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Stellar limb darkening must be properly accounted for to accurately determine the radii of exoplanets at various wavelengths. The standard approach to address limb darkening involves either using laws with coefficients from modelled stellar spectra or determining the coefficients empirically during light curve fitting of the data. Here, we test how accurately three common laws -- quadratic, power, and a three-parameter law -- can reproduce stellar limb darkening at different wavelengths and across a broad range of stars. We show that using a quadratic limb darkening law, which is most frequently employed by the community, leads to wavelength-dependent offsets in retrieved transmission spectra. For planets with high impact parameters ($b$ larger than about 0.5) the amplitude of these offsets can reach 1\% of the transit depth which is some cases is comparable to and can even exceed the expected signals from the planetary atmosphere. Furthermore, the quadratic law causes an offset in the value of the impact parameter when it is determined by fitting the broadband transit light curves. In contrast, using the Kipping--Sing three-parameter law leads to robust retrievals. We advocate the use of this law in retrievals, especially for transits with large impact parameters., Comment: submitted to ApJ

Besides a dense coverage of their high latitudes by starspots, rapidly rotating cool stars also display low-latitude spots in Doppler images, although generally with a lower coverage. In contrast, flux emergence models of fast-rotating stars predict strong poleward deflection of radially rising magnetic flux as the Coriolis effect dominates over buoyancy, leaving a spot-free band around the equator. To resolve this discrepancy, we consider a flux tube near the base of the convection zone in a solar-type star rotating eight times faster than the Sun, considering field intensification by weak-tube explosions. For the intensification to continue into to the buoyancy-dominated regime, the upper convection zone must have a significantly steeper temperature gradient than in the Sun, by a factor that is comparable with that found in 3D simulations of rotating convection. Within the hypothesis that stellar active regions stem from the base of the convection zone, flux emergence between 1-20 degree latitudes requires highly supercritical field strengths of up to 500 kG in rapidly rotating stars. These field strengths require explosions of 100-kG tubes within the convection zone, compatible with reasonable values of the superadiabatic temperature gradient associated with the more rapid rotation., Comment: 12 pages, 9 figures, accepted for publication in ApJ

We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles. These discrete cmc surfaces can be constructed from orthogonal ring patterns in the two-sphere and the hyperbolic plane. We present a variational principle that allows us to solve boundary value problems and to construct discrete analogues of some classical cmc surfaces. The data used for the construction is purely combinatorial - the combinatorics of the curvature line pattern. In the limit of orthogonal circle patterns we recover the theory of discrete minimal surfaces associated to Koebe polyhedra all edges of which touch a sphere. These are generalized to two-sphere Koebe nets, i.e., nets with planar quadrilateral faces and edges that alternately touch two concentric spheres., Comment: 47 pages, 25 figures

To determine the relative distances and peculiar velocities of 140 groups and clusters of galaxies at low redshifts ($z$ < 0.12), we used the fundamental plane (FP) of early-type galaxies (from the Sloan Digital Sky Survey (SDSS) data). We constructed the Hubble diagram for the relative distances of galaxy groups/clusters versus their radial velocities in the cosmic microwave background (CMB) reference frame in the flat $\Lambda$ cold dark matter ($\Lambda$CDM) model ($\Omega_m=0.3$, $H_0=70$~km~s$^{-1}$ Mpc$^{-1}$). We have found that the standard logarithmic deviation for groups and clusters of galaxies on the Hubble diagram (minus peculiar velocities) is $\pm0.0173$ ($N$ = 140), which corresponds to a deviation of $70\pm2.8$~km~s$^{-1}$ Mpc$^{-1}$ in the Hubble constant. For a sample of galaxy systems ($N$ = 63), the X-ray luminosity of which is in an interval of (0.151--4)~$\times 10^{44}$~erg/s, this quantity turned out to be $70\pm2.1$~km~s$^{-1}$ Mpc$^{-1}$. The root-mean-square deviations of peculiar velocities with quadratic accounting for errors are $^{1/2}$ = $714\pm7$~km/s and $600\pm7$~km/s, respectively. For five large superclusters of galaxies from the SDSS region, the average peculiar velocity relaive to the CMB reference frame is $+240\pm250$~km/s. We detected no outflow of galaxy systems from the void (Giant Void, $\alpha \approx 13^h, \delta \approx 40^\circ, z \approx 0.107$) formed by groups and clusters of galaxies., Comment: 10 pages, 5 figures. Accepted for publication in Astronomy Reports

One of the most important issues in modern condensed matter physics is the realization of fractionalized excitations, such as the Majorana excitations in the Kitaev quantum spin liquid. To this aim, the 3d-based Kitaev material Na2Co2TeO6 is a promising candidate whose magnetic phase diagram of B // a* contains a field-induced intermediate magnetically disordered phase within 7.5 T < |B| < 10 T. The experimental observations, including the restoration of the crystalline point group symmetry in the angle-dependent torque and the coexisting magnon excitations and spinon-continuum in the inelastic neutron scattering spectrum, provide strong evidence that this disordered phase is a field induced quantum spin liquid with partially polarized spins. Our variational Monte Carlo simulation with the effective K-J1-{\Gamma}-{\Gamma}'-J3 model reproduces the experimental data and further supports this conclusion.

