ShantanuT01/DACTYL-Pretraining huggingface dataset:
A new approach to the Helmholtz spectrum for arbitrarily shaped boundaries and a rather general class of boundary conditions is introduced. We derive the boundary induced change of the density of states in terms of the free Green's function from which we obtain both perturbative and non-perturbative results for the Casimir interaction between deformed surfaces. As an example, we compute the lateral electrodynamic Casimir force between two corrugated surfaces over a wide parameter range. Universal behavior, fixed only by the largest wavelength component of the surface shape, is identified at large surface separations. This complements known short distance expansions which are also reproduced.
We implement a multi-orbital cluster dynamical mean-field theory (DMFT), by improving a sample-update algorithm in the continuous-time quantum Monte Carlo method based on the interaction expansion. The proposed sampling scheme for the spin-flip and pair-hopping interactions in the two-orbital systems mitigates the sign problem, giving an efficient way to deal with these interactions. In particular, in the single-site DMFT, we see that the negative signs vanish. We apply the method to the two-dimensional two-orbital Hubbard model at half filling, where we take into account the short-range spatial correlation effects within a four-site cluster. We show that, compared to the single-site DMFT results, the critical interaction value for the metal-insulator transition decreases and that the effects of the spin-flip and pair-hopping terms are less significant in the parameter region we have studied. The present method provides a firm starting point for the study of inter-site correlations in multi-orbital systems. It also has a wide applicable scope in terms of realistic calculations in conjunction with density functional theory.
Kinetic Monte Carlo (kMC) simulations have emerged as a key tool for microkinetic modeling in heterogeneous catalysis and other materials applications. Systems, where site-specificity of all elementary reactions allows a mapping onto a lattice of discrete active sites, can be addressed within the particularly efficient lattice kMC approach. To this end we describe the versatile kmos software package, which offers a most user-friendly implementation, execution, and evaluation of lattice kMC models of arbitrary complexity in one- to three-dimensional lattice systems, involving multiple active sites in periodic or aperiodic arrangements, as well as site-resolved pairwise and higher-order lateral interactions. Conceptually, kmos achieves a maximum runtime performance which is essentially independent of lattice size by generating code for the efficiency-determining local update of available events that is optimized for a defined kMC model. For this model definition and the control of all runtime and evaluation aspects kmos offers a high-level application programming interface. Usage proceeds interactively, via scripts, or a graphical user interface, which visualizes the model geometry, the lattice occupations and rates of selected elementary reactions, while allowing on-the-fly changes of simulation parameters. We demonstrate the performance and scaling of kmos with the application to kMC models for surface catalytic processes, where for given operation conditions (temperature and partial pressures of all reactants) central simulation outcomes are catalytic activity and selectivities, surface composition, and mechanistic insight into the occurrence of individual elementary processes in the reaction network.
The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with non-commuting coordinates. This demonstrates that the algebraic extension keeps the simple structure of Quantum Mechanics, while it also introduces an effective quite involved structure in the 4-dimensional sub-space. The similarities to H. S. Snyder's work, a former proposal to include the effects of a minimal length, are exposed. The first steps to pseudo-complex Quantum Mechanics in 1-dimension are outlined, awaiting still the interpretation of some new emerging structures. As an example, two waves, out of phase by 90 degrees, are added which classically annihilate each other, while in the pseudo-complex description there is a non-zero amplitude.
We introduce RAFT-Stereo, a new deep architecture for rectified stereo based on the optical flow network RAFT. We introduce multi-level convolutional GRUs, which more efficiently propagate information across the image. A modified version of RAFT-Stereo can perform accurate real-time inference. RAFT-stereo ranks first on the Middlebury leaderboard, outperforming the next best method on 1px error by 29% and outperforms all published work on the ETH3D two-view stereo benchmark. Code is available at https://github.com/princeton-vl/RAFT-Stereo.
The structural inversion asymmetry-induced spin-orbit interaction of conduction band electrons in zinc-blende and wurtzite semiconductor structures is analysed allowing for a three-dimensional (3D) character of the external electric field and variation of the chemical composition. The interaction, taking into account all remote bands perturbatively, is presented with two contributions: a heterointerface term and a term caused by the external electric field. They have generally comparable strength and can be written in a unified manner only for 2D systems, where they can partially cancel each other. For quantum wires and dots composed of wurtzite semiconductors new terms appear, absent in zinc-blende structures, which acquire the standard Rashba form in 2D systems.
