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The kinetic energy of a multi-particle system is described by the one-particle kinetic energy density matrix $\tau(x, y)$. Alongside the one-particle density matrix $\gamma(x, y)$, it is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula $\lambda_k \sim (Bk)^{-2}$, $B \ge 0$, as $k\to\infty$, for the eigenvalues $\lambda_k$ of the self-adjoint operator $\boldsymbol{\sf T}\ge 0$ with kernel $\tau(x, y)$., Comment: arXiv admin note: substantial text overlap with arXiv:2103.11896 Author's note: bounds for singular values have been considerably simplified

The one-particle density matrix $\gamma(x, y)$ for a bound state of an atom or molecule is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula $\lambda_k \sim (Ak)^{-8/3}$, $A \ge 0$, as $k\to\infty$, for the eigenvalues $\lambda_k$ of the self-adjoint operator $\boldsymbol\Gamma\ge 0$ with kernel $\gamma(x, y)$., Comment: 27 pages, Remarks 2.4., 2.5 added. Subsection 3.3 simplified

We examine a fundamental material property called Poisson's ratio, which establishes the relationship for the relative deformation of a physical system in orthogonal directions. Architects and engineers have designed advanced systems using repeating patterns that can potentially exhibit auxetic behavior, which is the property of having a negative Poisson's ratio. Because two-dimensional cross sections of each of these patterns has an associated wallpaper group, we can look for useful correlations between this geometric information and the two-dimensional response as defined by Poisson's ratio. By analyzing the data, we find two properties of the wallpaper group that correlate with more effective Poisson's ratio required for applications. This paper also contains an introduction to wallpaper groups and orbifold notation and an appendix contains some literature references recreated to use our preferred notation., Comment: 17 pages, 8 figures

We study molecular emission in a massive condensation at the border of the HII region RCW 120, paying particular attention to the Core 1 and Core 2 objects, the most massive fragments of the condensation found previously by ALMA. The latter fragment was previously suggested to host a high-mass analogue of Class 0 young stellar object. We present spectra of molecular emission in the 1 mm range made with the APEX telescope. We detect CH$_3$OH and C$^{34}$S lines in Core 1 and Core 2. The CH$_3$CN series and the SO$_2$ lines are only found in Core 2. We estimate gas physical parameters using methanol lines and obtain gas temperature less than 100 K in both regions. Molecular hydrogen number density in Core 2 is in the range of $10^5-10^7$ cm$^{-3}$ and is more uncertain in Core 1. However, the detection of the CH$_3$CN lines corresponding to highly excited transitions ($E_{\rm u}> 400$~K) in Core~2 indicates that the region contains hot gas, while the abundances of CH$_3$OH, CS, SO$_2$ and CH$_3$CN are quite low for a hot core stage. We propose that Core 2 is in the warm-up phase prior to the establishing of the hot gas chemistry. We suggest that Core 2 is in the beginning of the hot core stage. There are no detected CH$_3$CN lines in Core 1, therefore, it might be on an even less evolved evolutionary stage., Comment: 11 pages, 6 figures, accepted by MNRAS

Class II methanol masers are signs of massive young stellar objects (MYSOs). Recent findings show that MYSO accretion bursts cause flares of these masers. Thus, maser monitoring can be used to identify such bursts. Burst-induced SED changes provide valuable information on a very intense phase of high-mass star formation. In mid-January 2019, a maser flare of the MYSO G358.93-0.03 was reported. ALMA and SMA imaging resolved the core of the star forming region and proved the association of the masers with the brightest continuum source MM1. However, no significant flux rise of the (sub)mm dust continuum was found. Thus, we performed NIR imaging with GROND and IFU spectroscopy with FIFI-LS aboard SOFIA to detect possible counterparts to the (sub)mm sources, and compare their photometry to archival measurements. The comparison of pre-burst and burst SEDs is of crucial importance to judge whether a luminosity increase due to the burst is present and if it triggered the maser flare. The FIR fluxes of MM1 measured with FIFI-LS exceed those from Herschel significantly, which clearly confirms the presence of an accretion burst. The second epoch data, taken about 16 months later, still show increased fluxes. Our RT modeling yielded major burst parameters and suggests that the MYSO features a circumstellar disk which might be transient. From the multi-epoch SEDs, conclusions on heating and cooling time-scales could be drawn. Circumstances of the burst-induced maser relocation have been explored. The verification of the accretion burst from G358 is another confirmation that Class II methanol maser flares represent an alert for such events. The few events known to date already indicate that there is a broad range in burst strength and duration as well as environmental characteristics. The G358 event is the shortest and least luminous MYSO accretion burst so far., Comment: 22 pages, 11 figures, accepted by A&A. Abstract abridged for arxiv submission