We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is a special case of the master integrable equation Q4. The variational description is given in terms of elliptic generalizations of the dilogarithm function. They have the same convexity principles as their circle-pattern counterparts. This allows us to prove existence and uniqueness results for the Dirichlet and Neumann boundary value problems. Some examples are computed numerically. In the limit of small smoothly varying rings, one obtains harmonic maps to the sphere and to the hyperbolic plane. A close relation to discrete surfaces with constant mean curvature is explained., Comment: 29 pages, 11 figures, some formulas for hyperbolic ring patters are corrected

This work is a continuation of the work of Kopylova and Kopylov (2016) to build a fundamental plane (FP) of groups and clusters of galaxies -- here a sample of galaxies systems is increased from 94 to 172 objects. We have studied the ratios between the basic characteristics of groups and clusters of galaxies according to the archival data of SDSS, 2MASX and NED catalogs. Measured parameters ($\log L_K$, $\log R_e$ and $\log \sigma$) of clusters of galaxies determine the fundamental plane in the near infrared region: $L_K \propto R_e^{0.77\pm0.09} \sigma^{1.44\pm0.12}$. The form of the FP of groups/clusters is consistent with the FP of the early -- types of galaxies (SDSS, $r$-band) determined in the same way. Direct regression relative to the padius $\log r_e$ in the kpc gives a projection of the FP -- $\log R_e=0.98(\pm0.06)\,\log \sigma-0.56(\pm0.04)<\log \langle I_e \rangle+3.57(\pm0.07)$, that can be used to determine the distances of the systems of galaxies. The root-mean-square deviation of the FP zero-point is 0.07 which is equal to the 16\% error in determining the distance of the group or cluster of galaxies. For the first time, we measured the peculiar velocities of the superclusters of galaxies. The mean peculiar velocity of the 5 superclusters of galaxies relative to the CMB is $+75\pm360$~km~s$^{-1}$., Comment: 14 pages, 7 figures, 1 table. Astrophysical Bulletin, 2024, 79, 1. Key results in Figures 6 and 7

Soft X-ray irradiation of molecules causes electronic core-level vacancies through photoelectronemission. In light elements, such as C, N, or O, which are abundant in the biosphere, these vacancies predominantly decay by Auger emission, leading inevitably to dissociative multiply charged states. It was recently demonstrated that an environment can prevent fragmentation of core-level-ionized small organic molecules through immediate non-local decay of the core hole, dissipating charge and energy to the environment. Here, we present an extended photoelectron-photoion-photoion coincidence (PEPIPICO) study of the biorelevant pyrimidine molecule embedded in a water cluster. It is observed and supported by theoretical calculations that the supposed protective effect of the environment is partially reversed if the vacancy is originally located at a water molecule. In this scenario, intermolecular energy or charge transfer from the core-ionized water environment to the pyrimidine molecule leads to ionization of the latter, however, presumably in non-dissociative cationic states. Our results contribute to a more comprehensive understanding of the complex interplay of protective and harmful effects of an environment in the photochemistry of microsolvated molecules exposed to X-rays.

Let $\operatorname{X}:=(\operatorname{X},\operatorname{d})$ be an arbitrary metric space. For each $p \in [1,\infty]$, we prove that a map $\gamma:[a,b] \to \operatorname{X}$ is $p$-absolutely continuous if and only if, for every Lipschitz function $h:\operatorname{X} \to \mathbb{R}$, the post-composition $h \circ \gamma$ is a $p$-absolutely continuous function. Furthermore, if $\operatorname{X}$ is complete and separable, then, for each $p \in (1,\infty)$, we show that the equivalence class (up to $\mathcal{L}^{1}$-a.e. equality) of a Borel map $\gamma:[a,b] \to \operatorname{X}$ belongs to the Sobolev $W_{p}^{1}([a,b],\operatorname{X})$-space if and only if, for every Lipschitz function $h:\operatorname{X} \to \mathbb{R}$, the equivalence class (up to $\mathcal{L}^{1}$-a.e. equality) of the post-composition $h \circ \gamma $ belongs to the Sobolev $W_{p}^{1}([a,b],\mathbb{R})$-space.