This paper proposes a novel generative adversarial layout refinement network for automated floorplan generation. Our architecture is an integration of a graph-constrained relational GAN and a conditional GAN, where a previously generated layout becomes the next input constraint, enabling iterative refinement. A surprising discovery of our research is that a simple non-iterative training process, dubbed component-wise GT-conditioning, is effective in learning such a generator. The iterative generator also creates a new opportunity in further improving a metric of choice via meta-optimization techniques by controlling when to pass which input constraints during iterative layout refinement. Our qualitative and quantitative evaluation based on the three standard metrics demonstrate that the proposed system makes significant improvements over the current state-of-the-art, even competitive against the ground-truth floorplans, designed by professional architects.
A family of magnetic halide double perovskites (HDPs) have recently attracted attention due to their potential to broaden application areas of halide double perovskites into e.g. spintronics. Up to date the theoretical modelling of these systems have relied on primitive approximations to the density functional theory (DFT). In this paper, we study structural, electronic and magnetic properties of the Fe$^{3+}$-containing HDPs Cs$_2$AgFeCl$_6$ and Cs$_2$NaFeCl$_6$ using a combination of more advanced DFT-based methods, including DFT+U, hybrid-DFT and treatments of various magnetic states. We examine the effect of varying the effective Hubbard parameter, U$_{eff}$, in DFT+U and the mixing-parameter, $\alpha$, in hybrid DFT on the electronic structure and structural properties. Our results reveal a set of localized Fe(d) states that are highly sensitive to these parameters. Cs$_2$AgFeCl$_6$ and Cs$_2$NaFeCl$_6$ are both antiferromagnets with Ne\'el temperatures well below room temperature and are thus in their paramagnetic (PM) state at the external conditions relevant to most applications. Therefore, we have examined the effect of disordered magnetism on the electronic structure of these systems and find that while Cs$_2$NaFeCl$_6$ is largely unaffected, Cs$_2$AgFeCl$_6$ shows significant renormalization of its electronic band structure.
With phase space analysis approach, we investigate thoroughly the self-trapping phenomenon for two weakly coupled Bose-Einstein condensates (BEC) in a symmetric double-well potential. We identify two kinds of self-trapping by their different relative phase behavior. With applying a periodic modulation on the energy bias of the system we find the occurrence of the self-trapping can be controlled, saying, the transition parameters can be adjusted effectively by the periodic modulation. Analytic expressions for the dependence of the transition parameters on the modulation parameters are derived for high and low frequency modulations. For an intermediate frequency modulation, we find the resonance between the periodic modulation and nonlinear Rabi oscillation dramatically affects the tunnelling dynamics and demonstrate many novel phenomena. Finally, we study the effects of many-body quantum fluctuation on self-trapping and discuss the possible experimental realization of the model.
We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice.
Building on work of Hardy and Ramanujan, Rademacher proved a well-known formula for the values of the ordinary partition function $p(n)$. More recently, Bruinier and Ono obtained an algebraic formula for these values. Here we study the smallest parts function introduced by Andrews; $\operatorname{spt}(n)$ counts the number of smallest parts in the partitions of $n$. The generating function for $\operatorname{spt}(n)$ forms a component of a natural mock modular form of weight $3/2$ whose shadow is the Dedekind eta function. Using automorphic methods (in particular the theta lift of Bruinier and Funke), we obtain an exact formula and an algebraic formula for its values. In contrast with the case of $p(n)$, the convergence of our expression is non-trivial, and requires power savings estimates for weighted sums of Kloosterman sums for a multiplier in weight $1/2$. These are proved with spectral methods (following an argument of Goldfeld and Sarnak).
We present a modified TREESPH code to model galaxies in 3d. The model includes a multi-phase description of the interstellar medium which combines two numerical techniques. A diffuse warm/hot gas phase is modelled by SPH while a sticky particle scheme is used to represent a cloudy medium. Interaction processes, such as star formation and feedback, cooling and mixing by condensation and evaporation, are taken into account. Here we apply our model to the evolution of a Milky Way type galaxy. After an initial stage, a quasi-equilibrium state is reached. It is characterised by a star formation rate of ~1 M_sun/year. Condensation and evaporation rates are in balance at 0.1-1 M_sun/year.
