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Given a tuple of $n \times n$ complex matrices ${\cal A} = (A_1,A_2,\ldots, A_m)$, the linear symbolic matrix $A = A_1x_1 + A_2x_2 + \cdots + A_m x_m$ is nonsingular in the noncommutative sense if and only if the completely positive operators $T_{\cal A} (X) = \sum_{i=1}^m A_i X A_i^{\dagger}$ and $T_{\cal A}^*(X) = \sum_{i=1}^m A_i^{\dagger} X A_i$ can be scaled to be doubly stochastic: For every $\epsilon > 0$ there are $g,h \in GL(n,\mathbb{C})$ such that $\|T_{g^{\dagger}{\cal A}h}(I)- I\| < \epsilon$, $\| T^*_{g^\dagger{\cal A}h}(I) - I\| < \epsilon$. In this paper, we show a refinement: The noncommutative corank of $A$ is equal to one-half of the minimum residual $\|T_{g^{\dagger}{\cal A}h}(I) - I\|_1 + \|T^*_{g^{\dagger}{\cal A}h}(I) - I\|_1$ over all possible scalings $g^{\dagger}{\cal A}h$, where $\|\cdot \|_1$ is the trace norm. To show this, we interpret the residuals as gradients of a convex function on symmetric space $GL(n,\mathbb{C})/U_n$, and establish a general duality relation of the minimum gradient-norm of a lower-unbounded convex function $f$ on $GL(n,\mathbb{C})/U_n$ with an invariant Finsler metric, by utilizing the unbounded gradient flow of $f$ at infinity.

Double perovskites containing heavy transition metal ions are an important family of compounds for the study of the interplay between electron correlation and spin-orbit coupling. Here, by combining magnetic susceptibility, heat capacity, and neutron scattering measurements, we investigate the dipolar and quadrupolar correlations in two prototype rhenium-based double perovskite compounds, Ba$_2$YReO$_6$ and Ba$_2$ScReO$_6$. A type-I dipolar antiferromagnetic ground state with a propagation vector $\mathbf{q} = (0, 0, 1)$ is observed in both compounds. At temperatures above the magnetic transitions, a quadrupolar ordered phase is identified. Weak spin excitations, which are gapped at low temperatures and softened in the correlated paramagnetic phase, are explained using a minimal model that considers both the dipolar and quadrupolar interactions. At larger wavevectors, we observe dominant phonon excitations that are well described by density functional calculations., Comment: 13 pages, 11 figures

We phenomenologically formulate and experimentally observe an adiabatic transverse thermoelectric conversion enhanced by a heat current re-orientation in artificially tilted multilayers (ATMLs). By alternately stacking two materials with different thermal conductivities and rotating its multilayered structure with respect to a longitudinal temperature gradient, off-diagonal components in the thermal conductivity tensor are induced. This off-diagonal thermal conduction (ODTC) generates a finite transverse temperature gradient and Seebeck-effect-induced thermopower in the adiabatic condition, which is superposed on the isothermal transverse thermopower driven by the off-diagonal Seebeck effect (ODSE). In this study, we calculate and observe the two-dimensional temperature distribution and the resultant transverse thermopower in ATMLs comprising thermoelectric Co$_{2}$MnGa Heusler alloys and Bi$_{2-a}$Sb$_{a}$Te$_{3}$ compounds. By changing the tilt angle from 0{\deg} to 90{\deg}, the transverse temperature gradient obviously appeared in the middle angles and the transverse thermopower increases up to -116.1 ${\mu}$V/K in Co$_{2}$MnGa/Bi$_{0.2}$Sb$_{1.8}$Te$_{3}$-based ATML at the tilt angle of 45{\deg} whereas the isothermal contribution is estimated to be -82.6 ${\mu}$V/K from the analytical calculation. This hybrid action derived from ODTC results in the significant variation of the maximum reduced efficiency for transverse thermoelectric conversion from 3.1% in the isothermal limit to 8.1% in the adiabatic limit., Comment: 12 pages, 6 figures