Transition metal dichalcogenide (TMD) single photon emitters (SPEs) offer numerous advantages to quantum information applications, such as high single photon purity and deterministic positioning. Strain in the host monolayer, induced by underlying dielectric Mie resonators, is known to localize their formation to positions co-located with near-field photonic hotspots providing further control over their optical properties. However, traditional materials used for the fabrication of nanoresonators, such as silicon or gallium phosphide (GaP), often require a high refractive index substrate resulting in losses of the emitted light and limited photonic enhancement. Here, we use nanoantennas (NAs) fabricated from multilayer TMDs, which allow complete flexibility with the choice of substrate due to the adhesive van der Waals forces, enabling high refractive index contrast or the use of highly reflective metallic surfaces. We demonstrate the localized formation of SPEs in WSe$_2$ monolayers transferred onto WS$_2$ NAs on both SiO$_2$ and Au substrates, enabling strong photonic enhancements and increased single photon collection. We provide evidence for enhanced quantum efficiencies (QE) reaching an average value of 43% (7%) for SPEs on WS$_2$ NAs on a SiO$_2$ (Au) substrate. We further combine the advantages offered by both dielectric and metallic substrates to numerically simulate an optimized NA geometry for maximum WSe$_2$ single photon excitation, emission, collection. Thus, the fluorescence is enhanced by a factor of over 4 orders of magnitude compared to vacuum and 5 orders of magnitude compared to a flat SiO$_2$/Si surface. Our work showcases the advantages offered by employing TMD material nanoresonators on various substrates for SPE formation and photonic enhancement.

Ultrafast all-optical logic devices based on nonlinear light-matter interactions hold the promise to overcome the speed limitations of conventional electronic devices. Strong coupling of excitons and photons inside an optical resonator enhances such interactions and generates new polariton states which give access to unique nonlinear phenomena, such as Bose-Einstein condensation, used for all-optical ultrafast polariton transistors. However, the pulse energies required to pump such devices range from tens to hundreds of pJ, making them not competitive with electronic transistors. Here we introduce a new paradigm for all-optical switching based on the ultrafast transition from the strong to the weak coupling regime in microcavities embedding atomically thin transition metal dichalcogenides. Employing single and double stacks of hBN-encapsulated MoS$_2$ homobilayers with high optical nonlinearities and fast exciton relaxation times, we observe a collapse of the 55-meV polariton gap and its revival in less than one picosecond, lowering the threshold for optical switching below 4 pJ per pulse, while retaining ultrahigh switching frequencies. As an additional degree of freedom, the switching can be triggered pumping either the intra- or the interlayer excitons of the bilayers at different wavelengths, speeding up the polariton dynamics, owing to unique interspecies excitonic interactions. Our approach will enable the development of compact ultrafast all-optical logical circuits and neural networks, showcasing a new platform for polaritonic information processing based on manipulating the light-matter coupling.

We present a general approach for the study of dimer model limit shape problems via variational and integrable systems techniques. In particular we deduce the limit shape of the Aztec diamond and the hexagon for quasi-periodic weights through purely variational techniques. Putting an M-curve at the center of the construction allows one to define weights and algebro-geometric structures describing the behavior of the corresponding dimer model. We extend the quasi-periodic setup of our previous paper [7] to include a diffeomorphism from the spectral data to the liquid region of the dimer. Our novel method of proof is purely variational and exploits a duality between the dimer height function and its dual magnetic tension minimizer and applies to dimers with gas regions. We apply this to the Aztec diamond and hexagon domains to obtain explicit expressions for the complex structure of the liquid region of the dimer as well as the height function and its dual. We compute the weights and the limit shapes numerically using the Schottky uniformization technique. Simulations and predicted results match completely.

We consider the remote state restoring and perfect transfer of the zero-order coherence matrix (PTZ) in a spin system governed by the XXZ-Hamiltonian conserving the excitation number. The restoring tool is represented by several nonzero Larmor frequencies in the Hamiltonian. To simplify the analysis we use two approximating models including either step-wise or pulse-type time-dependence of the Larmor frequencies. Restoring in spin chains with up to 20 nodes is studied. Studying PTZ, we consider the zigzag and rectangular configurations and optimize the transfer of the 0-order coherence matrix using geometrical parameters of the communication line as well as the special unitary transformation of the extended receiver. Overall observation is that XXZ-chains require longer time for state transfer than XX-chains, which is confirmed by the analytical study of the evolution under the nearest-neighbor approximation. We demonstrate the exponential increase of the state-transfer time with the spin chain length., Comment: 22 pages, 13 figures. arXiv admin note: text overlap with arXiv:2401.09569

