Momentum Space Research Articles

On the direct quantization of Maxwell field

In this paper, we apply the generalized integration constants (GCI) method (Belhadi 2023 https://arxiv.org/abs/2303.08236), in field theory to quantize Maxwell and the Klein–Gordon free fields. The study is performed in both position and momentum spaces, to obtain the equal-time Dirac brackets among the fields and their conjugate momenta. The idea is to compute the brackets near the initial instant using the Taylor polynomial expansion, and then deduce directly their expressions at any later time. In the case of the Maxwell field, the interdependence of the field components (constraints) requires the use of the Helmholtz theorem to separate the transversal and longitudinal parts. Our work finishes with the study of the O(3) nonlinear sigma model using the GCI approach.

Sublattice Structure and Topology in Spontaneously Crystallized Electronic States.

The prediction and realization of the quantum anomalous Hall effect are often intimately connected to honeycomb lattices in which the sublattice degree of freedom plays a central role in the nontrivial topology. Two-dimensional Wigner crystals, on the other hand, form triangular lattices without sublattice degrees of freedom, resulting in a topologically trivial state. Here, we discuss the possibility of spontaneously formed honeycomb-lattice crystals that exhibit the quantum anomalous Hall effect. Starting from a single-band system with nontrivial quantum geometry, we derive the mean-field energy functional of a class of crystal states and express it as a model of sublattice pseudospins in momentum space. We find that nontrivial quantum geometry leads to extra terms in the pseudospin model that break an effective "time-reversal symmetry" and favor a topologically nontrivial pseudospin texture. When the effects of these extra terms dominate over the ferromagnetic exchange coupling between pseudospins, the anomalous Hall crystal state becomes energetically favorable over the trivial Wigner crystal state.

AuriDESI: mock catalogues for the DESI Milky Way Survey

ABSTRACT The Dark Energy Spectroscopic Instrument Milky Way Survey (DESI MWS) will explore the assembly history of the Milky Way by characterizing remnants of ancient dwarf galaxy accretion events and improving constraints on the distribution of dark matter in the outer halo. We present mock catalogues that reproduce the selection criteria of MWS and the format of the final MWS data set. These catalogues can be used to test methods for quantifying the properties of stellar halo substructure and reconstructing the Milky Way’s accretion history with the MWS data, including the effects of halo-to-halo variance. The mock catalogues are based on a phase-space kernel expansion technique applied to star particles in the Auriga suite of six high-resolution lambda-cold dark matter magnetohydrodynamic zoom-in simulations. They include photometric properties (and associated errors) used in DESI target selection and the outputs of the MWS spectral analysis pipeline (radial velocity, metallicity, surface gravity, and temperature). They also include information from the underlying simulation, such as the total gravitational potential and information on the progenitors of accreted halo stars. We discuss how the subset of halo stars observable by MWS in these simulations corresponds to their true content and properties. These mock Milky Ways have rich accretion histories, resulting in a large number of substructures that span the whole stellar halo out to large distances and have substantial overlap in the space of orbital energy and angular momentum.

Observation of Momentum Space Josephson Effects in Weakly Coupled Bose-Einstein Condensates.

The momentum space Josephson effect describes the supercurrent flow between weakly coupled Bose-Einstein condensates (BECs) at two discrete momentum states. Here, we experimentally observe this exotic phenomenon using a BEC with Raman-induced spin-orbit coupling, where the tunneling between two local band minima is implemented by the momentum kick of an additional optical lattice. A sudden quench of the Raman detuning induces coherent spin-momentum oscillations of the BEC, which is analogous to the ac Josephson effect. We observe both plasma and regular Josephson oscillations in different parameter regimes. The experimental results agree well with the theoretical model and numerical simulation and showcase the important role of nonlinear interactions. We also show that the measurement of the Josephson plasma frequency gives the Bogoliubov zero quasimomentum gap, which determines the mass of the corresponding pseudo-Goldstone mode, a long-sought phenomenon in particle physics. The observation of momentum space Josephson physics offers an exciting platform for quantum simulation and sensing utilizing momentum states as a synthetic degree.

The topological space of Schur-concave copulas is homeomorphic to the Hilbert cube

Schur-concave copulas, a distinct subclass of copulas, have emerged as a crucial component in recent advancements of copula theory. In this paper, we employ techniques from infinite-dimensional topology to investigate the topological structure of the space of all Schur-concave copulas equipped with the uniform metric and its topological position in the (symmetric) copula space. Moreover, we show that there exists a homeomorphism from the copula space onto the Hilbert cube, which relates the symmetric copula space onto an end of the Hilbert cube and relates the Schur-concave copula space onto an end of the end of the Hilbert cube. As a consequence, the Schur-concave copula space has the fixed point property. Furthermore, we show that a subset of the family of all associative copulas is a Z-set in the Schur-concave copula space if and only if it is compact.