Harnessing quantum phenomena in energy storage systems offers an opportunity to introduce a new generation of batteries with quantum-enhanced performance. Until now, the quantum battery has largely remained a theoretical concept, with little progress towards experimental realisation, due to the challenges in quantum coherent control. Here, we experimentally demonstrate a scalable room-temperature quantum battery with a multi-layered organic-microcavity design. We show that it exhibits superextensive charging, metastabilisation of stored energy, and generates superextensive electrical power, the latter an unpredicted phenomenon. The combination of these properties in a single device is the first demonstration of the full cycle of a quantum battery, laying the framework for future designs., Comment: 53 pages, 18 figures

We propose and demonstrate a quantitative noncontact measurement method for the thermal Hall effect (THE) based on magnetic-field-modulated lock-in thermography. This method enables visualization of THE-induced temperature change and quantitative estimation of the thermal Hall angle $\theta_{\rm THE}$ by applying periodic magnetic fields to a sample and obtaining the first harmonic response of thermal images. By combining this method with LIT-based measurement techniques for the longitudinal thermal conductivity $\kappa_{xx}$, we also quantify the transverse thermal conductivity $\kappa_{xy}$. We validate our measurement methods by estimating $\theta_{\rm THE}$, $\kappa_{xx}$, and $\kappa_{xy}$ in a ferromagnetic Heusler alloy Co$_2$MnGa slab showing large THE., Comment: 18 pages, 6 figures

This study reports the observation of the large anomalous Nernst effect in polycrystalline ferromagnetic Co$_{2}$MnGa (CMG) slabs prepared by a spark plasma sintering method. By optimizing the sintering conditions, the anomalous Nernst coefficient reaches ~7.5 $\mu$V K$^{-1}$ at room temperature, comparable to the highest value reported in the single-crystalline CMG slabs. Owing to the sizable anomalous Nernst coefficient and reduced thermal conductivity, the dimensionless figure of merit in our optimized CMG slab shows the record-high value of ~8$\times$10$^{-4}$ at room temperature. With the aid of the nano/microstructure characterization and first-principles phonon calculation, this study discusses the dependence of the transport properties on the degree of crystalline ordering and morphology of crystal-domain boundaries in the sintered CMG slabs. The results reveal a potential of polycrystalline topological materials for transverse thermoelectric applications, enabling the construction of large-scale modules., Comment: 19 pages, 5 figures

The thermoelectric Thomson effect, predicted in the 1850s by William Thomson, produces volumetric heating/cooling in a conductor due to the concerted action of the Seebeck and Peltier effects. Recently, transverse thermoelectrics studies on the Nernst and Ettingshausen effects have progressed rapidly to enable versatile thermal management technologies and to explore topological transport properties. However, a transverse Thomson effect, arising from the concerted action of the Nernst and Ettingshausen effects, has not yet been observed. Here, we report the observation of the transverse Thomson effect in a conductor. We observed volumetric heating/cooling in a semimetallic Bi$_{88}$Sb$_{12}$ alloy induced by a charge current, temperature gradient, and magnetic field applied orthogonally to each other using thermoelectric imaging techniques. We found that the heating/cooling can be switched by the field direction. Our experiments and analyses reveal the essential difference between the conventional and transverse Thomson effects; the former depends sorely on the temperature derivative of the Seebeck coefficient, while the latter depends not only on the temperature derivative of the Nernst coefficient but also on its magnitude. The observation of the transverse Thomson effect fills a missing piece in the history of thermoelectrics and provides a new principle for active thermal management technologies., Comment: 18 pages, 7 figures

