in magnonics and candidate materials are also discussed and summarized. The aim of this review is to provide readers with a comprehensive and systematic understanding of the recent developments in topological magnonics., Comment: 17 pages, 12 figures

Ferromagnets generate an anomalous Hall effect even without the presence of a magnetic field, something that conventional antiferromagnets cannot replicate but noncollinear antiferromagnets can. The anomalous Hall effect governed by the resistivity tensor plays a crucial role in determining the presence of time reversal symmetry and the topology present in the system. In this work we reveal the complex origin of the anomalous Hall effect arising in noncollinear antiferromagnets by performing Hall measurements with fields applied in selected directions in space with respect to the crystalline axes. Our coplanar magnetic field geometry goes beyond the conventional perpendicular field geometry used for ferromagnets and allows us to suppress any magnetic dipole contribution. It allows us to map the in-plane anomalous Hall contribution and we demonstrate a 120$^\circ$ symmetry which we find to be governed by the octupole moment at high fields. At low fields we subsequently discover a surprising topological Hall-like signature and, from a combination of theoretical techniques, we show that the spins can be recast into dipole, emergent octupole and noncoplanar effective magnetic moments. These co-existing orders enable magnetization dynamics unachievable in either ferromagnetic or conventional collinear antiferromagnetic materials.

In this paper, we analyze the results of neutral-beam current drive (NBCD) experiments, performed in the TJ-II stellarator, with the aim of validating the theoretical predictions. Both parallel and anti-parallel injection with respect to the magnetic field were explored using co (NBI1) and counter (NBI2) beams at different injected beam power and plasma densities. The fast-ion current driven by both beams was simulated with the Monte Carlo code ASCOT and the electron response to the fast-ion current was calculated analytically using a model valid for an arbitrary magnetic configuration and a low collisionality plasma. The model reproduces with rather good agreement the toroidal current measured in NBI2 plasmas while the current driven by NBI1 is less than half the predicted one. Possible reasons for this discrepancy are discussed.

Spin-orbit torques in noncentrosymmetric polycrystalline magnetic heterostructures are usually described in terms of field-like and damping-like torques. However, materials with a lower symmetry point group can exhibit torques whose behavior substantially deviates from the conventional ones. In particular, based on symmetry arguments it was recently proposed that systems belonging to the C_{3v} point group display spin-orbit torques that can promote field-free switching [Liu et al. Nature Nanotechnology 16, 277 (2021)]. In the present work, we analyze the general form of the torques expected in C3v crystals using the Invariant Theory. We uncover several new components that arise from the coexistence of the three-fold rotation and mirror symmetries. Using both tight binding model and first principles simulations, we show that these unconventional torque components arise from the onset of trigonal warping of the Fermi surface and can be as large as the damping-like torque. In other words, the Fermi surface warping is a key indicator to the onset of field-free switching in low symmetry crystals.

Orbitronics has recently emerged as a very active research topic after several proposals aiming to exploit the orbital degree of freedom for charge-free electronics. In this communication, we investigate orbital transport in selected two-dimensional systems to better understand which parameters govern the intra-atomic and inter-atomic contributions to the orbital Hall effect. We study the impact of the gap, the role of the materials' topology and the influence of the disorder on spin and orbital Hall transport. Starting from the Kane-Mele model, we describe how the orbital moment behaves depending on the material's topology and clarify the influence of the gap on the orbital Hall conductivity. We then extend the study to realistic topologically trivial and non-trivial materials, and find that the topology has little qualitative influence on the orbital Hall conductivity. In contrast, we observe that the energy dispersion has a more dramatic impact, especially in the presence of disorder. Remarkably, our results suggest that the intra-atomic orbital Hall current is more robust against scattering than the inter-atomic one, without further impact of the topological properties of the system under consideration.

