Real Space Research Articles

Development of dual-beamline photoelectron momentum microscopy for valence orbital analysis.

The soft X-ray photoelectron momentum microscopy (PMM) experimental station at the UVSOR Synchrotron Facility has been recently upgraded by additionally guiding vacuum ultraviolet (VUV) light in a normal-incidence configuration. PMM offers a very powerful tool for comprehensive electronic structure analyses in real and momentum spaces. In this work, a VUV beam with variable polarization in the normal-incidence geometry was obtained at the same sample position as the soft X-ray beam from BL6U by branching the VUV beamline BL7U. The valence electronic structure of the Au(111) surface was measured using horizontal and vertical linearly polarized (s-polarized) light excitations from BL7U in addition to horizontal linearly polarized (p-polarized) light excitations from BL6U. Such highly symmetric photoemission geometry with normal incidence offers direct access to atomic orbital information via photon polarization-dependent transition-matrix-element analysis.

Orientation Relationship of the Intergrowth Al13Fe3 and Al13Fe4 Intermetallics Determined by Single-Crystal X-ray Diffraction

In the Al-Fe binary system, the Al13Fe3 phase as well as the Al13Fe4 phase has similar icosahedral building blocks like those appearing in quasicrystals. Therefore, it is of vital importance to clarify the formation process of these two phases. Coexistence of the Al13Fe3 and Al13Fe4 phases was discovered from the educts obtained with a nominal atomic ratio of Al/Fe of 9:2 by high-pressure sintering for the first time. Firstly, single crystal X-ray diffraction (SXRD) combined with a scanning electron microscope (SEM) with energy dispersive X-ray spectroscopy (EDX) measurement capabilities were adopted to determine the detailed crystal structures of both phases, which were sharply refined with regard to Al13Fe3 and Al13Fe4. Secondly, the orientation relationship between Al13Fe3 and Al13Fe4 was directly deduced from the SXRD datasets and the coexistence structure model was consequently constructed. Finally, seven pairs of parallel atomic planes and their unique orientation relations were determined from the reconstructed reciprocal space precession images. In addition, the real space structure model of the intergrowth crystal along with one kind of interfacial atomic structure were constructed from the determined orientation relations between two phases.

Departure from the statistical equilibrium of large scales in forced three-dimensional homogeneous isotropic turbulence

We study the statistically steady states of the forced dissipative three-dimensional homogeneous isotropic turbulence at scales larger than the forcing scale in real separation space. The probability density functions (p.d.f.s) of longitudinal velocity difference at large separations are close to, but deviate from, Gaussian, measured by their non-zero odd parts. The analytical expressions of the third-order longitudinal structure functions derived from the Kármán–Howarth–Monin equation prove that the odd-part p.d.f.s of velocity differences at large separations are small but non-zero. Specifically, when the forcing effect in the displacement space decays exponentially as the displacement tends to infinity, the odd-order longitudinal structure functions have a power-law decay with an exponent of $-$ 2, implying a significant coupling between large and small scales. Under the assumption that forcing controls the large-scale dynamics, we propose a conjugate regime to Kolmogorov's inertial range, independent of the forcing scale, to capture the odd parts of p.d.f.s. Thus, dynamics of large scales departs from the absolute equilibrium, and we can partially recover small-scale information without explicitly resolving small-scale dynamics. The departure from the statistical equilibrium is quantified and found to be viscosity-independent. Even though this departure is small, it is significant and should be considered when studying the large scales of the forced three-dimensional homogeneous isotropic turbulence.

Internally Disclosed Sets of a Real Space

There is no single set in a real space, for which an exact mathematical definition would not exist by the mathematical symmetry laws. We discuss a theory in which a real number axis is defined at the new level, namely, at the level of real space allowing one to formulate and prove the theorem on the basis of its internal disclosure. This new theory of a set makes it possible to introduce a notion of the full compactness of sets of a real space, confirming their availability in the defined symmetry of elements of a definitely symmetrical line.  