Compounds with the anti-PbFCl structure exhibit a variety of electronic instabilities and intriguing physical properties. NaAlSi and NaAlGe are similar topological nodal-line semimetals, but they have distinct properties. NaAlSi is a superconductor at 6.8 K, whereas NaAlGe is an insulator with a pseudogap of approximately 100 K. Using the potassium-indium flux method, we succeeded in synthesizing a single crystal of KAlGe, a new anti-PbFCl compound. First principles electronic structure calculations reveal that KAlGe is isoelectronic with NaAlSi and NaAlGe. KAlGe undergoes a metal-to-metal transition at 89 K and exhibits no superconductivity above 1.8 K. The low temperature phase has significantly lower carrier density and extremely high mobility, similar to Dirac electron systems. Furthermore, X-ray diffraction experiments show a structural change that breaks the fourfold symmetry during the phase transition. Electron-phonon interactions may be responsible for superconductivity in NaAlSi, whereas excitonic electron-hole interactions are thought to play an important role in KAlGe and possibly NaAlGe. Our findings demonstrate that fascinating physics lies within the compound family., Comment: 12 pages, 12 figures, accepted by Chemistry of Materials

We describe some of our group's recent work on common envelopes. Our goal is to understand the onset and outcomes of dynamically unstable mass transfer, including the properties of the binaries left behind and the outflows during the common envelope stage. We have also started thinking about light curves of common envelope events. During a talk at StanFest, a meeting in honour of Stan Owocki's retirement held in Leuven in July, 2024, the first author reported on some of the results we recently obtained and briefly outlined future prospects.

The global shift towards a carbon-neutral society has accelerated the demand for green energy, driving research into efficient technologies for harvesting energy from low-grade waste heat. Recently, transverse thermoelectrics based on the anomalous Nernst effect (ANE) has gained attention due to their simple device structure, scalability, and manufacturing-friendly nature. While topological single crystals and epitaxial films have been focused for enhancing the ANE-driven thermoelectric performance, further improvements in material design are necessary for practical applications. Here, we report an easy-to-implement strategy for designing mechanically flexible and magnetically hard transverse thermoelectric materials by creating amorphous-crystalline heterogeneous composites. We fabricated and optimized the heterogeneous composites through controlled heat treatment, achieving significant enhancements in the coercivity and anomalous Nernst coefficient, while maintaining flexibility. Additionally, using the developed material, we constructed a single-material-based coiled device and demonstrated the zero-field operation of the ANE-based energy harvesting from curved heat sources. These results validate the feasibility of using the ANE-based flexible materials for energy harvesting applications.

Using the Subaru/FOCAS IFU capability, we examine the spatially resolved relationships between gas-phase metallicity, stellar mass, and star-formation rate surface densities (Sigma_* and Sigma_SFR, respectively) in extremely metal-poor galaxies (EMPGs) in the local universe. Our analysis includes 24 EMPGs, comprising 9,177 spaxels, which span a unique parameter space of local metallicity (12+log(O/H) = 6.9 to 7.9) and stellar mass surface density (Sigma_* ~ 10^5 to 10^7 Msun/kpc^2), extending beyond the range of existing large integral-field spectroscopic surveys. Through spatially resolved emission line diagnostics based on the [NII] BPT-diagram, we verify the absence of evolved active galactic nuclei in these EMPGs. Our findings reveal that, while the resolved mass-metallicity relation exhibits significant scatter in the low-mass regime, this scatter is closely correlated with local star-formation surface density. Specifically, metallicity decreases as Sigma_SFR increases for a given Sigma_*. Notably, half of the EMPGs show a distinct metal-poor horizontal branch on the resolved mass-metallicity relation. This feature typically appears at the peak clump with the highest Sigma_* and Sigma_SFR and is surrounded by a relatively metal-enriched ambient region. These findings support a scenario in which metal-poor gas infall fuels episodic star formation in EMPGs, consistent with the kinematic properties observed in these systems. In addition, we identify four EMPGs with exceptionally low central metallicities (12+log(O/H) <~ 7.2), which display only a metal-poor clump without a surrounding metal-rich region. This suggests that such ultra-low metallicity EMPGs, at less than a few percent of the solar metallicity, may serve as valuable analogs for galaxies in the early stages of galaxy evolution., Comment: 29 pages, 14 figures. Submitted to ApJ

