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In this paper, we establish that the number of partitions of a natural number with positive odd rank is equal to the number of two-color partitions (red and blue), where the smallest part is even (say $2n$) and all red parts are even and lie within the interval $(2n,4n]$. This led us to derive a new representation for the third order mock theta function $f_3(q)$ and an analogue of the fundamental identity for the smallest part partition function Spt$(n)$, both of which are of significant interest in their own right. We also consider the odd smallest part version of the above two-color partition, whose generating function involves another third order mock theta function $\phi_3(q)$., Comment: Submitted for publication

Using the full four-year SPTpol 500 deg$^2$ dataset in both the 95 GHz and 150 GHz frequency bands, we present measurements of the temperature and $E$-mode polarization of the cosmic microwave background (CMB), as well as the $E$-mode polarization auto-power spectrum ($EE$) and temperature-$E$-mode cross-power spectrum ($TE$) in the angular multipole range $50<\ell<8000$. We find the SPTpol dataset to be self-consistent, passing several internal consistency tests based on maps, frequency bands, bandpowers, and cosmological parameters. The full SPTpol dataset is well-fit by the $\Lambda CDM$ model, for which we find $H_0=70.48\pm2.16$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega_m=0.271\pm0.026$, when using only the SPTpol data and a Planck-based prior on the optical depth to reionization. The $\Lambda CDM$ parameter constraints are consistent across the 95 GHz-only, 150 GHz-only, $TE$-only, and $EE$-only data splits. Between the $\ell<1000$ and $\ell>1000$ data splits, the $\Lambda CDM$ parameter constraints are borderline consistent at the $\sim2\sigma$ level. This consistency improves when including a parameter $A_L$, the degree of lensing of the CMB inferred from the smearing of acoustic peaks. When marginalized over $A_L$, the $\Lambda CDM$ parameter constraints from SPTpol are consistent with those from Planck. The power spectra presented here are the most sensitive measurements of the lensed CMB damping tail to date for roughly $\ell > 1700$ in $TE$ and $\ell > 2000$ in $EE$.

Motivated by two Legendre-type formulas for overpartitions, we derive a variety of their companions as Legendre theorems for overpartition pairs. This leads to equalities of subclasses of overpartitions and overpartition pairs., Comment: 16 pages. Accepted for publication

Cosmic shear, galaxy clustering, and the abundance of massive halos each probe the large-scale structure of the universe in complementary ways. We present cosmological constraints from the joint analysis of the three probes, building on the latest analyses of the lensing-informed abundance of clusters identified by the South Pole Telescope (SPT) and of the auto- and cross-correlation of galaxy position and weak lensing measurements (3$\times$2pt) in the Dark Energy Survey (DES). We consider the cosmological correlation between the different tracers and we account for the systematic uncertainties that are shared between the large-scale lensing correlation functions and the small-scale lensing-based cluster mass calibration. Marginalized over the remaining $\Lambda$CDM parameters (including the sum of neutrino masses) and 52 astrophysical modeling parameters, we measure $\Omega_\mathrm{m}=0.300\pm0.017$ and $\sigma_8=0.797\pm0.026$. Compared to constraints from Planck primary CMB anisotropies, our constraints are only 15% wider with a probability to exceed of 0.22 ($1.2\sigma$) for the two-parameter difference. We further obtain $S_8\equiv\sigma_8(\Omega_\mathrm{m}/0.3)^{0.5}=0.796\pm0.013$ which is lower than the Planck measurement at the $1.6\sigma$ level. The combined SPT cluster, DES 3$\times$2pt, and Planck datasets mildly prefer a non-zero positive neutrino mass, with a 95% upper limit $\sum m_\nu<0.25~\mathrm{eV}$ on the sum of neutrino masses. Assuming a $w$CDM model, we constrain the dark energy equation of state parameter $w=-1.15^{+0.23}_{-0.17}$ and when combining with Planck primary CMB anisotropies, we recover $w=-1.20^{+0.15}_{-0.09}$, a $1.7\sigma$ difference with a cosmological constant. The precision of our results highlights the benefits of multiwavelength multiprobe cosmology., Comment: Submitted to Phys. Rev. D

The influence of growth regimes of the silicon capping layer on the optical properties of heterostructures with submonolayer InAs quantum dots embedded in a silicon matrix has been studied. The photoluminescence signal at 1650 nm from submonolayer quantum dots at low temperatures up to 120 K was obtained. It was established that the use of a two-stage method of silicon overgrowing InAs nanoislands makes it possible to increase the photoluminescence intensity by improving the crystalline quality of heterostructures. Analysis of the temperature dependence allowed us to calculate an activation energy for electrons confined in the quantum dots potential well at the level of the thermal energy at room temperature., Comment: 22 pages, in Russian language, 4 figures