Tuning the A‐site Element in LaCo0.8Fe0.2O3 Perovskite‐based Catalyst for High Temperature N2O Decomposition in Nitric Acid Plant

AbstractThe effect of La‐deficiency and Ce/Sr‐substitution in the benchmark LaCo0.8Fe0.2O3 has been investigated for the decomposition of N2O between 500 and 900 °C. Real inlet gas composition and space velocity reveal that La‐deficiency and Ce/Sr‐substitution can improve the thermal stability of catalyst, while La1‐xSrxCo0.8Fe0.2O3 with x≥0.1 was highlighted as a promising formula due to the strongest resistance to deactivation and suppressed undesired NOx decomposition at high space velocity. This phenomenon is mainly ascribed to the incorporation of Sr2+ into the perovskite lattice during the reaction consequently stabilizing the Co3+ species and creating the oxygen vacancies in La1‐xSrxCoO3‐δ. On the contrary, the loss of activity on Ce‐substituted LaCo0.8Fe0.2O3 has been preferentially related to the cobalt exsolution to extra framework of perovskite making the catalytic cycle with Co3+ unfavorable. All these bulk and surface changes are accompanied with opposite evolution of apparent activation energy and pre‐exponential factor which can be discussed based on a redox mechanism.

Using Kondo entanglement to induce spin correlations between disconnected quantum dots

We investigate the entanglement between the spins of two quantum dots that are not simultaneously connected to the same system. Quantum entanglement among localized spins is a crucial property for the advancement of quantum computing and quantum information. Generating and controlling an entangled state between quantum dots have garnered significant attention in recent years for this reason. In this study, we demonstrate that information about the spin orientation of a quantum dot can be preserved, utilizing Kondo entanglement, within a reservoir of electrons. Subsequently, this information can be transmitted to another dot after the initial dot has been decoupled from the reservoirs. We employ a double quantum dot system in a parallel geometry to establish the initial state, where each dot interacts with reservoirs of different symmetries. A specific phase in the couplings is chosen to induce antiferromagnetic spin correlation between the dots. The time evolution of the initial state is analyzed using the time-dependent density matrix renormalization group method. Our findings reveal that a partially entangled state between the dots can be achieved, even when they are not simultaneously connected. This entangled state arises transiently and dissipates in the stationary state. The stability of the state observed during the transient phase is demonstrated. To comprehend the details of these phenomena, we employ a canonical transformation of real space.

Эволюция роли библиотеки в контексте сохранения национальных языков

<p>The article is devoted to the analysis of the role of the library institution in the preservation, dissemination and development of national languages. The author attempted a retrospective, comparative, axiological analysis of changes in the image of the library in accordance with the cultural characteristics of different eras. The main attention was aimed at identifying the linguistic and cultural features of library texts. It has been revealed and substantiated that in the ancient East the library served as a sacralized archive of texts mainly in the ancient Sumerian and Assyrian languages. Linguistic texts of ancient Eastern libraries connected sacred meanings and everyday life. In antiquity, lively dialogue and the dialectical development of thought came to the fore, so the library became a place for debate. The libraries of Alexandria, Pergamon, and private collections contained scrolls in different languages, but many of them were professionally translated into Greek. In medieval culture, the library became a library of one book, the Bible, which was copied in Greek and Latin. In the late Middle Ages, books in vernacular languages appeared in libraries, which contributed to the development of the latter. In modern times, the library becomes a way of education and mass dissemination of national literary languages. In the information age, the library acquires the global features of a «universal library»; the boundaries of the virtual and real space of the library are erased. A modern library acquires many functions: it provides information to users, is a place for holding various educational events, and educational games. In modern Russia, the library institution plays a huge role in preserving the languages of the small peoples of our country. Thus, libraries in all eras play an important role in the formation, preservation, dissemination and development of national languages.</p>

On Thurston's Geometrical Space Form Problem: On Quasi Space Forms

A proposal is made for what may well be the most elementary Riemannian spaces which are homogeneous but not isotropic. In other words: a proposal is made for what may well be the nicest symmetric spaces beyond the real space forms, that is, beyond the Riemannian spaces which are homogeneous and isotropic. The above qualification of ‘’nicest symmetric spaces” finds a justification in that, together with the real space forms, these spaces are most natural with respect to the importance in human vision of our ability to readily recognise conformal things and in that these spaces are most natural with respect to what inWeyl’s view is symmetry in Riemannian geometry. Following his suggestion to remove the real space forms’ isotropy condition, the quasi space forms thus introduced do offer a metrical, local geometrical solution to the geometrical space form problem as posed by Thurston in his 1979 Princeton Lecture Notes on ‘’The Geometry and Topology of 3- manifolds”. Roughly speaking, quasi space forms are the Riemannian manifolds of dimension greater than or equal to 3, which are not real space forms but which admit two orthogonally complementary distributions such that at all points all the 2-planes that in the tangent spaces there are situated in a same position relative to these distributions do have the same sectional curvatures.