Metal-poor stars enriched by a single supernova (mono-enriched stars) are direct proof (and provide valuable probes) of supernova nucleosynthesis. Photometric and spectroscopic observations have shown that metal-poor stars have a wide variety of chemical compositions; the star's chemical composition reflects the nucleosynthesis process(es) that occurred before the star's formation. While the identification of mono-enriched stars enables us to study the ejecta properties of a single supernova, the fraction of mono-enriched stars among metal-poor stars remains unknown. Here we identify mono-enriched stars in a dwarf galaxy cosmological zoom-in simulation resolving individual massive stars. We find that the fraction of mono-enriched stars is higher for lower metallicity, stars with [Fe/H] $< -2.5$. The percentages of mono-enriched stars are 11% at [Fe/H] = $-$5.0 and 1% at [Fe/H] = $-$2.5, suggesting that most metal-poor stars are affected by multiple supernovae. We also find that mono-enriched stars tend to be located near the center of the simulated dwarf. Such regions will be explored in detail in upcoming surveys such as the Prime Focus Spectrograph (PFS) on the Subaru telescope., Comment: 8 pages, 5 figures, accepted for publication in ApJL

In February and March 2024, a series of many Type I X-ray bursts from the accreting neutron star SRGA J144459.2$-$604207, which has been identified by multiple X-ray satellites, with the first reports coming from INTEGRAL and NinjaSat. These observations reveal that after exhibiting very regular behavior as a ``clocked'' burster, the peak luminosity of the SRGA J144459.2$-$604207 X-ray bursts shows a gradual decline. The observed light curves exhibit a short plateau feature, potentially with a double peak, followed by a rapid decay in the tail-features unlike those seen in previously observed clocked bursters. In this study, we calculate a series of multizone X-ray burst models with various compositions of accreted matter, specifically varying the mass fractions of hydrogen ($X$), helium ($Y$), and heavier CNO elements or metallicity ($Z_{\rm CNO}$). We demonstrate that a model with higher $Z_{\rm CNO}$ and/or lower $X/Y$ compared to the solar values can reproduce the observed behavior of SRGA J144459.2$-$604207. Therefore, we propose that this new X-ray burster is likely the first clocked burster with non-solar elemental compositions. Moreover, based on the X-ray burst light curve morphology in the decline phase observed by NinjaSat, a He-enhanced model with $X/Y \approx 1.5$ seems preferred over high-metallicity cases. We also give a brief discussion on the implications for the neutron star mass, binary star evolution, inclination angle, and the potential for a high-metallicity scenario, the last of which is closely related to the properties of the hot CNO cycle., Comment: 7 pages, 5 figures, accepted for publication in PASJ Letter

The CubeSat X-ray observatory NinjaSat was launched on 2023 November 11 and has provided opportunities for agile and flexible monitoring of bright X-ray sources. On 2024 February 23, the NinjaSat team started long-term observation of the new X-ray source SRGA J144459.2$-$604207 as the first scientific target, which was discovered on 2024 February 21 and recognized as the sixth clocked X-ray burster. Our 25-day observation covered almost the entire decay of this outburst from two days after the peak at $\sim$100 mCrab on February 23 until March 18 at a few mCrab level. The Gas Multiplier Counter onboard NinjaSat successfully detected 12 Type-I X-ray bursts with a typical burst duration of $\sim$20 s, shorter than other clocked burster systems. As the persistent X-ray emission declined by a factor of five, X-ray bursts showed a notable change in its morphology: the rise time became shorter from 4.4(7) s to 0.3(3) s (1$\sigma$ errors), and the peak amplitude increased by 44%. The burst recurrence time $\Delta t_{\rm rec}$ also became longer from 2 hr to 10 hr, following the relation of $\Delta t_{\rm rec} \propto F_{\rm per}^{-0.84}$, where $F_{\rm per}$ is the persistent X-ray flux, by applying a Markov chain Monte Carlo method. The short duration of bursts is explained by the He-enhanced composition of accretion matter and the relation between $\Delta t_{\textrm{rec}}$ and $F_{\rm per}$ by a massive neutron star. This study demonstrated that CubeSat pointing observations can provide valuable astronomical X-ray data., Comment: 7 pages, 5 figures, accepted for publication in PASJ Letter