Monolayers of semiconducting transition metal dichalcogenides (TMDs) have long attracted interest for their intriguing optical and electronic properties. Recently TMDs in their quasi-bulk form have started to show considerable promise for nanophotonics thanks to their high refractive indices, large optical anisotropy, wide transparency windows reaching to the visible, and robust room temperature excitons promising for nonlinear optics. Adherence of TMD layers to any substrate via van der Waals forces is a further key enabler for nanofabrication of sophisticated photonic structures requiring heterointegration. Here, we capitalize on these attractive properties and realize topological spin-Hall photonic lattices made of arrays of triangular nanoholes in 50 to 100 nm thick WS$_2$ flakes exfoliated on SiO$_2$/Si substrates. High quality structures are achieved taking advantage of anisotropic dry etching dictated by the crystal axes of WS$_2$. Reflectance measurements at room temperature show a photonic gap opening in the near-infrared in trivial and topological phases. Unidirectional propagation along the domain interface is demonstrated in real space via circularly polarized laser excitation in samples with both zigzag and armchair domain boundaries. Finite-difference time-domain simulations are used to interpret optical spectroscopy results. Our work opens the way for future sophisticated nanophotonic devices based on the layered (van der Waals) materials platform., Comment: 34 pages, 18 figures

We study the Hanle and spin polarization recovery effects on resident electrons in a monolayer MoSe$_2$ on EuS. We demonstrate that localized electrons provide the main contribution to the spin dynamics signal at low temperatures below 15~K for small magnetic fields of only a few mT. The spin relaxation of these electrons is determined by random effective magnetic fields due to a contact spin interaction, namely the hyperfine interaction with the nuclei in MoSe$_2$ or the exchange interaction with the magnetic ions of the EuS film. From the magnetic field angular dependence of the spin polarization we evaluate the anisotropy of the intervalley electron $g$-factor and the spin relaxation time. The non-zero in-plane $g$-factor $|g_x|\approx 0.1$, the value of which is comparable to its dispersion, is attributed to randomly localized electrons in the MoSe$_2$ layer., Comment: 6 pages, 4 figures

In this study, a novel material from the rare-earth based breathing pyrochlore family, Ba3Tm2Zn5O11, was successfully synthesized. Powder X-ray diffraction and high-resolution powder neutron diffraction confirmed phase purity and crystal structure, while thermogravimetric analysis revealed incongruent melting behavior compared to its counterpart, Ba3Yb2Zn5O11. High-quality single crystals of Ba3Tm2Zn5O11 were grown using the traveling solvent floating zone technique and assessed using Laue diffractometer and single crystal X-ray diffraction. Thermodynamic characterization indicated paramagnetic behavior down to 0.05 K, and inelastic neutron scattering measurements identified distinct crystal electric field bands. Additional low-energy excitation studies on single crystals revealed dispersionless bands at 0.8 and 1 meV. Computed phonon dispersions from first principles calculations ruled out phonons as the source of these modes, further illustrating the puzzling and unique properties of Ba3Tm2Zn5O11.

We study the ultrafast dynamics initiated by a coherent superposition of core-excited states of nitrous oxide molecule. Using high-level \textit{ab-initio} methods, we show that the decoherence caused by the electronic decay and the nuclear dynamics is substantially slower than the induced ultrafast quantum beatings, allowing the system to undergo several oscillations before it dephases. We propose a proof-of-concept experiment using the harmonic up-conversion scheme available at X-ray free-electron laser facilities to trace the evolution of the created core-excited-state coherence through a time-resolved X-ray photoelectron spectroscopy.

In this paper we study the field of Hahn-Witt series $HW(\overline{\mathbb{F}}_p)$ with residue field $\overline{\mathbb{F}}_p$ (also known as a $p$-adic Malcev-Neumann field \cite{La86, P93}), and its generalizations. Informally, the Hahn-Witt series are possibly infinite linear combinations of rational powers of $p,$ in which the coefficients are Teichm\"uller representatives, and the set of exponents is well-ordered. They form an algebraically closed extension of $\mathbb{Q}_p,$ with a canonical automorphism $\varphi,$ coming from the absolute Frobenius of $\overline{\mathbb{F}}_p.$ We prove that the action of $\varphi$ on the $p$-power roots of unity is given by $\varphi(\zeta)=\zeta^{-1},$ answering a question of Kontsevich. More generally, we consider the $\pi$-typical Hahn-Witt series $HW_{(K,\pi)}(\overline{\mathbb{F}}_q)$, where $\pi$ is a uniformizer in a local field $K$ with residue field $\mathbb{F}_q.$ Again, this field is an algebraically closed extension of $K,$ and it has a canonical automorphism $\varphi_{\pi},$ coming from the relative Frobenius of $\overline{\mathbb{F}}_q$ over $\mathbb{F}_q.$ We prove that the action of $\varphi_{\pi}$ on the maximal abelian extension $K^{ab}$ corresponds via local class field theory to the uniformizer $-\pi\in K^*.$, Comment: 19 pages

We study compact minimal surfaces in the 3-sphere which are constructed by successive reflections from a minimal $n$-gon -- so-called minimal reflection surfaces. The minimal $n$-gon solves a free boundary problem in a fundamental piece of the respective reflection group. We investigate the combinatorics of the curvature lines of reflection surfaces, and construct new examples of minimal reflection surfaces based on pentagons. We end the paper by discussing the area of these minimal surfaces., Comment: 32 pages, 9 figures