Switching the spin cycloid in BiFeO3 with an electric field

Bismuth ferrite (BiFeO3) is a multiferroic material that exhibits both ferroelectricity and canted antiferromagnetism at room temperature, making it a unique candidate in the development of electric-field controllable magnetic devices. The magnetic moments in BiFeO3 are arranged into a spin cycloid, resulting in unique magnetic properties which are tied to the ferroelectric order. Previous understanding of this coupling has relied on average, mesoscale measurements. Using nitrogen vacancy-based diamond magnetometry, we observe the magnetic spin cycloid structure of BiFeO3 in real space. This structure is magnetoelectrically coupled through symmetry to the ferroelectric polarization and this relationship is maintained through electric field switching. Through a combination of in-plane and out-of-plane electrical switching, coupled with ab initio studies, we have discovered that the epitaxy from the substrate imposes a magnetoelastic anisotropy on the spin cycloid, which establishes preferred cycloid propagation directions. The energy landscape of the cycloid is shaped by both the ferroelectric degree of freedom and strain-induced anisotropy, restricting the spin spiral propagation vector to changes to specific switching events.

Roudneff’s Conjecture in Dimension 4

J.-P. Roudneff conjectured in 1991 that every arrangement of n ≥ 2 d + 1 ≥ 5 pseudohyperplanes in the real projective space P d has at most ∑ i = 0 d − 2 ( n − 1 i ) complete cells (i.e., cells bounded by each hyperplane). The conjecture is true for d = 2, 3 and for arrangements arising from Lawrence oriented matroids. Our main contribution is to show the validity of Roudneff’s conjecture for d = 4. Moreover, based on computational data we show that for d ≤ 4 and n ≤ 2 d + 1 the maximum number of complete cells is only obtained (up to isomorphism) by cyclic arrangements.

Fast computation of the observer motion effects induced on monopole frequency spectra for tabulated functions

Context. Various methods have been studied to compute the boosting effects produced by the observer peculiar motion, which modifies and transfers the isotropic monopole frequency spectrum of the cosmic background radiation to higher multipoles. Explicit analytical solutions for the spherical harmonic expansion coefficients were already presented and applied to different types of background spectrum, strongly alleviating the computational effort needed for accurate theoretical predictions. The frequency spectra at higher multipoles are inherently led by higher-order derivatives of the monopole spectrum. Provided that it can be well described by analytic or semi-analytic functions, the computation of its transfer is not affected by numerical instabilities when evaluated at the required level of numerical accuracy. Instead, monopole frequency spectra described by tabulated functions are computed with a relatively poor frequency resolution in comparison with the Doppler shift, which necessitates interpolation of the tabular representation. The spectra are also affected by uncertainties related to intrinsic inaccuracies in the modelling or in the related observational data as well as to limited accuracy in their numerical computation. These uncertainties propagate and increase with the derivative order, possibly preventing the trustworthy computation of the transfer to higher multipoles and of the observed monopole. Aims. We study methods to filter the original function or its derivatives and the multipole spectra, to mitigate numerical instabilities, and to derive reliable predictions of the harmonic coefficients for different cosmic background models. Methods. From the analytical solutions, and assuming that the monopole spectrum can be expanded in Taylor’s series, we derive explicit expressions for the harmonic coefficients up to the multipole ℓmax = 6 in terms of monopole spectrum derivatives. We then consider different low-pass filters: prefiltering in Fourier space of the tabular representation; filtering in both real and Fourier space of the numerical derivatives; interpolation approaches; and a dedicated method based on amplification and deamplification of the boosted signal. We study the quality of these methods when applied to suitable analytical approximations of the tabulated functions, possibly polluted with simulated noise. These methods are then applied to the tabulations. Results. We consider two very different types of monopole spectra superimposed to the cosmic microwave background: the (smooth) extragalactic source microwave background signal from radio-loud active galactic nuclei and the (feature-rich) redshifted 21 cm line, and present our results in terms of spherical harmonic coefficients. The direct prediction of these coefficients can be noisy at ℓ > 1 or, depending on the uncertainty level, even at ℓ ≤ 1. Without assuming a functional form for the extragalactic background spectrum, the Gaussian prefiltering coupled to the sequential real-space filtering of derivatives allows us to derive accurate predictions up to ℓ ∼ 6, while a log–log polynomial representation, which is appropriate over several decades, gives accurate solutions at any ℓ. Instead, it is difficult to characterise the 21 cm line model variety, and so it is relevant to work without assumptions about the underlying function. Typically, the prefiltering provides accurate predictions up to ℓ ≃ 3 or 4, while the further sequential filtering of the derivatives or the boosting amplification and deamplification method improves the results up to ℓ = 4, while also allowing reasonable estimations of the spectrum at higher ℓ. Conclusions. The proposed methods can significantly extend the range of realistic cosmic background models manageable with a fast computation, beyond the cases characterised a priori by analytical or semi-analytical functions. These methods require only an affordable increase in computation time compared to the direct calculation via simple interpolation.