We will consider two-color integer partitions in which the smallest part is odd and the odd or the even parts may occur only in one color. It turns out that these partitions are generated by the mock theta functions of third order due to Ramanujan and Watson. Motivated by this, we will also consider two-color partitions in which the parts of the same parity may occur in both colors., Comment: 12 pages, submitted

It is well known that the number of partitions into distinct even parts equals the number of $4$-regular partitions. In this paper we prove identities relating certain restricted partitions into distinct even parts with restricted $4$-regular partitions., Comment: 7 pages, Accepted for publication

This paper is devoted to the study of $$ U_t(a,q):=\sum_{1\leq n_1

One of the greatest debates of our time is whether our macroscopic world (i) naturally emerges from quantum mechanics or (ii) requires new physics. We argue for (ii) and propose a simple gravitational self-decoherence mechanism. The purity loss for a free quantum particle is evaluated and shown to be extremely inefficient for elementary particles but very effective for those at the Planck scale. The physical picture behind it is that coherence would easily leak from heavy enough particles to (non-observable) spacetime quantum degrees of freedom., Comment: 8 pages (added appendix with complementary information), 5 figures

Perovskite oxides hetero-structures are host to a large number of interesting phenomena such as ferroelectricity and 2D-superconductivity. Ferroelectric perovskite oxides have been of significant interest due to their possible use in MOSFETs and FRAM. SrHfO$_3$ (SHO) is a perovskite oxide with pseudo-cubic lattice parameter of 4.1 $\mathring{A}$ that previous DFT calculations suggest can be stabilized in a ferroelectric P4mm phase, similar to STO, when stabilized with sufficient compressive strain. Additionally, it is insulating, possesses a large band gap, and a high dielectric constant, making it an ideal candidate for oxide electronic devices. In this work, SHO films were grown by hybrid molecular beam epitaxy with a tetrakis(ethylmethylamino)hafnium(IV) source on GdScO$_3$ and TbScO$_3$ substrates. Equilibrium and strained SHO phases were characterized using X-ray diffraction, X-ray absorption spectroscopy, and scanning transmission electron microscopy to determine the perovskite phase of the strained films, with the results compared to density functional theory models of phase stability versus strain. Contrary to past reports, we find that compressively-strained SrHfO$_3$ undergoes octahedral tilt distortions and most likely takes on the I4/mcm phase with the a$^0$a$^0$c$^-$ tilt pattern., Comment: 36 pages, 11 figures

Optimizing the interfaces in perovskite solar cells (PSCs) is essential for enhancing their performance, improving their stability, and making them commercially viable for large-scale deployment in solar energy harvesting applications. Point defects, like vacancies, have a dual role, as they can inherently provide a proper doping, but they can also reduce the collected current by trap-assisted recombination. Moreover, they can play an active role in ion migration. Using {\it ab initio} density functional theory (DFT) calculations we investigate the changes in the band alignment induced by interfacial vacancy defects in a TiO$_2$/MAPI/Cu$_2$O based PSC. Depending on the type of the vacancy (Ti, Cu, O, Pb, I) in the oxide and perovskite materials, additional doping is superimposed on the already existing background. Their effect on the performance of the PSCs becomes visible, as shown by SCAPS simulations. The most significant impact is observed for $p$ type doping of TiO$_2$ and $n$ type doping of Cu$_2$O, while the effective doping of the perovskite layer affects one of the two interfaces. We discuss these results based on modification of the band structure near the active interfaces and provide further insights concerning the optimization of electron and hole collection., Comment: 7 pages, 8 figures, 4 sections, 44 references

The authors of Ref.[1] (referred to here as "Moskal et al.") claim to have performed the most precise test of P, T and CP invariance in the decay of ortho-Positronium. In this note: 1) we demonstrate, assuming standard properties for Compton scattering, that the average value of the correlation measured by Moskal et al. must necessarily be zero, independently of any physics occurring in o-Ps decay; 2) we point out that there is no formal justification to equate the normal vector to the Compton scattering plane with the incident photon polarization, as done by Moskal et al.; 3) we observe the absence of characterization of the device as a Compton polarimeter, which is paramount in photon polarimetry; 4) we review previous measurements of the polarization of photons from o-Ps decay, properly implementing the Compton polarimetry technique, and make the connection with tests of discrete symmetries; and 5) we stress that the correlation proposed by Moskal et al. cannot be generated solely by the physics of o-Ps decay, including possible violations of discrete symmetries., Comment: Submitted to Nature Communications

The inflation of an inner radial (or spherical) cavity in an amorphous solids confined in a disk (or a sphere), served as a fruitful case model for studying the effects of plastic deformations on the mechanical response. It was shown that when the field associated with Eshelby quadrupolar charges is non-uniform, the displacement field is riddled with dipole charges that screen elasticity, reminiscent of Debye monopoles screening in electrostatics. In this paper we look deeper into the screening phenomenon, taking into account the consequences of irreversibility that are associated with the breaking of Chiral symmetry. We consider the equations for the displacement field with the presence of ``Odd Dipole Screening", solve them analytically and compare with numerical simulations. Suggestions how to test the theory in experiments are provided.