Here we present the results of benchmarking of a quantum processor based on trapped $^{171}$Yb$^{+}$ ions by performing basic quantum machine learning algorithms. Specifically, we carry out a supervised binary classification of small-scale digits images, which are intentionally chosen so that they can be classified with 100% accuracy, using a quantum-enhanced Support Vector Machine algorithm with up to four qubits. In our work, we specifically consider different types of quantum encodings of the dataset and different levels of transpilation optimizations for the corresponding quantum circuits. For each quantum encoding, we obtain a classifier that is of 100% accuracy on both training and test sets, which demonstrates that the quantum processor can correctly solve the basic classification task considered. As we expect, with the increase of the capabilities quantum processors, they can become a useful tool for machine learning., Comment: 8 pages, 1 figure

Energy-transfer processes can be viewed as being due to the emission of a virtual photon. It is demonstrated that the emission of virtual photons and thus of energy transfer is stimulated by the sheer presence of photons. We concentrate here on interatomic/intermolecular Coulombic decay (ICD) where an excited system relaxes by transferring its excess energy to a neighbor ionizing it. ICD is inactive if this excess energy is insufficiently large. However, in the presence of photons, the long-range interaction between the system and its neighbor can utilize the photon field making ICD active. The properties of this stimulated-ICD mechanism are discussed. The concept can be transferred to other scenarios. We discuss collective-ICD where two excited molecules concertedly transfer their excess energy. Also here, the presence of photons can make the process active if the sum of excess energies were insufficient to do so. Examples with typical molecules and atoms are presented to demonstrate that these stimulated processes can play a role.

We report the results of a study of the distribution of galaxies in the projection along the radius ($R \leq 3R_{200c}$) for 157~groups and clusters of galaxies in the local Universe (0.01 < $z$ < 0.10) with line-of-sight velocity dispersions~200~km~s$^{-1}$ < $ \sigma$ < 1100~km~s$^{-1}$. We introduce a new observed boundary for the halos of clusters of galaxies, which we identify with the splashback radius $R_{\rm{sp}}$. We also identified the core of groups/clusters of galaxies with the radius$R_c$. These radii are determined by the observed integrated distribution of the number of galaxies as a function of squared angular radius from the center of the group/cluster, which (usually) coincides with the brightest galaxy. We found for the entire sample that the boundary of dark matter $R_{\rm{sp}}$ for groups/clusters of galaxies is proportional to the radius $R_{\rm{200c}}$ of the virialized region. We measured the mean radius $\langle R_{\rm{sp}} \rangle = 1.14\pm0.02$~Mpc for groups of galaxies ($\sigma \leq 400$~km~s$^{-1}$) and $\langle R_{\rm{sp}} \rangle = 2.00\pm0.07$~Mpc for clusters of galaxies ($\sigma > 400$~km~s$^{-1}$). The mean ratio of radii is $\langle R_{\rm{sp}}/R_{\rm{200c}} \rangle = 1.40\pm0.02$}, or $\langle R_{\rm{sp}}/R_{\rm{200m}} \rangle = 0.88\pm0.02$., Comment: 15 pages, 7 figures, 2 tables. The article provides references to the X-ray luminosity of galaxy clusters and clarifies the descriptions of the columns

In this paper we introduce and study the so-called continuous $K$-theory for a certain class of "large" stable $\infty$-categories, more precisely, for dualizable presentable categories. For compactly generated categories, the continuous $K$-theory is simply the usual (non-connective) $K$-theory of the full subcategory of compact objects. More generally, we show that any localizing invariant of small stable $\infty$-categories can be uniquely extended to a localizing invariant of dualizable categories. We compute the continuous $K$-theory for categories of sheaves on locally compact Hausdorff spaces. Using the special case for sheaves on the real line, we give an alternative proof of the theorem of Kasprowski and Winges \cite{KW19} on the commutation of $K$-theory with infinite products for small stable $\infty$-categories. We also study the general theory of dualizable categories. In particular, we give an "explicit" proof of Ramzi's theorem \cite{Ram} on the $\omega_1$-presentability of the category of dualizable categories. Among other things, we prove that dualizability is equivalent to "flatness" in the category of presentable stable categories., Comment: 123 pages; v2: minor changes, some typos corrected, a reference added

Geometrically frustrated magnetic systems, such as those based on the Shastry-Sutherland lattice, offer a rich playground for exploring unconventional magnetic states. The delicate balance between competing interactions in these systems leads to the emergence of novel phases. We present the characterization of Er2Be2GeO7, an SSL compound with Er3+ ions forming orthogonal dimers separated by non-magnetic layers. Neutron scattering reveals an antiferromagnetic dimer structure at zero field, typical of Ising spins on that lattice and consistent with the anisotropic magnetization observed. However, magnetization measurements exhibit fractional plateaus at 1/4 and 1/2 of saturation, by contrast to the expected 1/3 plateau of the SSL Ising model. We show that this behaviour requires spatially anisotropic interactions, and, using a tensor network approach, we show that all properties, including thermodynamics, can be quantitatively explained by an Anisotropic Shastry-Sutherland Ising Model whose microscopic origin can be traced back to Dzyaloshinskii-Moriya interactions. This study highlights Er2Be2GeO7 as a promising platform for investigating exotic magnetic phenomena and potential applications in spintronics.