Predictions for the Higgs masses are a distinctive feature of supersymmetric extensions of the Standard Model, where they play a crucial role in constraining the parameter space. The discovery of a Higgs boson and the remarkably precise measurement of its mass at the LHC have spurred new efforts aimed at improving the accuracy of the theoretical predictions for the Higgs masses in supersymmetric models. The "Precision SUSY Higgs Mass Calculation Initiative" (KUTS) was launched in 2014 to provide a forum for discussions between the different groups involved in these efforts. This report aims to present a comprehensive overview of the current status of Higgs-mass calculations in supersymmetric models, to document the many advances that were achieved in recent years and were discussed during the KUTS meetings, and to outline the prospects for future improvements in these calculations., Comment: iv, 79 pages; 5 figures. v2: iv, 99 pages; added appendix on public codes for the Higgs-mass calculation in SUSY models. v3: minor modifications, references updated; matches version published in EPJC. v4: hyperlinks enabled

A new oxide, sodium iron antimonate, Na2FeSbO5, was synthesized and structurally characterized, and its static and dynamic magnetic properties were comprehensively studied both experimentally by dc and ac magnetic susceptibility, magnetization, specific heat, electron spin resonance (ESR) and Moessbauer measurements, and theoretically by density functional calculations. The resulting single-crystal structure (a = 15.6991(9) A; b = 5.3323 (4) A; c = 10.8875(6) A; S.G. Pbna) consists of edge-shared SbO6 octahedral chains, which alternate with vertex-linked, magnetically active FeO4 tetrahedral chains. The 57Fe Moessbauer spectra confirmed the presence of high-spin Fe3+ (3d5) ions in a distorted tetrahedral oxygen coordination. The magnetic susceptibility and specific heat data show the absence of a long-range magnetic ordering in Na2FeSbO5 down to 2 K, but ac magnetic susceptibility unambigously demonstrates spin-glass-type behavior with a unique two-step freezing at Tf1 about 80 K and Tf2 about 35 K. Magnetic hyperfine splitting of 57Fe Moessbauer spectra was observed below T* about 104 K (Tf1 < T*). The spectra just below T* (Tf1 < T < T*) exhibit a relaxation behavior caused by critical spin fluctuations, indicating the existence of short-range correlations. The stochastic model of ionic spin relaxation was used to account for the shape of the Moessbauer spectra below the freezing temperature. A complex slow dynamics is further supported by ESR data revealing two different absorption modes presumably related to ordered and disordered segments of spin chains. The data imply a spin-cluster ground state for Na2FeSbO5.

In this letter we report the first multi-differential measurement of correlated pion-proton pairs from 2 billion Au+Au collisions at \sqrt{s_{NN}} = 2.42 GeV collected with HADES. In this energy regime the population of \Delta(1232) resonances plays an important role in the way energy is distributed between intrinsic excitation energy and kinetic energy of the hadrons in the fireball. The triple differential d3N/dM{\pi}pdpTdy distributions of correlated {\pi}p pairs have been determined by subtracting the {\pi}p combinatorial background using an iterative method. The invariant-mass distributions in the \Delta(1232) mass region show strong deviations from a Breit-Wigner function with vacuum width and mass. The yield of correlated pion-proton pairs exhibits a complex isospin, rapidity and transverse-momentum dependence. In the invariant mass range 1.1 < Minv (GeV/c2) < 1.4, the yield is found to be similar for {\pi}+p and {\pi}-p pairs, and to follow a power law ^{\alpha}, where is the mean number of participating nucleons. The exponent {\alpha} depends strongly on the pair transverse momentum (pT) while its pT-integrated and charge-averaged value is {\alpha} = 1.5 \pm 0.08stat \pm 0.2sys., Comment: 9 pages, 9 figures

It is now a widely held view that, in their formation and early evolution, stars build up mass in bursts. The burst mode of star formation scenario proposes that the stars grow in mass via episodic accretion of fragments migrating from their gravitationally-unstable circumstellar discs and it naturally explains the existence of observed pre-main-sequence bursts from high mass protostars. We present a parameter study of hydrodynamical models of massive young stellar objects (MYSOs) that explores the initial masses of the collapsing clouds (Mc = 60-200Mo) and ratio of rotational-to-gravitational energies (beta = 0:005-0:33). An increase in Mc and/or beta produces protostellar accretion discs that are more prone to develop gravitational instability and to experience bursts. We find that all MYSOs have bursts even if their pre-stellar core is such that beta <= 0.01. Within our assumptions, the lack of stable discs is therefore a major difference between low- and high-mass star formation mechanisms. All our disc masses and disk-to-star mass ratios Md=M* > 1 scale as a power-law with the stellar mass. Our results confirm that massive protostars accrete about 40-60% of their mass in the burst mode. The distribution of time periods between two consecutive bursts is bimodal: there is a short duration (~ 1-10 yr) peak corresponding to the short, faintest bursts and a long duration peak (at ~ 10^3-10^4 yr) corresponding to the long, FU-Orionis-type bursts appearing in later disc evolution, i.e., around 30 kyr after disc formation. We discuss this bimodality in the context of the structure of massive protostellar jets as potential signatures of accretion burst history., Comment: 22 pages, 11 figures. Accepted at MNRAS