We introduce new high-resolution galaxy simulations accelerated by a surrogate model that reduces the computation cost by approximately 75 percent. Massive stars with a Zero Age Main Sequence mass of about 8 solar masses and above explode as core-collapse supernovae (CCSNe), which play a critical role in galaxy formation. The energy released by CCSNe is essential for regulating star formation and driving feedback processes in the interstellar medium (ISM). However, the short integration timesteps required for SNe feedback present significant bottlenecks in star-by-star galaxy simulations that aim to capture individual stellar dynamics and the inhomogeneous shell expansion of SNe within the turbulent ISM. Our new framework combines direct numerical simulations and surrogate modeling, including machine learning and Gibbs sampling. The star formation history and the time evolution of outflow rates in the galaxy match those obtained from resolved direct numerical simulations. Our new approach achieves high-resolution fidelity while reducing computational costs, effectively bridging the physical scale gap and enabling multi-scale simulations., Comment: 20 pages, 14 figures, 3 tables, submitted to ApJ

We investigate SN 2014C using three-dimensional hydrodynamic modeling, focusing on its early interaction with dense circumstellar medium (CSM). Our objective is to uncover the pre-supernova (SN) CSM structure and constrain the progenitor star's mass-loss history prior to core collapse. Our comprehensive model traces the evolution from the progenitor star through the SN event and into the SN remnant (SNR) phase. We simulate the remnant's expansion over approximately 15 years, incorporating a CSM derived from the progenitor star's outflows through dedicated hydrodynamic simulations. Analysis reveals that the remnant interacted with a dense toroidal nebula extending from $4.3\times 10^{16}\,$cm to $1.5\times 10^{17}$ cm in the equatorial plane, with a thickness of approximately $1.2\times 10^{17}$ cm. The nebula's density peaks at approximately $3\times 10^6\,$cm$^{-3}$ at the inner boundary, gradually decreasing as $\approx r^{-2}$ at greater distances. This nebula formed due to intense mass-loss from the progenitor star between approximately 5000 and 1000 years before collapse. During this period, the maximum mass-loss rate reached about $8\times 10^{-4}\,M_{\odot}\,$yr$^{-1}$, ejecting $\approx 2.5\,M_{\odot}$ of stellar material into the CSM. Our model accurately reproduces Chandra and NuSTAR spectra, including the Fe K line, throughout the remnant's evolution. Notably, the Fe line is self-consistently reproduced, originating from shocked ejecta, with $\approx 0.05\,M_{\odot}$ of pure-Fe ejecta shocked during the remnant-nebula interaction. These findings suggest that the 3D geometry and density distribution of the CSM, as well as the progenitor star's mass-loss history, align with a scenario where the star was stripped through binary interaction, specifically common envelope evolution., Comment: 43 Pages, 25 Figures, 4 Tables, accepted for publication in The Astrophysical Journal

We study the formation of stars with varying amounts of heavy elements synthesized by the rapid neutron-capture process ($r$-process) based on our detailed cosmological zoom-in simulation of a Milky Way-like galaxy with an $N$-body/smoothed particle hydrodynamics code, ASURA. Most stars with no overabundance in $r$-process elements, as well as the strongly $r$-process enhanced $r$-II stars ([Eu/Fe] $>+0.7$), are formed in dwarf galaxies accreted by the Milky Way within the 6 Gyr after the Big Bang. In contrast, over half of the moderately enhanced $r$-I stars ($+0.3 <$ [Eu/Fe] $\leq +0.7$) are formed in the main in-situ disk after 6 Gyr. Our results suggest that the fraction of $r$-I and $r$-II stars formed in disrupted dwarf galaxies is larger the higher their [Eu/Fe] is. Accordingly, the most strongly enhanced $r$-III stars ([Eu/Fe] $> +2.0$) are formed in accreted components. These results suggest that non-$r$-process-enhanced stars and $r$-II stars are mainly formed in low-mass dwarf galaxies that hosted either none or a single neutron star merger, while the $r$-I stars tend to form in the well-mixed in-situ disk. We compare our findings with high-resolution spectroscopic observations of $r$-process-enhanced metal-poor stars in the halo and dwarf galaxies, including those collected by the R-Process Alliance. We conclude that observed [Eu/Fe] and [Eu/Mg] ratios can be employed in chemical tagging of the Milky Way's accretion history., Comment: 16 pages, 11 figures, submitted to ApJ