Spontaneous strain and spontaneous folding of thin nanoplatelets are known phenomena whose microscopic mechanisms are still debating. In this work, first-principles calculations are used to study the mechanical stresses that arise in Janus CdSe nanoplatelets and result in their spontaneous strain. Calculations reveal the existence of three microscopic mechanisms of this phenomenon. Two bulk mechanisms are associated with the inverse piezoelectric effect in an electric field created by the difference in electronegativities of ligands and by the depolarizing field resulting from the difference in the potential jumps in electrical double layers on the surfaces of nanoplatelets. These mechanisms account for 5-25% of the observed effect. The third mechanism is associated with the surface strain of nanoplatelets by bridging bonds, and its influence is predominant. It is shown that the latter mechanism cause spontaneous folding of thin CdSe nanoplatelets and, depending on the values of surface stresses and lateral orientation of nanoplatelets, can result in formation of their experimentally observed structures such as scrolls, spirals, and twisted ribbons., Comment: 10 pages, 7 figures, 3 tables

A complex hyperplane arrangement $\mathcal{A}$ is said to be decomposable if there are no elements in the degree 3 part of its holonomy Lie algebra besides those coming from the rank 2 flats. When this purely combinatorial condition is satisfied, it is known that the associated graded Lie algebra of the arrangement group $G$ decomposes (in degrees greater than 1) as a direct product of free Lie algebras. It follows that the $I$-adic completion of the Alexander invariant $B(G)$ also decomposes as a direct sum of "local" invariants and the Chen ranks of $G$ are the sums of the local contributions. Moreover, if $B(G)$ is separated, then the degree 1 cohomology jump loci of the complement of $\mathcal{A}$ have only local components, and the algebraic monodromy of the Milnor fibration is trivial in degree 1., Comment: 56 pages

Two-dimensional (2D) layered materials, whether in bulk form or reduced to just a single layer, have potential applications in spintronics and capacity for advanced quantum phenomena. A prerequisite for harnessing these opportunities lies in gaining a comprehensive understanding of the spin behavior in 2D materials. The low dimensionality motivates an understanding of the spin correlations over a wide length scale, from local to long range order. In this context, we focus on the magnetism in bulk \MPSe ~and \MPS, 2D layered van der Waals antiferromagnetic semiconductors. These materials have similar honeycomb Mn layers and magnetic ordering temperatures, but distinct spin orientations and exchange interactions. We utilize neutron scattering to gain deeper insights into the local magnetic structures and spin correlations in the paramagnetic and ordered phases by systematically investigating a MnPS$_{x}$Se$_{3-x}$ ($x$ = 0, 1, 1.5, 2, 3) series of powder samples using total neutron scattering measurements. By employing magnetic pair distribution function (mPDF) analysis, we unraveled the short-range magnetic correlations in these materials and explored how the non-magnetic anion S/Se mixing impacts the magnetic correlations. The results reveal that the magnetism can be gradually tuned through alteration of the non-magnetic S/Se content, which tunes the atomic structure. The change in magnetic structure is also accompanied by a control of the magnetic correlation length within the 2D honeycomb layers. Complimentary inelastic neutron scattering measurements allowed a quantification of the change in the magnetic exchange interactions for the series and further highlighted the gradual evolution of spin interactions in the series MnPS$_{x}$Se$_{3-x}$.

We investigate both ensemble and time-averaged mean-squared displacements of particles in a polydisperse granular system in a homogeneous cooling state. The system contains an arbitrary number of species of different sizes and masses. The collisions between granular particles are described in terms of the models both of constant and time-dependent restitution coefficients. In our study, we use a powerful low-rank algorithm that allows for efficient simulation of highly polydisperse granular systems. The Monte Carlo simulations are in good agreement with the analytical results.

The paper investigates H\"older and log-H\"older regularity of spectral measures for weakly mixing substitutions and the related question of quantitative weak mixing. It is assumed that the substitution is primitive, aperiodic, and its substitution matrix is irreducible over the rationals. In the case when there are no eigenvalues of the substitution matrix on the unit circle, our main theorem says that a weakly mixing substitution $\mathbb{Z}$-action has uniformly log-H\"older regular spectral measures, and hence admits power-logarithmic bounds for the rate of weak mixing. In the more delicate Salem substitution case, our second main result says that H\"older regularity holds for algebraic spectral parameters, but the H\"older exponent cannot be chosen uniformly.