Understanding how local distortions determine the functional properties of high entropy materials, containing five or more elements at a crystallographic site, is an open challenge. We address this for a compositionally complex spinel oxide (Mn$_{0.2}$Co$_{0.2}$Ni$_{0.2}$Cu$_{0.2}$Zn$_{0.2}$)Cr$_2$O$_4$ ($A^5$Cr$_2$O$_4$). By comparatively examining extended X-ray absorption fine structure on $A^5$Cr$_2$O$_4$ and its parent counterparts $A$Cr$_2$O$_4$ along with density functional theory calculations for multiple configurations, we find that the element-specific distortions go beyond the first neighbor. Specifically, the strong Jahn-Teller distortion present in CuCr$_2$O$_4$ is found to be completely suppressed in $A^5$Cr$_2$O$_4$. Instead, there is a broad distribution of Cu-O and Cu-Cr bond distances while other $A$-O distances acquire certain specific values. This study demonstrates the additional flexibility of a cationic sublattice in maintaining a uniform long-range structure, in contrast to previous reports showing only the accommodative anionic sublattice. Remarkably, despite the presence of multiple magnetic ions and variable bond lengths, the mean field magnetic interactions of $A^5$Cr$_2$O$_4$ exhibit a striking resemblance to those of NiCr$_2$O$_4$. This compelling observation originates from the comparability of bond lengths around Cr in both materials. Our study paves the way for a deeper understanding of the impact of local structural distortions in compositionally complex quantum materials, enabling the targeted design with tailored properties.

Modern Tabletop Games present various interesting challenges for Multi-agent Reinforcement Learning. In this paper, we introduce PyTAG, a new framework that supports interacting with a large collection of games implemented in the Tabletop Games framework. In this work we highlight the challenges tabletop games provide, from a game-playing agent perspective, along with the opportunities they provide for future research. Additionally, we highlight the technical challenges that involve training Reinforcement Learning agents on these games. To explore the Multi-agent setting provided by PyTAG we train the popular Proximal Policy Optimisation Reinforcement Learning algorithm using self-play on a subset of games and evaluate the trained policies against some simple agents and Monte-Carlo Tree Search implemented in the Tabletop Games framework.

The large spin-orbit coupling in iridium oxides plays a significant role in driving novel physical behaviors, including emergent phenomena in the films and heterostructures of perovskite and Ruddlesden-Popper iridates. In this work, we study the role of epitaxial strain on the electronic behavior of thin SrIrO$_3$ films. We find that compressive epitaxial strain leads to metallic transport behavior, but a slight tensile strain shows gapped behavior. Temperature-dependent resistivity measurements are used to examine different behaviors in films as a function of strain. We find Kondo contributions to the resistivity, with stronger effects in films that are thinner and under less compressive epitaxial strain. These results show the potential to tune SrIrO$_3$ into Kondo insulating states and open possibilities for a quantum critical point that can be controlled with strain in epitaxial films., Comment: 13 pages, 4 figures

We report results from an analysis aimed at detecting the trispectrum of the kinematic Sunyaev-Zel{'}dovich (kSZ) effect by combining data from the South Pole Telescope (SPT) and {\it Herschel}-SPIRE experiments over a 100 ${\rm deg}^{2}$ field. The SPT observations combine data from the previous and current surveys, namely SPTpol and SPT-3G, to achieve depths of 4.5, 3, and 16 $\mu {\rm K-arcmin}$ in bands centered at 95, 150, and 220 GHz. For SPIRE, we include data from the 600 and 857 GHz bands. We reconstruct the velocity-induced large-scale correlation of the small-scale kSZ signal with a quadratic estimator that uses two cosmic microwave background (CMB) temperature maps, constructed by optimally combining data from all the frequency bands. We reject the null hypothesis of a zero trispectrum at $10.3\sigma$ level. However, the measured trispectrum contains contributions from both the kSZ and other undesired components, such as CMB lensing and astrophysical foregrounds, with kSZ being sub-dominant. We use the \textsc{Agora} simulations to estimate the expected signal from CMB lensing and astrophysical foregrounds. After accounting for the contributions from CMB lensing and foreground signals, we do not detect an excess kSZ-only trispectrum and use this non-detection to set constraints on reionization. By applying a prior based on observations of the Gunn-Peterson trough, we obtain an upper limit on the duration of reionization of $\Delta z_{\rm re, 50} < 4.5$ (95\% C.L). We find these constraints are fairly robust to foregrounds assumptions. This trispectrum measurement is independent of, but consistent with, {\it Planck}'s optical depth measurement. This result is the first constraint on the epoch of reionization using the non-Gaussian nature of the kSZ signal., Comment: 15 pages, 5 figures (3 in main text and 2 in Appendix); Accepted for publication in PRL; Some texts have been moved to Appendix; Minor change in Fig. 2 to include nomalization; Data products and plotting scripts can be downloaded from https://github.com/sriniraghunathan/kSZ_4pt_SPT_SPIRE