Quantum entanglement between the spin, orbital and lattice degrees of freedom in condensed matter systems can emerge due to an interplay between spin-orbit and vibronic interactions. Heavy transition metal ions decorated on a face-centered cubic lattice, for example in $5d^1$ double perovskites, are particularly suited to support these quantum entangled states, but direct evidence has not yet been presented. In this work, we report additional peaks in the low-energy spectra of a $5d^1$ double perovskite, Ba$_2$CaReO$_6$, which cannot be explained by adopting a purely classical description of lattice vibrations. Instead, our theoretical analysis demonstrates that these spectroscopic signatures are characteristic of orbital-lattice entangled states in Ba$_2$CaReO$_6$. Crucially, both theory and experiment demonstrate that these quantum-entangled states persist to low temperatures, despite the onset of multipolar order., Comment: 7 pages, 4 figures

Exotic quantum phases, arising from a complex interplay of charge, spin, lattice and orbital degrees of freedom, are of immense interest to a wide research community. A well-known example of such an entangled behavior is the Jahn-Teller effect, where the lifting of orbital degeneracy proceeds through lattice distortions, often accompanied by ordering of spins and metal-insulator transitions. Static distortions, including cooperative behavior, have been associated with colossal magneto-resistance, multiferroicity, high-$T_\mathrm{C}$ superconductivity and other correlated phenomena. Realizations of the dynamic Jahn-Teller effect, on the other hand, are scarce since the preservation of vibronic symmetries requires subtle tuning of the local environment. Here we demonstrate that a highly-symmetrical 5d$^1$ double perovskite Ba$_2$MgReO$_6$, comprising of a 3D array of isolated ReO$_6$ octahedra, fulfils these requirements, resulting in a unique case of a dynamic Jahn-Teller system with strong spin-orbit coupling. Thermodynamic and resonant inelastic x-ray scattering experiments undoubtedly show that the Jahn-Teller instability leads to a ground-state doublet, invoking a paradigm shift for this family of compounds. The restoration of vibronic degrees of freedom arises from a quantum-mechanical zero-point motion, as revealed by detailed quantum chemistry calculations. The dynamic state of ReO$_6$ octahedra persists down to the lowest temperatures, where a multipolar order sets in, allowing for investigations of the interplay between a dynamic JT effect and strongly correlated electron behavior.

We construct a semi-analytical model that describes the convective core mass evolution of massive stars experiencing mass loss during the main-sequence stage. We first conduct a suite of 1D stellar evolution calculations to build insight into how convective core masses behave under idealized mass loss. Based on these simulations, we find several universal relations between global properties of the star that hold regardless of the mass loss history. By combining these relations, we construct a semi-analytic framework that can predict the convective core mass evolution for arbitrary mass loss histories and hence the helium core mass at the end of the main sequence. Our formulae improve upon existing methods for predicting the core mass in rapid population synthesis codes., Comment: 12 pages, 10 figures