We investigate the intertwining of Laguerre processes of parameter $\alpha$ in different dimensions. We introduce a Feller kernel that depends on $\alpha $ and intertwines the $\alpha$-Laguerre process in $N+1$ dimensions and that in $N$ dimensions. When $\alpha $ is a non-negative integer, the new kernel is interpreted in terms of the conditional distribution of the squared singular values: if the singular values of a unitarily invariant random matrix of order $(N+\alpha +1) \times (N+1)$ are fixed, then the those of its $(N+\alpha) \times N $ truncation matrix are given by the new kernel., Comment: 15 pages

Stars appear darker at their limbs than at their disk centers because at the limb we are viewing the higher and cooler layers of stellar photospheres. Limb darkening derived from state-of-the-art stellar atmosphere models systematically fails to reproduce recent transiting exoplanet light curves from the Kepler, TESS, and JWST telescopes -- stellar brightness obtained from measurements drops less steeply towards the limb than predicted by models. All previous models assumed atmosphere devoid of magnetic fields. Here we use our new stellar atmosphere models computed with the 3D radiative magneto-hydrodynamic code MURaM to show that small-scale concentration of magnetic fields on the stellar surface affect limb darkening at a level that allows us to explain the observations. Our findings provide a way forward to improve the determination of exoplanet radii and especially the transmission spectroscopy analysis for transiting planets, which relies on a very accurate description of stellar limb darkening from the visible through the infrared. Furthermore, our findings imply that limb darkening allows measuring the small-scale magnetic field on stars with transiting planets., Comment: 19 pages, 6 figures This is the submission version of manuscript to Nature Astronomy

In this paper we develop a general approach to dimer models analogous to Krichever's scheme in the theory of integrable systems. We start with a Riemann surface and the simplest generic meromorphic functions on it and demonstrate how to obtain integrable dimer models. These are dimer models on doubly periodic bipartite graphs with quasi-periodic positive weights. Dimer models with periodic weights and Harnack curves are recovered as a special case. This generalization from Harnack curves to general M-curves leads to transparent algebro-geometric structures. In particular explicit formulas for the Ronkin function and surface tension as integrals of meromorphic differentials on M-curves are obtained. Furthermore we describe the variational principle for the height function in the quasi-periodic case. Based on Schottky uniformizations of Riemann surfaces we present concrete computational results including computing the weights and sampling dimer configurations with them. The computational results are in complete agreement with the theoretical predictions.

We propose an algorithm for calculating the determinant of a square matrix, and construct the quantum circuit realizing it, using multiqubit control gates (representable in terms of Toffoli gates, CNOTs and SWAPs), Hadamard transformations and $Z$-operators. Each row of the matrix is encoded as a pure state of some quantum system. The admitted matrix is therefore arbitrary up to the normalization of quantum states of those systems. The depth of the proposed algorithm is $O(N^3\log \, N)$ for the $N\times N$ matrix., Comment: 8 pages, 3 figures, minor change in presentation

Recent advances in the study of cobaltites have unveiled their potential as a promising platform for realizing Kitaev physics in honeycomb systems and the Ising model in weakly coupled chain materials. In this manuscript, we explore the magnetic properties of pyroxene SrCoGe$_2$O$_6$ using a combination of neutron scattering, {\it ab initio} methods, and linear spin-wave theory. Through careful examination of inelastic neutron scattering powder spectra, we propose a modified Kitaev model to accurately describe the twisted chains of edge-sharing octahedra surrounding Co$^{2+}$ ions. The extended Kitaev-Heisenberg model, including a significant anisotropic bond-dependent exchange term with $K/|J|=0.96$, is identified as the key descriptor of the magnetic interactions in SrCoGe$_2$O$_6$. Furthermore, our heat capacity measurements reveal an effect of an external magnetic field (approximately 13~T) which shifts the system from a fragile antiferromagnetic ordering with $T_{\mathrm{N}}=9$~K to a field-induced state. We argue that pyroxenes, particularly those modified by substituting Ge with Si and its less extended $p$ orbitals, emerge as a novel platform for the Kitaev model. This opens up possibilities for advancing our understanding of Kitaev physics., Comment: 11 + 2 pages, 7 + 3 figures

Optimization under uncertainty is important in many applications, particularly to inform policy and decision making in areas such as public health. A key source of uncertainty arises from the incorporation of environmental variables as inputs into computational models or simulators. Such variables represent uncontrollable features of the optimization problem and reliable decision making must account for the uncertainty they propagate to the simulator outputs. Often, multiple, competing objectives are defined from these outputs such that the final optimal decision is a compromise between different goals. Here, we present emulation-based optimization methodology for such problems that extends expected quantile improvement (EQI) to address multi-objective optimization. Focusing on the practically important case of two objectives, we use a sequential design strategy to identify the Pareto front of optimal solutions. Uncertainty from the environmental variables is integrated out using Monte Carlo samples from the simulator. Interrogation of the expected output from the simulator is facilitated by use of (Gaussian process) emulators. The methodology is demonstrated on an optimization problem from public health involving the dispersion of anthrax spores across a spatial terrain. Environmental variables include meteorological features that impact the dispersion, and the methodology identifies the Pareto front even when there is considerable input uncertainty.