Leveraging the potential of third space faculty developers to foster individual and collective flourishing faculty professional identities in higher education

In the context of higher education, which is a complex environment of shifting landscapes, academic identity is perceived as being eroded, and new identities associated with hybrid roles abound. Flexible support mechanisms are needed to counter the destabilising effects of the recent erosion of tradition-bound structures. This study explores how an understanding of faculty professional identity might be used by faculty developers to inform individual and collective development initiatives and foster flourishing. Using a qualitative methodology, focus group discussions with faculty developers probe the potential utility of a measure of faculty professional identity. Utility is evaluated at three levels of practice: institutional, collective and individual. Findings demonstrate the potential for faculty developers, with their third space positioning, to play a pivotal role in guiding individuals and institutions as they navigate increasingly complex higher education contexts. Recommendations include recognising the strategic potential of faculty developers as institutional gatekeepers of sensitive data and enablers of collective flourishing. A data-informed, adaptive, person-centred approach to individual faculty development that delves into the being as well as the doing to facilitate individual flourishing is proposed.

A new framework for higher loop Witten diagrams

The differential representation is a novel formalism for studying boundary correlators in (d + 1)-dimensional anti-de Sitter space. In this letter, we generalize the differential representation beyond tree level using the notion of operator-valued integrals. We use the differential representation to compute three-point bubble and triangle Witten diagrams with external states of conformal dimension ∆ = d. We compare the former to a position space computation.

Near-Field Spin Chern Number Quantized by Real-Space Topology of Optical Structures.

The Chern number has been widely used to describe the topological properties of periodic structures in momentum space. Here, we introduce a real-space spin Chern number for the optical near fields of finite-sized structures. This new spin Chern number is intrinsically quantized and equal to the structure's Euler characteristic. The relationship is robust against continuous deformation of the structure's geometry and is irrelevant to the specific material constituents or external excitation. Our Letter enriches topological physics by extending the Chern number to real space, opening exciting possibilities for exploring the real-space topological properties of light.

Treatment options of periapical cysts of deciduous teeth: report of a case and systematic review of the literature.

Periapical cysts of primary teeth are pathologic entities which are seldom encountered in the clinical practice. Most frequently, these lesions arise in correspondence with primary teeth presenting previous pulp therapy, severe carious lesions, or a history of previous trauma. The aim of the present study is to systematically review the treatment modalities of periapical cysts of the deciduous, along with the reporting of a clinical case. A case of periapical cyst treated with marsupialization occurring in an 11-year-old patient is described. A literature search was devised to retrieve studies reporting the treatment of periapical cysts, and involved papers published in the Cochrane Oral Health Group specialist trials, MEDLINE via PubMed, and EMBASE up to March 2023. A total of 39 articles were retrieved. Following title and abstract analysis, 27 articles were selected for full-text analysis, with the final inclusion of 24 articles. Periapical cysts of primary teeth present an overall good prognosis irrespective of the treatment option adopted. The performance of a prompt diagnosis appears of utmost importance, as the extraction of the primary teeth involved implies the management of the residual space for the correct positioning of the corresponding permanent teeth.

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence.

We consider a nearly collisionless plasma consisting of a species of "test particles" in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field-a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space-known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C_{2}∝∫∫dxdv〈f^{2}〉-a quantity that here plays the role of (negative) entropy of the distribution function. We find that C_{2} is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C_{2} in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equationfor the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C_{2} to high s (towards the collisional dissipation range) at every k, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C_{2} is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k-space (s-space) flux of C_{2} is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the (k,s) plane, with power-law asymptotics at large k and s. Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a "critical balance" in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.

A Bionic Localization Memristive Circuit Based on Spatial Cognitive Mechanisms of Hippocampus and Entorhinal Cortex.

In this article, a bionic localization memristive circuit is proposed, which mainly consists of head direction cell module, grid cell module, place cell module and decoding module. This work modifies the two-dimensional Continuous Attractor Network (CAN) model of grid cells into two one-dimensional models in X and Y directions. The head direction cell module utilizes memristors to integrate angular velocity and represents the real orientation of an agent. The grid cell module uses memristors to sense linear velocity and orientation signals, which are both self-motion cues, and encodes the position in space by firing in a periodic mode. The place cell module receives the grid cell module's output and fires in a specific position. The decoding module decodes the angle or place information and transfers the neuron state to a 'one-hot' code. This proposed circuit completes the localizing task in space and realizes in-memory computing due to the use of memristors, which can shorten the execution time. The functions mentioned above are implemented in LTSPICE. The simulation results show that the proposed circuit can realize path integration and localization. Moreover, it is shown that the proposed circuit has good robustness and low area overhead. This work provides a possible application idea in a prospective robot platform to help the robot localize and build maps.