Given its velocity dispersion, the early-type galaxy NGC 1600 has an unusually massive ($M_\bullet = 1.7 \times 10^{10} M_\odot$) central supermassive black hole (SMBH), surrounded by a large core ($r_\mathrm{b} = 0.7$ kpc) with a tangentially biased stellar distribution. We present high-resolution equal-mass merger simulations including SMBHs to study the formation of such systems. The structural parameters of the progenitor ellipticals were chosen to produce merger remnants resembling NGC 1600. We test initial stellar density slopes of $\rho \propto r^{-1}$ and $\rho \propto r^{-3/2}$ and vary the initial SMBH masses from $8.5 \times 10^8$ to $8.5 \times 10^9$ $M_\odot$. With increasing SMBH mass the merger remnants show a systematic decrease in central surface brightness, an increasing core size, and an increasingly tangentially biased central velocity anisotropy. Two-dimensional kinematic maps reveal decoupled, rotating core regions for the most massive SMBHs. The stellar cores form rapidly as the SMBHs become bound, while the velocity anisotropy develops more slowly after the SMBH binaries become hard. The simulated merger remnants follow distinct relations between the core radius and the sphere-of-influence, and the SMBH mass, similar to observed systems. We find a systematic change in the relations as a function of the progenitor density slope, and present a simple scouring model reproducing this behavior. Finally, we find the best agreement with NGC 1600 using SMBH masses totaling the observed value of $M_\bullet = 1.7 \times 10^{10} M_\odot$. In general, density slopes of $\rho \propto r^{-3/2}$ for the progenitor galaxies are strongly favored for the equal-mass merger scenario.
In this paper we consider linear, time dependent Schr\"odinger equations of the form $i \partial_t \psi = K_0 \psi + V(t) \psi $, where $K_0$ is a positive self-adjoint operator with discrete spectrum and whose spectral gaps are asymptotically constant.   We give a strategy to construct bounded perturbations $V(t)$ such that the Hamiltonian $K_0 + V(t)$ generates unbounded orbits. We apply our abstract construction to three cases: (i) the Harmonic oscillator on $\mathbb R$, (ii) the half-wave equation on $\mathbb T$ and (iii) the Dirac-Schr\"odinger equation on the sphere. In each case, $V(t)$ is a smooth and periodic in time pseudodifferential operator and the Schr\"odinger equation has solutions fulfilling $\| \psi(t) \|_r \gtrsim |t|^{r }$ as $|t| \gg 1$.
Fast radio bursts offer the opportunity to place new constraints on the mass and density profile of hot and ionized gas in galactic haloes. We test here the X-ray emission and dispersion measure predicted by different gas profiles for the halo of the Milky Way. We examine a range of models, including entropy stability conditions and external pressure continuity. We find that incorporating constraints from X-ray observations leads to favouring dispersion measures on the lower end of the range given by these models. We show that the dispersion measure of the Milky Way halo could be less than 10 cm$^{-3}$ pc in the most extreme model we consider, which is based on constraints from O VII absorption lines. However, the models allowed by the soft X-ray constraints span more than an order of magnitude in dispersion measures. Additional information on the distribution of gas in the Milky Way halo could be obtained from the signature of a dipole in the dispersion measure of fast radio bursts across the sky, but this will be a small effect for most cases.
Relevance of the M\"ossbauer spectroscopy in the study of harmonically modulated electronic structures i.e. spin-density waves (SDWs) and charge-density waves (CDWs) is presented and discussed. First, the effect of various parameters pertinent to the SDWs and CDWs is outlined on simulated 119Sn spectra and distributions of the hyperfine field and the isomer shift. Next, various examples of the 119Sn spectra measured on single-crystals and polycrystalline samples of Cr and Cr-V are reviewed.
We start with formulation of the generalized Fermat's principle for light propagation in a curved spacetime. We apply Pontryagin's minimum principle of the optimal control theory and obtain an effective Hamiltonian for null geodesics in a curved spacetime. We explicitly demonstrate that dynamical equations for this Hamiltonian correctly reproduce null geodesic equations. Other forms of the action for light rays in a curved spacetime are also discussed.
An online software tool for the easy preparation of ephemerides of the solar surface features is presented. It was developed as a helper tool for the preparation of observations of the Sun with the Atacama Large Millimeter/submillimeter Array (ALMA), but it can be used at other observatories as well. The tool features an easy to use point-and-click graphical user interface with the possibility to enter or adjust input parameters, while the result is a table of predicted positions in the celestial equatorial coordinate system, suitable for import into the ALMA Observing Tool software. The tool has been successfully used for the preparation and execution of solar observations with ALMA.
This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characterizations of traveling water waves; analytical and numerical studies of periodic waves with critical layers that may overhang; existence, nonexistence, and qualitative theory of solitary waves and fronts; traveling waves with localized vorticity or density stratification; and waves in three dimensions.
We revisit the moment method to obtain a slightly strengthened version of the usual semicircular law. Our version assumes only that the upper triangular entries of Hermitian random matrices are independent, have mean zero and variances close to $1/n$ in a certain sense, and satisfy a Lindeberg-type condition. As an application, we derive another semicircular law for the case when the sum of a row converges in distribution to the standard normal distribution, including the case where all matrix entries may have infinite variance. The appendix, making up the majority of the paper, provides for those new to the subject, a rigorous exposition of most details involved, including also a proof of a semicircular law that uses the Stieltjes transform method.