The cosmological constant problem is a fundamental issue that has puzzled researchers in the fields of theoretical physics and cosmology for a long time. It arises from the discrepancy between the observed value of the cosmological constant and the value predicted by quantum field theory. A new spacetime model based on nonassociative geometry and statistical physics of complex networks offers a fresh perspective on the problem. Our research indicates that spacetime topology plays a crucial role in solving the cosmological constant problem and addressing the dark energy issue. We discovered that spacetime foam significantly impacts the effective cosmological constant, which is determined by the density of topological geons. Furthermore, we demonstrate that the source of dark energy is topological geons, Comment: 8 pages

The clustering coefficient is a valuable tool for understanding the structure of complex networks. It is widely used to analyze social networks, biological networks, and other complex systems. While there is generally a single common definition for the local clustering coefficient, there are two different ways to calculate the global clustering coefficient. The first approach takes the average of the local clustering coefficients for each node in the network. The second one is based on the ratio of closed triplets to all triplets. It is shown that these two definitions of the global clustering coefficients are strongly inequivalent and may significantly impact the accuracy of the outcome., Comment: 4 pages, 5 figures

The aim of this note is to estimate the tail of the distribution of the number of particles in an interval under determinantal and Pfaffian point processes. The main result of the note is that the square of the number of particles under the determinantal point process whose correlation kernel is an entire function of finite order has sub-Poissonian tails. The same result also holds in the symplectic Pfaffian case. As a corollary, sub-Poissonian estimates are also obtained for exponential moments of additive functionals over pairs of particles., Comment: 18 pages

The main result of this note is that the shift of the parameter by 1 in the parameter space of decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group corresponds to the taking of the reduced Palm measure at infinity for our decomposing measures. The proof proceeds by finite-dimensional approximation of our measures by orthogonal polynomial ensembles. The key remark is that the taking the reduced Palm measure commutes with the scaling limit transition from finite to infinite particle systems., Comment: 23 pages

The two-dimensional (2D) material Cr$_2$Ge$_2$Te$_6$ is a member of the class of insulating van der Waals magnets. Here, using high resolution angle-resolved photoemission spectroscopy in a detailed temperature dependence study, we identify a clear response of the electronic structure to a dimensional crossover in the form of two distinct temperature scales marking onsets of modifications in the electronic structure. Specifically, we observe Te $p$-orbital-dominated bands to undergo changes at the Curie transition temperature T$_C$ while the Cr $d$-orbital-dominated bands begin evolving at a higher temperature scale. Combined with neutron scattering, density functional theory calculations, and Monte Carlo simulations, we find that the electronic system can be consistently understood to respond sequentially to the distinct temperatures at which in-plane and out-of-plane spin correlations exceed a characteristic length scale. Our findings reveal the sensitivity of the orbital-selective electronic structure for probing the dynamical evolution of local moment correlations in vdW insulating magnets., Comment: PRB, in press

In 1883, Darboux gave a local classification of isothermic surfaces with one family of planar curvature lines using complex analytic methods. His choice of real reduction cannot contain tori. We classify isothermic tori with one family of planar curvature lines. They are found in the second real reduction of Darboux's description. We give explicit theta function formulas for the family of plane curves. These curves are particular area constrained hyperbolic elastica. With a Euclidean gauge, the Euler--Lagrange equation is lower order than expected. In our companion paper (arXiv:2110.06335) we use such isothermic tori to construct the first examples of compact Bonnet pairs: two isometric tori related by a mean curvature preserving isometry. They are also the first pair of isometric compact immersions that are analytic. Additionally, we study the finite dimensional moduli space characterizing when the second family of curvature lines is spherical. Isothermic tori with planar and spherical curvature lines are natural generalizations of Wente constant mean curvature tori, discovered in 1986. Wente tori are recovered in a limit case of our formulas., Comment: 39 pages, 6 figures. Comments welcome! (split off from arXiv:2110.06335v1 and added relationship to hyperbolic elastica; v2 fixes small typos)

High-order harmonic generation in multiphoton ionization regime is studied theoretically to examine the resonant effects of the generating particle. We solve the time-dependent Schr\"odinger equation for In+ in the laser field by expanding the solution in terms of unperturbed eigenstates obtained in the Hartree-Fock approximation. The intensity enhancement of the high harmonic is demonstrated under 7-photon resonance with the energy of the transition from the ground state to the 4d^9 5p ^1P_1 autoionizing state. Attosecond pulse generation using harmonics of the fifth and higher orders is studied. We find a train of almost spectral limited pulses with duration of 190 as.