We discuss the information loss issue for completely evaporating black holes in the context of a globally hyperbolic spacetime that maintains unchanged the entire semiclassical picture except for the "last evaporation breath," which pertains to full quantum gravity. Even though observers outside the black hole cannot access information that enters the horizon, there is no actual loss of information imposed by the spacetime causal structure since it is carried over from one Cauchy surface to the next (provided the local evolution is unitary)., Comment: 22 pages (with an added section discussing the 'Page time'), 8 figures

We present cosmological constraints from the abundance of galaxy clusters selected via the thermal Sunyaev-Zel'dovich (SZ) effect in South Pole Telescope (SPT) data with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample is constructed from the combined SPT-SZ, SPTpol ECS, and SPTpol 500d surveys, and comprises 1,005 confirmed clusters in the redshift range $0.25-1.78$ over a total sky area of 5,200 deg$^2$. We use DES Year 3 weak-lensing data for 688 clusters with redshifts $z<0.95$ and HST weak-lensing data for 39 clusters with $0.6

In recent work, it was shown that elasticity theory can break down in amorphous solids subjected to nonuniform {\em static} loads. The elastic fields are screened by geometric dipoles; these stem from gradients of the quadrupole field associated with plastic responses. Here we study the dynamical responses induced by {\em oscillatory} loads. The required modification to classical elasticity is described. Exact solutions for the displacement field in circular geometry are presented, demonstrating that dipole screening results in essential departures from the expected predictions of classical elasticity theory. Numerical simulations are conducted to validate the theoretical predictions and to delineate their range of validity., Comment: 9 pages, 7 figures

We have measured the absolute doubly differential angular sputtering yield for 20 keV Kr+ impacting a polycrystalline Cu slab at an incidence angle of {\theta}i = 45{\deg} relative to the surface normal. Sputtered Cu atoms were captured using collectors mounted on a half dome above the sample, and the sputtering distribution was measured as a function of the sputtering polar, {\theta}s, and azimuthal, phi, angles. Absolute results of the sputtering yield were determined from the mass gain of each collector, the ion dose, and the solid angle subtended, after irradiation to a total fluence of ~ 1 x 10^18 ions/cm^2. Our approach overcomes shortcomings of commonly used methods that only provide relative yields as a function of {\theta}s in the incidence plane (defined by the ion velocity and the surface normal). Our experimental results display an azimuthal variation that increases with increasing {\theta}s and is clearly discrepant with simulations using binary collision theory. We attribute the observed azimuthal anisotropy to ion-induced formation of micro- and nano-scale surface features that suppress the sputtering yield through shadowing and redeposition effects, neither of which are accounted for in the simulations. Our experimental results demonstrate the importance of doubly differential angular sputtering studies to probe ion sputtering processes at a fundamental level and to explore the effect of ion-beam-generated surface roughness., Comment: 29 pages, 9 figures

In 2010, G.-N. Han obtained the generating function for the number of size $t$ hooks among integer partitions. Here we obtain these generating functions for self-conjugate partitions, which are particularly elegant for even $t$. If $n_t(\lambda)$ is the number of size $t$ hooks in a partition $\lambda,$ then for even $t$ we have $$\sum_{\lambda\in \mathcal{SC}} x^{n_t(\lambda)} q^{\vert\lambda\vert} = (-q;q^2)_{\infty} \cdot ((1-x^2)q^{2t};q^{2t})_{\infty}^{\frac{t}2}. $$ As a consequence, if $a_t^*(n)$ is the number of such hooks among the self-conjugate partitions of $n,$ then for even $t$ we obtain the simple formula $$ a_t^*(n)=t\sum_{j\geq 1} q^*(n-2tj), $$ where $q^*(m)$ is the number of partitions of $m$ into distinct odd parts. As a corollary, we find that $t\mid a_t^*(n),$ which confirms a conjecture of Ballantine, Burson, Craig, Folsom, and Wen., Comment: 12 pages; minor revision based on referee reports