Fractional operators as traces of operator-valued curves

We relate non integer powers Ls, s>0 of a given (unbounded) positive self-adjoint operator L in a real separable Hilbert space H with a certain differential operator of order 2⌈s⌉, acting on even curves R→H. This extends the results by Caffarelli–Silvestre and Stinga–Torrea regarding the characterization of fractional powers of differential operators via an extension problem.

Asymptotic expansions about infinity for solutions of nonlinear differential equations with coherently decaying forcing functions

This paper studies, in fine details, the long-time asymptotic behavior of decaying solutions of a general class of dissipative systems of nonlinear differential equations in complex Euclidean spaces. The forcing functions decay, as time tends to infinity, in a coherent way expressed by combinations of the exponential, power, logarithmic and iterated logarithmic functions. The decay may contain sinusoidal oscillations not only in time but also in the logarithm and iterated logarithm of time. It is proved that the decaying solutions admit corresponding asymptotic expansions, which can be constructed concretely. In the case of the real Euclidean spaces, the real-valued decaying solutions are proved to admit real-valued asymptotic expansions. Our results unite and extend the theory investigated in many previous works.

Resonant Raman scattering of few layers CrBr3

We investigate the vibrational and magnetic properties of thin layers of chromium tribromide (CrBr3) with a thickness ranging from three to twenty layers (3–20 L) revealed by the Raman scattering (RS) technique. Systematic dependence of the RS process efficiency on the energy of the laser excitation is explored for four different excitation energies: 1.96 eV, 2.21 eV, 2.41 eV, and 3.06 eV. Our characterization demonstrates that for 12 L CrBr3, 3.06 eV excitation could be considered resonant with interband electronic transitions due to the enhanced intensity of the Raman-active scattering resonances and the qualitative change in the Raman spectra. Polarization-resolved RS measurements for 12 L CrBr3 and first-principles calculations allow us to identify five observable phonon modes characterized by distinct symmetries, classified as the Ag\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_\ ext {g}$$\\end{document} and Eg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_\ ext {g}$$\\end{document} modes. The evolution of phonon modes with temperature for a 16 L CrBr3 encapsulated in hexagonal boron nitride flakes demonstrates alterations of phonon energies and/or linewidths of resonances indicative of a transition between the paramagnetic and ferromagnetic state at Curie temperature (TC≈50\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_\ ext {C} \\approx 50$$\\end{document} K). The exploration of the effects of thickness on the phonon energies demonstrated small variations pronounces exclusively for the thinnest layers in the vicinity of 3–5 L. We propose that this observation can be due to the strong localization in the real space of interband electronic excitations, limiting the effects of confinement for resonantly excited Raman modes to atomically thin layers.

Bulk-Boundary Correspondence in Point-Gap Topological Phases.

A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and point-gap topology, respectively. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can be different from that in periodic boundary conditions. On the basis of real space topological invariants and the K theory, we give a complete classification of the open boundary point-gap topology with symmetry and show that the nontrivial open boundary topology results in robust and exotic surface states.

Excitons, optical spectra, and electronic properties of semiconducting Hf-based MXenes.