In previous papers I and II under the same title, we proposed a practical method called Efficient stairway up to the Sky, and apply it to some typical finite groups $G$, with Schur multiplier $M(G)$ containing prime number 3, to construct explicitly their representation groups $R(G)$, and then, to construct a complete set of representatives of linear IRs of $R(G)$, which gives naturally, through sectional restrictions, a complete set of representatives of spin IRs of $G$. In the present paper, we are concerned mainly with group $G=G_{39}$ of order 27 in a list of Tahara's paper, with $M(G)={\mathbb Z}_3\times {\mathbb Z}_3$. In this case, to arrive up to the Sky, we have two steps of one-step efficient central extensions. By the 1st step, we obtain a covering group of order 81, and by the 2nd step we arrive to $R(G)$ of order 243. At the 1st step, to construct explicitly a complete set of representatives of IRs of the group, we apply Mackey's induced representations, and at the 2nd step, with a help of this result, we apply so-called classical method for semidirect product groups given by Hirai and arrive to a complete list of IRs of $R(G)$. Then, using explicit realization of these IRs, we can compute their characters (called spin characters)., Comment: 6 pages

In the previous paper, we proposed a practical method of constructing explicitly representation groups $R(G)$ for finite groups $G$, and apply it to certain typical finite groups $G$ with Schur multiplier $M(G)$ containing prime number 3. In this paper, we construct a complete list of irreducible projective (or spin) representations of $G$ and compute their characters (called spin characters). It is a continuation of our study of spin representations in the cases where $M(G)$ contains prime number 2 to the cases where other prime $p$ appears, firstly $p=3$. We classify irreducible spin representations and calculate spin characters according to their spin types., Comment: 6 pages

Recent neutron star surface observations corroborate a long-standing theory that neutron stars may be accelerated over extended periods after their birth. We analyze how these prolonged rocket-like accelerations, combined with rapid birth kicks, impact binary orbits. We find that even a small contribution of rocket kicks combined with instantaneous natal kicks can allow binaries to reach period--eccentricity combinations unattainable in standard binary evolution models. We propose these kick + rocket combinations as a new channel to form wide low-eccentricity neutron star binaries such as Gaia NS1, as well as inducing stellar mergers months to years after a supernova to cause peculiar high-energy transients., Comment: 11 pages, 7 figures, published in ApJL

We performed numerical simulations of the common envelope (CE) interaction between two intermediate-mass asymptotic giant branch (AGB) stars and their low-mass companions. For the first time, formation and growth of dust in the envelope is calculated explicitly. We find that the first dust grains appear as early as $\sim$1-3 yrs after the onset of the CE, and are smaller than grains formed later. As the simulations progress, a high-opacity dusty shell forms, resulting in the CE photosphere being up to an order of magnitude larger than it would be without the inclusion of dust. At the end of the simulations, the total dust yield is $0.0082~M_{\odot}$ ($0.022~M_{\odot}$) for a CE with a $1.7~M_{\odot}$ ($3.7~M_{\odot}$) AGB star. Dust formation does not substantially lead to more mass unbinding or substantially alter the orbital evolution., Comment: 6 pages, 6 figures, contributed talk to the Proceedings IAU Symposium No. 384

Schur multiplier $M(G)$ of a finite group $G$ has been studied heavily. To proceed further to the study of projective (or spin) representations of $G$ and their characters (called spin characters), it is necessary to construct explicitly a representation group $R(G)$ of $G$, a certain central extension of $G$ by $M(G)$, since projective representations of $G$ correspond bijectively to linear representations of $R(G)$. We propose here a practical method to construct $R(G)$ by repetition of one-step efficient central extensions according to a certain choice of a series of elements of $M(G)$. This method is also helpful for constructing linear representations of $R(G)$ and accordingly for calculating spin characters. Actually, we will apply this method to several examples of $G$ with prime number 3 in $M(G)$., Comment: 6pages

Intermediate-mass black holes (IMBHs) are those between 100 and 10$^5$ solar masses ($M_{\odot}$); their formation process is debated. One possible origin is the growth of less massive black holes (BHs) via mergers with stars and compact objects within globular clusters (GCs). However, previous simulations have indicated that this process only produces IMBHs $<500 M_{\odot}$ because the gravitational wave recoil ejects them when they merge with other BHs. We perform star-by-star simulations of GC formation, finding that high-density star formation in a GC's parent giant molecular cloud can produce sufficient mergers of massive stars to overcome that mass threshold. We conclude that GCs can form with IMBHs $\gtrsim 10^3 M_{\odot}$, which is sufficiently massive to be retained within the GC even with the expected gravitational wave recoil., Comment: Published online on 30 May 2024 in Science. Main (15 pages, 4 figures) and Supplementary materials (19 pages, 10 figures and 4 tables). The accepted version