A two-dimensional harmonic oscillator confined in a circle in the presence of a constant electric field: an informational approach

In this work, we study an electron subjected to a harmonic oscillator potential confined in a circle of radius r0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_0$$\\end{document} and in the presence of a constant electric field. We obtain energies and eigenfunctions for three different confinement radii as a function of the electric field strength. We have used the linear variational method by constructing the trial function as a linear combination of two-dimensional confined harmonic oscillator wave functions. We calculate the radial standard deviation as a measure of the dispersion of the probability density. We also computed the Shannon entropy and Fisher information, in configuration and momentum spaces, as localization-delocalization measures for three different confinement radii and as a function of the electric field strength. We find that Shannon entropy and Fisher information are more reliable than variance in determining electron location. The behaviour of Shannon entropy and Fisher information curves is shown to depend on each specific state under study.Graphical abstract

Finding origins of CMB anomalies in the inflationary quantum fluctuations

In this paper, we present compelling evidence for the parity asymmetry (a discrete symmetry separate from isotropy) in the Cosmic Microwave Background (CMB) map, measured through two-point temperature correlations. Any asymmetry associated with discrete symmetries, such as parity, challenges our understanding of quantum physics associated with primordial physics rather than LCDM (Λ Cold-Dark-Matter) itself. We commence by conducting a comprehensive analysis of the Planck CMB, focusing on the distribution of power in low-multipoles and temperature anticorrelations at parity conjugate points in position space. We find tension with the near scale-invariant power-law power spectrum of Standard Inflation (SI), with p-values of the order 𝒪(10-4 - 10-3). Alternatively, we explore the framework of direct-sum inflation (DSI), where a quantum fluctuation arises as a direct sum of two components evolving forward and backward in time at parity conjugate points in physical space. This mechanism results in a parity-asymmetric scale-dependent power spectrum, particularly prominent at low-multipoles, without any additional free model parameters. Our findings indicate that DSI is consistent with data on parity asymmetry, the absence of power at θ > 60°, and power suppression at low-even-multipoles which are major data anomalies in the SI model. Furthermore, we discover that the parameters characterizing the hemispherical power asymmetry anomaly become statistically insignificant when the large SI quadrupole amplitude is reduced to align with the data. DSI explains this low quadrupole with a p-value of 3.5%, 39 times higher than SI. Combining statistics from parameters measuring parity and low-ℓ angular power spectrum, we find that DSI is 50-650 times more probable than SI. In summary, our investigation suggests that while CMB temperature fluctuations exhibit homogeneity and isotropy, they also display parity-asymmetric behavior consistent with predictions of DSI. This observation provides a tantalizing evidence for the quantum mechanical nature of gravity.

Guest Editorial for the TAES Special Section on Machine Learning Methods for Aerial and Space Positioning and Navigation

Guest Editorial for the TAES Special Section on Machine Learning Methods for Aerial and Space Positioning and Navigation

Enhancing model identification with SINDy via nullcline reconstruction.

Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse Identification of Nonlinear Dynamics (SINDy). This paper illustrates the importance of accurately determining the system's limit cycle position in phase space for identifying sparse and effective models. We introduce a method for identifying the limit cycle position and the system's nullclines by applying SINDy to datasets adjusted with various offsets. This approach is evaluated using three criteria: model complexity, coefficient of determination, and generalization error. We applied this method to several models: the oscillatory FitzHugh-Nagumo model, a more complex model consisting of two coupled cubic differential equations with a single stable state, and a multistable model of glycolytic oscillations. Our results confirm that incorporating detailed information about the limit cycle in phase space enhances the accuracy of model identification in oscillatory systems.

Probability of He+ Ion at Quantum Number 3 ≤ n ≤ 4 in Momentum Space

Ions resulting from the ionization of helium atoms are known as helium ions. Atom of Helium The probability distribution of the particle locations and velocities inside a helium atom is referred to as probability. Using theoretical study methods, the goal of this research is to find the probability of an electron's position in a helium atom at the quantum number 3 ≤ n ≤ 4. This type of research is non-experimental research by developing previously existing theories. This type of research is non-experimental research by transforming the radial wave function of hydrogenic atoms in position space into a radial wave function in momentum space using the Fourier transformation, then including a number of Gegenbauer functions and using the probability equation of finding an electron in a Helium ion in momentum space. The results of this research provide information regarding the position and probability of the existence of electrons in the helium atom. The probability value for the Helium ion is obtained using the equation P(p) = which is used to indicate the probability of finding an electron in a helium atom is directly proportional to the principal quantum number (n) and the value of the electron's momentum. The larger the electron momentum interval, the greater the probability.