Semiconducting MXenes are an intriguing two-dimensional (2D) material class with promising electronic and optoelectronic properties. Here, we focused on recently prepared Hf-based MXenes, namely, Hf3C2O2 and Hf2CO2. Using the first-principles calculation and excited state corrections, we proved their dynamical stability, reconciled their semiconducting behavior, and obtained fundamental gaps by using the many-body GW method (indirect 1.1 and 2.2eV; direct 1.4 and 3.5eV). Using the Bethe-Salpeter equation, we subsequently provided optical gaps (0.9 and 2.7eV, respectively), exciton binding energies, absorption spectra, and other properties of excitons in both Hf-based MXenes. The indirect character of both 2D materials further allowed for a significant decrease of excitation energies by considering indirect excitons with exciton momentum along the Γ-M path in the Brillouin zone. The first bright excitons are strongly delocalized in real space while contributed by only a limited number of electron-hole pairs around the M point in the k-space from the valence and conduction band. A diverse range of excitonic states in Hf3C2O2 MXene lead to a 4% and 13% absorptance for the first and second peaks in the infrared region of absorption spectra, respectively. In contrast, a prominent 28% absorptance peak in the visible region appears in Hf2CO2 MXene. Results from radiative lifetime calculations indicate the promising potential of these materials in optoelectric devices requiring sustained and efficient exciton behavior.

Approximation of an Inertial Iteration Method for a Set-Valued Quasi Variational Inequality

Approximation of an Inertial Iteration Method for a Set-Valued Quasi Variational Inequality

Exact asymptotics of long-range quantum correlations in a non-equilibrium steady state

Out-of-equilibrium states of many-body systems tend to evade a description by standard statistical mechanics, and their uniqueness is epitomized by the possibility of certain long-range correlations that cannot occur in equilibrium. In quantum many-body systems, coherent correlations of this sort may lead to the emergence of remarkable entanglement structures. In this work, we analytically study the asymptotic scaling of quantum correlation measures—the mutual information (MI) and the fermionic negativity—within the zero-temperature steady state of voltage-biased free fermions on a one-dimensional lattice containing a non-interacting impurity. Previously, we have shown that two subsystems on opposite sides of the impurity exhibit volume-law entanglement, which is independent of the absolute distances of the subsystems from the impurity. Here, we go beyond that result and derive the exact form of the subleading logarithmic corrections to the extensive terms of correlation measures, in excellent agreement with numerical calculations. In particular, the logarithmic term of the MI asymptotics can be encapsulated in a concise formula, depending only on simple four-point ratios of subsystem length scales and on the impurity scattering probabilities at the Fermi energies. This echoes the case of equilibrium states, where such logarithmic terms may convey universal information about the physical system. To compute these exact results, we devise a hybrid method that relies on Toeplitz determinant asymptotics for correlation matrices in both real space and momentum space, successfully circumventing the inhomogeneity of the system. This method could potentially find wider use for analytical calculations of entanglement measures in similar scenarios.

Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guarantees (Abstract Reprint)

Safety is a critical component of autonomous systems and remains a challenge for learning-based policies to be utilized in the real world. In particular, policies learned using reinforcement learning often fail to generalize to novel environments due to unsafe behavior. In this paper, we propose Sim-to-Lab-to-Real to bridge the reality gap with a probabilistically guaranteed safety-aware policy distribution. To improve safety, we apply a dual policy setup where a performance policy is trained using the cumulative task reward and a backup (safety) policy is trained by solving the Safety Bellman Equation based on Hamilton-Jacobi (HJ) reachability analysis. In Sim-to-Lab transfer, we apply a supervisory control scheme to shield unsafe actions during exploration; in Lab-to-Real transfer, we leverage the Probably Approximately Correct (PAC)-Bayes framework to provide lower bounds on the expected performance and safety of policies in unseen environments. Additionally, inheriting from the HJ reachability analysis, the bound accounts for the expectation over the worst-case safety in each environment. We empirically study the proposed framework for ego-vision navigation in two types of indoor environments with varying degrees of photorealism. We also demonstrate strong generalization performance through hardware experiments in real indoor spaces with a quadrupedal robot. See https://sites.google.com/princeton.edu/sim-to-lab-to-real for supplementary material.

Modified inertial viscosity extrapolation method for solving quasi-monotone variational inequality and fixed point problems in real Hilbert spaces

In this paper, we introduce and study a viscous-type extrapolation algorithm for finding a solution of the variational inequality problem and a fixed point constraint of quasi-nonexpansive mappings under the scope of real Hilbert spaces when the underlying cost operator is quasi-monotone. The method involves inertial viscosity approximation and a constructed self-adjustable step size condition that depends solely on the information of the previous step. We establish a strong convergence result of the proposed method under certain mild conditions on the algorithm parameters. Finally, to demonstrate the gain of our method, some numerical examples are presented in comparison with some related methods in literature.