Most research in the area of machine learning-based user beam selection considers a structure where the model proposes appropriate user beams. However, this design requires a specific model for each user-device beam codebook, where a model learned for a device with a particular codebook can not be reused for another device with a different codebook. Moreover, this design requires training and test samples for each antenna placement configuration/codebook. This paper proposes a device-agnostic beam selection framework that leverages context information to propose appropriate user beams using a generic model and a post processing unit. The generic neural network predicts the potential angles of arrival, and the post processing unit maps these directions to beams based on the specific device's codebook. The proposed beam selection framework works well for user devices with antenna configuration/codebook unseen in the training dataset. Also, the proposed generic network has the option to be trained with a dataset mixed of samples with different antenna configurations/codebooks, which significantly eases the burden of effective model training., Comment: 30 pages, 19 figures. This article was submitted to IEEE Trans. Wirel. Commun. on Nov 14 2022

Van der Waals (vdW) magnets are appealing candidates for realising spintronic devices that exploit current control of magnetization (e.g. switching or domain wall motion), but so far experimental demonstrations have been sparse, in part because of challenges associated with imaging the magnetization in these systems. Widefield nitrogen-vacancy (NV) microscopy allows rapid, quantitative magnetic imaging across entire vdW flakes, ideal for capturing changes in the micromagnetic structure due to an electric current. Here we use a widefield NV microscope to study the effect of current injection in thin flakes ($\sim10$nm) of the vdW ferromagnet Fe$_3$GeTe$_2$ (FGT). We first observe current-reduced coercivity on an individual domain level, where current injection in FGT causes substantial reduction in the magnetic field required to locally reverse the magnetisation. We then explore the possibility of current-induced domain-wall motion, and provide preliminary evidence for such a motion under relatively low current densities, suggesting the existence of strong current-induced torques in our devices. Our results illustrate the applicability of widefield NV microscopy to imaging spintronic phenomena in vdW magnets, highlight the possibility of efficient magnetization control by direct current injection without assistance from an adjacent conductor, and motivate further investigations of the effect of currents in FGT and other vdW magnets., Comment: 18 pages, 9 figures

We investigate the influence of surface states on the nonlinear Hall response of non-centrosymmetric time-reversal invariant Weyl semimetals. To do so, we perform a tomography of the Berry curvature dipole in a slab system using a minimal two-band model. We find that in the type-I phase, the nonlinear Hall response is not particularly sensitive to the presence of Fermi arcs or other trivial surface states. However, in the type-II phase, we find that these surface states contribute substantially to the Berry curvature dipole, leading to a strong thickness dependence of the nonlinear Hall response. This feature depends on the nature of the surface states and, henceforth, on the slab geometry adopted. In order to assess the validity of this scenario for realistic systems, we performed Berry curvature dipole calculations by first principles on the WTe$_2$, confirming the dramatic impact of surface states for selected slab geometries. Our results suggest that surface states, being topological or not, can contribute much more efficiently to the nonlinear Hall response than bulk states. This prediction is not limited to topological semimetals and should apply to topologically trivial non-centrosymmetric materials and heterostructures, paving the way to interfacial engineering of the nonlinear Hall effect.

Understanding the algebraic structure underlying a manifold with a general affine connection is a natural problem. In this context, A. V. Gavrilov introduced the notion of framed Lie algebra, consisting of a Lie bracket (the usual Jacobi bracket of vector fields) and a magmatic product without any compatibility relations between them. In this work we will show that an affine connection with curvature and torsion always gives rise to a post-Lie algebra as well as a $D$-algebra. The notions of torsion and curvature together with Gavrilov's special polynomials and double exponential are revisited in this post-Lie algebraic framework. We unfold the relations between the post-Lie Magnus expansion, the Grossman-Larson product and the $K$-map, $\alpha$-map and $\beta$-map, three particular functions introduced by Gavrilov with the aim of understanding the geometric and algebraic properties of the double-exponential, which can be understood as a geometric variant of the Baker-Campbell-Hausdorff formula. We propose a partial answer to a conjecture by Gavrilov, by showing that a particular class of geometrically special polynomials is generated by torsion and curvature. This approach unlocks many possibilities for further research such as numerical integrators and rough paths on Riemannian manifolds., Comment: 33 pages, one figure, uses Forest package