Low-energy effective field theories (EFT) encode information about the physics at high energies--i.e., the high-energy theory (HET). To extract this information the EFT and the HET have to be matched to each other. At the one-loop level, general results for the matching of renormalizable operators have already been obtained in the literature. In the present paper, we take a step towards a better understanding of renormalizable operator matching at the two-loop level: Focusing on the diagrammatic method, we discuss in detail the various contributions to two-loop matching conditions and compare different approaches to derive them. Moreover, we discuss which observables are best suited for the derivation of matching conditions. As a concrete application, we calculate the $\mathcal{O}\left(\alpha_t \alpha_s \right)$ and $\mathcal{O} \left(\alpha_t^2 \right)$ matching conditions of the scalar four-point couplings between the Standard Model (SM) and the Two-Higgs-Doublet Model (THDM) as well as the THDM and the Minimal Supersymmetric Standard Model (MSSM). We use the derived formulas to improve the prediction of the SM-like Higgs mass in the MSSM using the THDM as EFT., Comment: 42 pages, 4 figures, 4 ancillary files; matches version published in JHEP

We present a study of the association between class I methanol masers and cold dust clumps from the ATLASGAL survey. It was found that almost 100% of class I methanol masers are associated with objects listed in the ATLASGAL compact source catalog. We find a statistically significant difference in the flux density, luminosity, number and column density and temperature distributions of ATLASGAL sources associated with 95/44 GHz methanol masers compared with those ATLASGAL sources devoid of 95 GHz methanol masers. The masers tend to arise in clumps with higher densities, luminosities and temperatures compared with both the full sample of the ATLASGAL clumps, as well as the sample of ATLASGAL sources that were cross-matched with positions previously searched for methanol masers but with no detections. Comparison between the peak position of ATLASGAL clumps and the interferometric positions of the associated class I and II methanol masers reveals that class I masers are generally located at larger physical distances from the peak submillimetre emission than class II masers. We conclude that the tight association between ATLASGAL sources and class I methanol masers may be used as a link toward understanding the conditions of the pumping of these masers and evolutionary stages at which they appear., Comment: Accepted to the Astronomical Journal, 14 pages, 7 figures

We discuss various improvements of the prediction for the light MSSM Higgs boson mass in the hybrid framework of the public code FeynHiggs, which combines fixed-order and effective field theory results. First, we discuss the resummation of logarithmic contributions proportional to the bottom-Yukawa coupling including two-loop $\Delta_b$ resummation. For large $\tan\beta$, these improvements can lead to large upward shifts of the Higgs mass compared to the existing fixed-order calculations. Second, we improve the implemented EFT calculation by fully taking into account the effect of $\mathcal{CP}$-violating phases. As a third improvement, we discuss the inclusion of partial N$^3$LL resummation. The presented improvements will be implemented into FeynHiggs., Comment: 53 pages, 9 figures, 12 ancillary files; v2: matches version published in EPJC

It is shown that the eigenvalues $\lambda_k, k=1, 2, \dots,$ of the one-particle density matrix satisfy the bound $\lambda_k\le C k^{-8/3}$ with a positive constant $C$., Comment: 16 pages

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the Canonical Polyadic tensor Decomposition is one of the most suited models. However, fitting the convolutional tensors by numerical optimization algorithms often encounters diverging components, i.e., extremely large rank-one tensors but canceling each other. Such degeneracy often causes the non-interpretable result and numerical instability for the neural network fine-tuning. This paper is the first study on degeneracy in the tensor decomposition of convolutional kernels. We present a novel method, which can stabilize the low-rank approximation of convolutional kernels and ensure efficient compression while preserving the high-quality performance of the neural networks. We evaluate our approach on popular CNN architectures for image classification and show that our method results in much lower accuracy degradation and provides consistent performance., Comment: This paper is accepted to ECCV2020