Transverse thermoelectric conversion holds significant potential in addressing complex challenges faced by classical Seebeck/Peltier modules. A promising transverse thermoelectric phenomenon is the anomalous Nernst effect (ANE) originating from nontrivial band structures in magnetic topological materials. However, the currently reported performance for ANE in topological materials, e.g., Co$_2$MnGa, remains insufficient for practical thermoelectric applications. Here, we unveil a new availability for ANE by integrating magnetic topological materials into artificially tilted multilayers (ATMLs), known to exhibit the structure-induced transverse thermoelectric conversion due to the off-diagonal Seebeck effect. Our experiments reveal that the transverse thermoelectric performance in Co$_2$MnGa-based ATMLs is improved through the hybrid action of ANE and the off-diagonal Seebeck effect, with the modulation of performance dependent on magnetization being significantly greater than the performance achievable with ANE alone. This unconventional synergy underscores the importance of hybrid transverse thermoelectric conversion and paves a way for advancing thermoelectric applications using magnetic materials., Comment: 26 pages, 15 figures, 1 table

General ridge estimators are typical linear estimators in a general linear model. The class of them include some shrinkage estimators in addition to classical linear unbiased estimators such as the ordinary least squares estimator and the weighted least squares estimator. We derive necessary and sufficient conditions under which two general ridge estimators coincide. In particular, two noteworthy conditions are added to those from previous studies. The first condition is given as a seemingly column space relationship to the covariance matrix of the error term, and the second one is based on the biases of general ridge estimators. Another problem studied in this paper is to derive an equivalence condition such that equality between two residual sums of squares holds when general ridge estimators are considered., Comment: 19 pages

The L\'evy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, L\'evy walks with power exponents close to two, also known as Cauchy walks, are frequently observed, though their underlying causes remain elusive. This study proposes a walk model in which agents move toward a destination in multi-dimensional space and their movement strategy is parameterized by the extent to which they pursue the shortest path to the destination. This parameter is taken to represent the attractiveness of the destination to the agents. Our findings reveal that if the destination is very attractive, agents intensively search the area around it using Brownian walks, whereas if the destination is unattractive, they explore a distant region away from the point using L\'evy walks with power exponents less than two. In the case where agents are unable to determine whether the destination is attractive or unattractive, Cauchy walks emerge. The Cauchy walker searches the region with a probability inversely proportional to the distance from the destination. This suggests that it preferentially searches the area close to the destination, while concurrently having the potential to extend the search area much further. Our model, which can change the search method and search area depending on the attractiveness of the destination, has the potential to be utilized for exploring the parameter space of optimization problems.

Altermagnetism refers to a wide class of magnetic orders featuring magnetic sublattices with opposite spins related by rotational symmetries, resulting in non-trivial spin splitting and magnetic multipoles. However, the direct observation of the altermagnetic order parameter remains elusive. Here, by combining theoretical analysis, electrical transport, X-ray and optical spectroscopies, we establish a phase diagram in hybrid molecular beam epitaxy-grown RuO2/TiO2 (110) films, mapping symmetries along with altermagnetic/electronic/structural phase transitions as functions of film thickness and temperature. This features a novel altermagnetic metallic polar phase in epitaxially-strained 2 nm films, extending the concept of multiferroicity to altermagnets. Such a clear signature of a magnetic phase transition at ~500 K is observed exclusively in ultrathin strained films, unlike in bulk RuO2 single crystals. These results demonstrate the potential of epitaxial heterostructure design to induce altermagnetism, paving the way for emergent novel phases with multifunctional properties., Comment: 23 pages