While initial beam alignment (BA) in millimeter-wave networks has been thoroughly investigated, most research assumes a simplified terminal model based on uniform linear/planar arrays with isotropic antennas. Devices with non-isotropic antenna elements need multiple panels to provide good spherical coverage, and exhaustive search over all beams of all the panels leads to unacceptable overhead. This paper proposes a location- and orientation-aware solution that manages the initial BA for multi-panel devices. We present three different neural network structures that provide efficient BA with a wide range of training dataset sizes, complexity, and feedback message sizes. Our proposed methods outperform the generalized inverse fingerprinting and hierarchical panel-beam selection methods for two considered edge and edge-face antenna placement designs., Comment: 5 pages, 7 figure. This article was submitted to IEEE SPAWC 2022 on Mar 11 2022

Topological phases of matter are conventionally characterized by the bulk-boundary correspondence in Hermitian systems: The topological invariant of the bulk in $d$ dimensions corresponds to the number of $(d-1)$-dimensional boundary states. By extension, higher-order topological insulators reveal a bulk-edge-corner correspondence, such that $n$-th order topological phases feature $(d-n)$-dimensional boundary states. The advent of non-Hermitian topological systems sheds new light on the emergence of the non-Hermitian skin effect (NHSE) with an extensive number of boundary modes under open boundary conditions. Still, the higher-order NHSE remains largely unexplored, particularly in the experiment. We introduce an unsupervised approach -- physics-graph-informed machine learning (PGIML) -- to enhance the data mining ability of machine learning with limited domain knowledge. Through PGIML, we experimentally demonstrate the second-order NHSE in a two-dimensional non-Hermitian topolectrical circuit. The admittance spectra of the circuit exhibit an extensive number of corner skin modes and extreme sensitivity of the spectral flow to the boundary conditions. The violation of the conventional bulk-boundary correspondence in the second-order NHSE implies that modification of the topological band theory is inevitable in higher dimensional non-Hermitian systems.

This article is the first of a trilogy that addresses various aspects of the perturbative response of general quantum systems, with possibly nontrivial ground state geometry, beyond linear order. Here, we use group theoretical considerations to investigate the structure of retarded correlators, and demonstrate how they decompose according to irreducible representations of a `time-reversal group' and relevant permutation groups, with the former probing dissipative and time-reversal properties, and the latter discerning configurational properties -- longitudinal, transverse and their generalizations. We establish second order fluctuation-dissipation and fluctuation-reaction theorems, and connect them to well-known second order transport effects such as the shift and injection currents. Exploiting the Schur-Weyl duality between irreducible representations of general linear groups and irreducible representations of permutation groups, we show how to decide which terms in the decomposition based on the latter can be supported by different crystals described via the 32 point groups, and perform the full point group classification for rank 3 and 4 polar and axial tensors. Our results provide a formal basis for the extraction of uniquely differing physical effects from retarded correlators. Applications to second order charge current responses in selected cases are given in part III., Comment: 37+12 pages

This article is the second of a trilogy that addresses the perturbative response of general quantum systems, with possibly nontrivial ground state geometry, beyond linear order. Here, we establish concise, general formulae for second order response to a spatially uniform, time-varying electric field in the velocity gauge that are $\textit{manifestly}$ free of static limit spurious divergences. We first discuss general quantum evolution in a curved space, then detail how such a situation is a natural byproduct of Hilbert space truncation, and point out crucial subtleties associated with the resulting finite curvatures. We then present a geometric perspective of the two popular gauges often used in quantum transport theories, the velocity gauge and the length gauge, and discuss how they, taking truncation-induced curvature effects into account, naturally lead to the same results in spite of the truncation. We highlight subtle formal discrepancies in the literature. Finally, we provide a general scheme for removing static limit spurious divergences in the velocity gauge $\textit{without}$ frequency expansions and present concise and comprehensive Green's function formulae for responses up to second order. As an application of specific aspects of our theory, second order charge current responses in selected cases are analyzed in parts I and III., Comment: 33+16 pages