The aim of the present work is to study structure and gas kinematics in the photodissociation regions (PDRs) around the compact HII regions S235A and S235C. We observe the [CII], [13CII] and [OI] line emission, using SOFIA/upGREAT and complement them by data of HCO+ and CO. We use the [13CII] line to measure the optical depth of the [CII] emission, and find that the [CII] line profiles are influenced by self-absorption, while the [13CII] line remains unaffected by these effects. Hence, for dense PDRs, [13CII] emission is a better tracer of gas kinematics. The optical depth of the [CII] line is up to 10 in S235A. We find an expanding motion of the [CII]-emitting layer of the PDRs into the front molecular layer in both regions. Comparison of the gas and dust columns shows that gas components visible neither in the [CII] nor in low-J CO lines may contribute to the total column across S235A. We test whether the observed properties of the PDRs match the predictions of spherical models of expanding HII region + PDR + molecular cloud. Integrated intensities of the [13CII], [CII] and [OI] lines are well-represented by the model, but the models do not reproduce the double-peaked [CII] line profiles due to an insufficient column density of C+. The model predicts that the [OI] line could be a more reliable tracer of gas kinematics, but the foreground self-absorbing material does not allow using it in the considered regions., Comment: accepted to MNRAS

We consider the ideal Fermi gas of indistinguishable particles without spin but with electric charge, confined to a Euclidean plane $\mathbb R^2$ perpendicular to an external constant magnetic field of strength $B>0$. We assume this (infinite) quantum gas to be in thermal equilibrium at zero temperature, that is, in its ground state with chemical potential $\mu\ge B$ (in suitable physical units). For this (pure) state we define its local entropy $S(\Lambda)$ associated with a bounded (sub)region $\Lambda\subset \mathbb R^2$ as the von Neumann entropy of the (mixed) local substate obtained by reducing the infinite-area ground state to this region $\Lambda$ of finite area $|\Lambda|$. In this setting we prove that the leading asymptotic growth of $S(L\Lambda)$, as the dimensionless scaling parameter $L>0$ tends to infinity, has the form $L\sqrt{B}|\partial\Lambda|$ up to a precisely given (positive multiplicative) coefficient which is independent of $\Lambda$ and dependent on $B$ and $\mu$ only through the integer part of $(\mu/B-1)/2$. Here we have assumed the boundary curve $\partial\Lambda$ of $\Lambda$ to be sufficiently smooth which, in particular, ensures that its arc length $|\partial\Lambda|$ is well-defined. This result is in agreement with a so-called area-law scaling (for two spatial dimensions). It contrasts the zero-field case $B=0$, where an additional logarithmic factor $\ln(L)$ is known to be present. We also have a similar result, with a slightly more explicit coefficient, for the simpler situation where the underlying single-particle Hamiltonian, known as the Landau Hamiltonian, is restricted from its natural Hilbert space $\text L^2(\mathbb R^2)$ to the eigenspace of a single but arbitrary Landau level. Both results extend to the whole one-parameter family of quantum R\'enyi entropies.

It is proved that the one-particle density matrix $\gamma(x, y)$ for multi-particle systems is analytic away from the nuclei and from the diagonal $x = y$., Comment: 31 pages. Compared to the previous version, the introduction has been rewritten, presentation in Sect. 4,5 has been improved

Flow coefficients $v_{n}$ of the orders $n = 1 - 6$ are measured with the High-Acceptance DiElectron Spectrometer (HADES) at GSI for protons, deuterons and tritons as a function of centrality, transverse momentum and rapidity in Au+Au collisions at $\sqrt{s_{NN}} = 2.4$ GeV. Combining the information from the flow coefficients of all orders allows to construct for the first time, at collision energies of a few GeV, a multi-differential picture of the angular emission pattern of these particles. It reflects the complicated interplay between the effect of the central fireball pressure on the emission of particles and their subsequent interaction with spectator matter. The high precision information on higher order flow coefficients is a major step forward in constraining the equation-of-state of dense baryonic matter., Comment: 6 pages, 5 figures; Figs. 2, 3 and 5 updated from re-analysis of data including UrQMD model predictions. Plotting error in Fig. 4 corrected; Accepted for publication in Phys. Rev. Lett

We present high-statistic data on charged pion emission from Au+Au collisions at $\sqrt{s_{\rm{NN}}}$ = 2.4 GeV (corresponding to $E_{beam}$ = 1.23 A GeV) in four centrality classes in the range 0 - 40$\%$ of the most central collisions. The data are analyzed as a function of transverse momentum, transverse mass, rapidity, and polar angle. Pion multiplicity per participating nucleon decreases moderately with increasing centrality. The polar angular distributions are found to be non-isotropic even for the most central event class. Our results on pion multiplicity fit well into the general trend of the world data, but undershoot by $2.5 \sigma$ data from the FOPI experiment measured at slightly lower beam energy. We compare our data to state-of-the-art transport model calculations (PHSD, IQMD, PHQMD, GiBUU and SMASH) and find substantial differences between the measurement and the results of these calculations., Comment: 17 pages, 19 figures, 4 tables