A famous theorem of Kirkman says that there exists a Steiner triple system of order $n$ if and only if $n\equiv 1,3\mod{6}$. In 1973, Erd\H{o}s conjectured that one can find so-called `sparse' Steiner triple systems. Roughly speaking, the aim is to have at most $j-3$ triples on every set of $j$ points, which would be best possible. (Triple systems with this sparseness property are also referred to as having high girth.) We prove this conjecture asymptotically by analysing a natural generalization of the triangle removal process. Our result also solves a problem posed by Lefmann, Phelps and R\"odl as well as Ellis and Linial in a strong form, and answers a question of Krivelevich, Kwan, Loh, and Sudakov. Moreover, we pose a conjecture which would generalize the Erd\H{o}s conjecture to Steiner systems with arbitrary parameters and provide some evidence for this.
We study numerically the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying the main attention to their differences from the standard (Klauder--Glauber--Sudarshan) coherent states, especially in the case of high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is, roughly, twice weaker than for the vacuum squeezed states. The Robertson--Schr\"odinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of (non)Gaussianity of CPS are considered.
It is shown that the mechanism of order out of disorder is at work in the antisymmetric pyrochlore antiferromagnet. Quantum as well as thermal fluctuations break the continuous degeneracy of the classical ground state manifold and reduce its symmetry to $\mathbb{Z}_3 \times \mathbb{Z}_2$. The role of anisotropic symmetric exchange is also investigated and we conclude that this discrete like ordering is robust with respect to these second order like interactions. The antisymmetric pyrochlore antiferromagnet is therefore expected to order at low temperatures, whatever the symmetry type of its interactions, in both the classical and semi classical limits.
The relativistic nucleus-nucleus collisions can produce hypernuclei and low-temperature hyper-matter as a result of hyperon capture by nuclear residues and free nucleons. We use the transport, coalescence and statistical models to describe the whole process, and point at the important advantages of such reactions: A broad variety of formed hypernuclei in masses and isospin allows for investigating properties of exotic hypernuclei, as well as the hypermatter both at high and low temperatures. The abundant production of multi-strange nuclei that can give an access to multi-hyperon systems and strange nuclear matter. The de-excitation of hot hyper-cluster will allow for the hyperon correlation studies. There is a saturation of the hypernuclei production at high energies, therefore, the optimal way to pursue this experimental study is to use the accelerator facilities of intermediate energies.
I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables.
Real-space topological magnetic structures such as skyrmions and merons are promising candidates for information storage and transport. However, the microscopic mechanisms that control their formation and evolution are still not clear. Here, using in-situ Lorentz transmission electron microscopy, we demonstrate that skyrmion crystals (SkXs) can nucleate, grow, and evolve from the conical phase in the same ways that real nanocrystals form from vapors or solutions. More intriguingly, individual skyrmions can also "reproduce" by division in a mitosis-like process that allows them to annihilate SkX lattice imperfections, which is not available to crystals made of mass-conserving particles. Combined string method and micromagnetic calculations show that competition between repulsive and attractive interactions between skyrmions governs particle-like SkX growth, but non-conservative SkX growth appears to be defect-mediated. Our results provide insights towards manipulating magnetic topological states by applying established crystal growth theory, adapted to account for the new process of skyrmion mitosis.
Based on preliminary results from the Causal Fermion Systems framework regarding the matter-antimatter asymmetry in the universe, I propose a novel story line for the universe that would, if correct, resolve a number of problems in cosmology. First and foremost, the here-presented arguments suggest to identify cold dark matter as third generation (anti-)neutrino mass-eigenstates $\nu_3$. Furthermore, the proposal suggests a new look at the problem of initial conditions. Last but not least, the proposal also provides a new angle on the cosmological constant.
The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here we review some methods that may be used for performing that task. We start by presenting a simple procedure for generating random state vectors, for which the main tool is the random sampling of unbiased discrete probability distributions (DPD). Afterwards the creation of random density matrices is addressed. In this context we first present the standard method, which consists in using the spectral decomposition of a quantum state for getting RQS from random DPDs and random unitary matrices. In the sequence the Bloch vector parametrization method is described. This approach, despite being useful in several instances, is not in general convenient for RQS generation. In the last part of the article we regard the overparametrized method (OPM) and the related Ginibre and Bures techniques. The OPM can be used to create random positive semidefinite matrices with unit trace from randomly produced general complex matrices in a simple way that is friendly for numerical implementations. We consider a physically relevant issue related to the possible domains that may be used for the real and imaginary parts of the elements of such general complex matrices. Subsequently a too fast concentration of measure in the quantum state space that appears in this parametrization is noticed.