Modeling Polarization Signals from Cloudy Brown Dwarfs Luhman 16 A and B in Three Dimensions

The detection of disk-integrated polarization from Luhman 16 A and B in the H band, and subsequent modeling, has been interpreted in the framework of zonal cloud bands on these bodies. Recently, Tan and Showman investigated the 3D atmospheric circulation and cloud structures of brown dwarfs with general circulation models (GCMs), and their simulations yielded complex cloud distributions showing some aspects of zonal jets, but also complex vortices that cannot be captured by a simple model. Here we use these 3D GCMs specific to Luhman 16 A and B, along with the 3D Monte Carlo radiative transfer code ARTES, to calculate their polarization signals. We adopt the 3D temperature–pressure and cloud profiles from the GCMs as our input atmospheric structures. Our polarization calculations at 1.6 μm agree well with the measured degree of linear polarization from both Luhman 16 A and B. Our calculations reproduce the measured polarization for both objects with cloud particle sizes between 0.5 and 1 μm for Luhman 16 A and of 5 μm for Luhman 16 B. We find that the degree of linear polarization can vary on hour-long timescales over the course of a rotation period. We also show that models with azimuthally symmetric band-like cloud geometries, typically used for interpreting polarimetry observations of brown dwarfs, overpredict the polarization signal if the cloud patterns do not include complex vortices within these bands. This exploratory work shows that GCMs are promising for modeling and interpreting polarization signals of brown dwarfs.

Topological states between inversion symmetric atomic insulators

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary correspondence has been well-tested for strong topological invariants, and forms the basis for all proposed technological applications of topology. Here, we report that a group of weak topological invariants, which depend only on the symmetries of the atomic lattice, also induces a particular type of bulk-boundary correspondence. It predicts the presence or absence of states localised at the interface between two inversion-symmetric band insulators with trivial values for their strong invariants, based on the space group representation of the bands on either side of the junction. We show that this corresponds with symmetry-based classifications of topological materials. The interface modes are protected by the combination of band topology and symmetry of the interface, and may be used for topological transport and signal manipulation in heterojunction-based devices.

A class of symmetric and non-symmetric band matrices via binomial coefficients

Symmetric matrix classes of bandwidth 2r + 1 was studied in 1972 through binomial coefficients. In this paper, non-symmetric matrix classes with the binomial coefficients are considered where r + s + 1 is the bandwidth, r is the lower bandwidth and s is the upper bandwidth. Main results for inverse, determinants and norm-infinity of inverse are presented. The binomial coefficients are used for the derivation of results.

Third-Octave and Bark Graphic-Equalizer Design with Symmetric Band Filters

This work proposes graphic equalizer designs with third-octave and Bark frequency divisions using symmetric band filters with a prescribed Nyquist gain to reduce approximation errors. Both designs utilize an iterative weighted least-squares method to optimize the filter gains, accounting for the interaction between the different band filters, to ensure excellent accuracy. A third-octave graphic equalizer with a maximum magnitude-response error of 0.81 dB is obtained, which outperforms the previous state-of-the-art design. The corresponding error for the Bark equalizer, which is the first of its kind, is 1.26 dB. This paper also applies a recently proposed neural gain control in which the filter gains are predicted with a multilayer perceptron having two hidden layers. After the training, the resulting network quickly and accurately calculates the filter gains for third-order and Bark graphic equalizers with maximum errors of 0.86 dB and 1.32 dB, respectively, which are not much more than those of the corresponding weighted least-squares designs. Computing the filter gains is about 100 times faster with the neural network than with the original optimization method. The proposed designs are easy to apply and may thus lead to widespread use of accurate auditory graphic equalizers.

Random matrices with exchangeable entries

We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general, the entries of the upper triangular parts of these matrices are correlated and no smallness or sparseness of these correlations is assumed. It is shown that the eigenvalue distribution measures still converge to a semicircle but with random scaling. We also investigate the asymptotic behavior of the corresponding [Formula: see text]-operator norms. The key to our analysis is a generalization of a classic result by de Finetti that allows to represent the underlying probability spaces as averages of Wigner band ensembles with entries that are not necessarily centered. Some of our results appear to be new even for such Wigner band matrices.

Evidence of the Poisson/Gaudin–Mehta phase transition for band matrices on global scales

We prove that the Poisson/Gaudin–Mehta phase transition conjectured to occur when the bandwidth of an [Formula: see text] symmetric band matrix grows like [Formula: see text] is naturally observable in the rate of convergence of the level density to the Wigner semi-circle law. Specifically, we show for periodic and non-periodic band matrices the rate of convergence of the fourth moment of the level density is independent of the boundary conditions in the localized regime [Formula: see text] with a rate of [Formula: see text] for both cases, whereas in the delocalized regime [Formula: see text] where boundary effects become important, the rate of convergence for the two ensembles differs significantly, slowing to [Formula: see text] for non-periodic band matrices. Additionally, we examine the case of thick non-periodic band matrices [Formula: see text], showing that the fourth moment is maximally deviated from the Wigner semi-circle law when [Formula: see text], and provide numerical evidence that the eigenvector statistics also exhibit critical behavior at this point.