ANALYSIS OF THE INFLUENCE OF EXTERNAL FACTORS ON THE DEFORMATION OF HIGH-RISE BUILDINGS IN THE PROCESS OF THEIR CONSTRUCTION AND OPERATION

During the construction and operation of high-rise buildings, their vertical axis changes its position in space. The greater the height of the structure, the greater the amplitude of oscillations. This causes problems of geodetic construction support and the need to monitor deformations during the operation of high-rise structures. In real conditions, part of the structures will be in the shade and their temperature will be lower than the structures that will be under the influence of solar radiation, the temperature of which will be much higher. Thus, the building will deform as a result of uneven thermal expansion, that is, it will bend. From DBN B.1.3-2:2010 "Geodesic works in construction". Also, during the geodetic provision of the construction and operation of high-rise buildings, changes in the temperature regime of building structures should be taken into account in connection with significant absolute values of changes in the geometric dimensions of the building as a result of thermal expansion, which significantly exceed the accuracy regulated by the regulatory document. The article examines and analyzes the influence of external forces on changes in the geometry of high-rise structures and focuses attention on solving the scientific problem of geodetic support for the construction and operation of modern high-rise structures under dynamic loads.

Observation of photonic chiral edge states in penrose quasicrystals

Photonic chiral edge states with one-way propagation and robust topological protection are hallmark features of photonic Chern insulators. To date, photonic chiral edge states have been observed in two-dimensional (2D) periodic and amorphous gyromagnetic photonic crystals. Recent theoretical studies reveal that photonic chiral edge states can also exist in 2D Penrose quasicrystals with long-range order but lack translational symmetry. Here, we report the first experimental observation of photonic chiral edge states in a 2D Penrose-tiled gyromagnetic photonic quasicrystal. By using microwave measurements, we observe a complete photonic band gap in the Penrose photonic quasicrystal despite the absence of bulk Bloch bands in momentum space. Moreover, we directly observe unidirectional backscattering-immune photonic chiral edge states within the photonic bandgap of the 2D Penrose quasicrystal. These results broaden our understanding of photonic chiral edge states and provide a new platform for exploring the intriguing properties of topological photonic quasicrystals.

Dynamics of potential‐induced structural changes at the Ag(111)/alkaline interface

AbstractThe dynamics of the structural changes in the electrochemical double layer at the interface between a Ag(111) electrode and 0.1 M KOH electrolyte have been probed using surface X‐ray diffraction measurements. The X‐ray measurements utilised a lock‐in amplifier technique to obtain a time resolution down to the millisecond scale. Two potential step regions were explored in an attempt to separate the dynamics of the reversible adsorption/desorption of hydroxide species (OHad) and the subsequent cation (K+) ordering in the double layer. By probing different positions in reciprocal space, sensitive to different structural changes, the time‐dependent response of the electrode surface was probed and time constants for the different associated processes were obtained.

Wafer-Scale Synthesis of Highly Oriented 2D Topological Semimetal PtTe2 via Tellurization.

Platinum ditelluride (1T-PtTe2) is a two-dimensional (2D) topological semimetal with a distinctive band structure and flexibility of van der Waals integration as a promising candidate for future electronics and spintronics. Although the synthesis of large-scale, uniform, and highly crystalline films of 2D semimetals system is a prerequisite for device application, the synthetic methods meeting these criteria are still lacking. Here, we introduce an approach to synthesize highly oriented 2D topological semimetal PtTe2 using a thermally assisted conversion called tellurization, which is a cost-efficient method compared to the other epitaxial deposition methods. We demonstrate that achieving highly crystalline 1T-PtTe2 using tellurization is not dependent on epitaxy but rather relies on two critical factors: (i) the crystallinity of the predeposited platinum (Pt) film and (ii) the surface coverage ratio of the Pt film considering lateral lattice expansion during transformation. By optimizing the surface coverage ratio of the epitaxial Pt film, we successfully obtained 2 in. wafer-scale uniformity without in-plane misalignment between antiparallelly oriented domains. The electronic band structure of 2D topological PtTe2 is clearly resolved in momentum space, and we observed an interesting 6-fold gapped Dirac cone at the Fermi surface. Furthermore, ultrahigh electrical conductivity down to ∼3.8 nm, which is consistent with that of single crystal PtTe2, was observed, proving its ultralow defect density.