Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of ...topological order exist for topological insulators and quantum Hall devices. In quantum Hall systems, the quantized conductivity and the associated robust propagating edge modes—guaranteed by the existence of nontrivial topological invariants—have been observed through transport and spectroscopy measurements. Here, we show that optical-lattice-based experiments can be tailored to directly visualize the propagation of topological edge modes. Our method is rooted in the unique capability for initially shaping the atomic gas and imaging its time evolution after suddenly removing the shaping potentials. Our scheme, applicable to an assortment of atomic topological phases, provides a method for imaging the dynamics of topological edge modes, directly revealing their angular velocity and spin structure.
Energy densities and related Laplacian distributions for CuCu bondings in various structural environments.
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•Quantum theory of atoms in molecules (QTAIM) is used to study bonding in ...materials.•Complete Laplacian distributions are related to local energies densities.•A simple method is proposed to characterize bondings from local properties.•H/ρ = f(|V|/G) provides insights on the charge density polarizability in bonds.
The quantum theory atoms in molecules (QTAIM) method has been used in this paper to characterize various bonding interactions in molecules and solid compounds. By using DFT-PAW calculations, complete electron density Laplacian distributions have been obtained and related to energies densities calculated at the bond critical points. From the analysis of these results a simple and rapid method, based solely on local energies densities calculations, is proposed to diagnose the bonding state, the polarizability and the deformation of the charge distribution.
The aim of this paper is to present the topological properties and wave structures of the Gilson–Pickering equation. By the traveling wave transformation, the corresponding traveling wave system of ...the original equation is obtained, and then a conserved quantity, namely the Hamiltonian is constructed via it. After that, the existences of the soliton and periodic solutions are established by the bifurcation method. To verify our conclusion explicitly, the corresponding exact traveling wave solutions are constructed. In particular, via the generalized trial equation method which is proposed in this paper, a special kind of soliton solution, namely the Gaussian soliton solution is given. To the best of our knowledge, this is the first time that a Gaussian soliton solution has been constructed to an equation with no logarithmic nonlinearity.
Cognitive deficits are core symptoms of schizophrenia (SZ) and are associated with impaired resilience to stress. Different cognitive functions appeared to be interrelated, and the mechanism may ...involve neural alterations. The disrupted topological organization indicated abnormalities in the segregation and integration of brain networks that support various cognitive processes in SZ patients. Therefore, this study aimed to assess the direct and indirect effects of resilience on cognitive functions. We hypothesized that topological properties would moderate these associations.
Forty-nine SZ patients and fifty-two healthy controls (HCs) were recruited in this study. The Connor-Davidson Resilience Scale and the MATRICS Consensus Cognitive Battery were used to examine resilience and cognitive functions, respectively, and a graph theory approach was used to assess white matter topological organization.
Compared to HCs, SZ patients showed lower levels of resilience and cognitive functions in multiple domains as well as abnormal global properties and nodal metrics. In addition, shorter characteristic path length was associated with a stronger indirect effect of resilience on working memory through processing speed in SZ patients.
Characteristic path length might moderate the mediating effects of processing speed in the relationship between resilience and working memory in schizophrenia patients.
•Schizophrenia patients showed deficits in resilience and cognitive domains.•Graph theoretical approach was used to assess white matter network metrics.•Lp moderated the mediating effects of processing speed in relationship between resilience and working memory in SZ.
With the development of science and technology, phononic crystals can be fabricated at nanoscale. The advancement yields significant applications in thermo-electric, acousto-optical and ...electron-phonon devices. At nanoscale, the surface heterogeneity of structures is a result of the differences between the arrangement and environment of the surface atoms and those of their counterparts in the body. This characteristic plays an important role in determining the mechanical properties of the structures. The effects of surface heterogeneity on band structures of the phononic crystals at nanoscale are studied in this paper. We also investigate the topological properties of phononic nanobeams through theoretical and numerical approaches. The topological edge mode, which is affected by the surface heterogeneity, is observed. Particularly, a theoretical method based on the plane wave expansion method is proposed to conveniently calculate the Zak phase, which is an important constant describing the topological properties. The numerical results show that surface heterogeneity mainly influences the response frequency for the dispersion relations and the topological behaviors in the phononic nanobeam. The study may be beneficial for the understanding of the size-dependent behaviors of phononic crystals at nanoscale and for the design of nanodevices based on the dispersion and topological properties of phononic crystals.
Many unusual wave phenomena in artificial structures are governed by their topological properties. However, the topology of diffusion remains almost unexplored. One reason is that diffusion is ...fundamentally different from wave propagation because of its purely dissipative nature. The other is that the diffusion field is mostly composed of modes that extend over wide ranges, making it difficult to be rendered within the tight‐binding theory as commonly employed in wave physics. Here, the above challenges are overcome and systematic studies are performed on the topology of heat diffusion. Based on a continuum model, the band structure and geometric phase are analytically obtained without using the tight‐binding approximation. A deterministic parameter is found to link the geometric phase with the edge state, thereby proving the bulk‐boundary correspondence for heat diffusion. The topological edge state is experimentally demonstrated as localized heat diffusion and its dependence on the boundary conditions is verified. This approach is general, rigorous, and able to reveal rich knowledge about the system with great accuracy. The findings set up a solid foundation to explore the topology in novel thermal management applications.
Topological thermal metamaterials are presented. An accurate theoretical framework is established to study the geometric phase and dynamics of the thermal lattices. The topological properties of diffusive systems and localized heat diffusion protected by the topological edge states are revealed. The work can be applied to facilitate the heat dissipation of hot spots.
•Monozygotic ASD showed an abnormal topological properties of white matter network.•Monozygotic ASD had unique hubs distribution.•Global properties were associated with repetitive behavior.•Nodal ...efficiency of hubs was correlated with core symptoms of ASD.•Twin difference of network topological properties related to autism symptoms.
Twins provide a valuable perspective for exploring the pathological mechanism of autism spectrum disorder (ASD). We aim to analyze differences in the topological properties of the white matter (WM) network between monozygotic twins with ASD (MZCo-ASD) and children with typical development (TD). We enrolled 67 subjects aged 2–9 years. Twenty-three pairs of MZCo-ASD and 21 singleton children with TD completed clinical assessments and diffusion tensor imaging (DTI). Graph theory was used to compare the topological properties of the WM network between the two groups, and analyzed their correlations with the severity of clinical symptoms. We found that the global efficiency (Eg) of MZCo-ASD is weaker than that of TD children, while the shortest path length (Lp) of MZCo-ASD is longer than that of TD children, and MZCo-ASD have three unique hubs (the bilateral dorsolateral superior frontal gyrus and right insula). Eg and Lp were both correlated with the repetitive behavior scores of the Autism Diagnostic Interview-Revised (ADI-R) in the MZCo-ASD group, and the nodal efficiency of the dorsal superior frontal gyrus (SFGdor) was correlated with the ADI-R scores of repetitive behaviors. Left SFGdor nodal efficiency was correlated with Repetitive Behavior and Communication, two core symptoms of autism. The results implicated that MZCo-ASD had atypical brain structural network attributes and node distributions. Using MZCo-ASD, we found that the WM topological properties that correlate with the severity of ASD core symptoms were Eg, Lp, and the nodal efficiency of the SFGdor.
C0-transport of flux geometry Tchuiaga, Stephane; Houenou, Franck; Madengko, Carole ...
Topology and its applications,
12/2022, Letnik:
322
Journal Article
Recenzirano
The goal of this paper is to study, in a large scale point of view, the flux geometry of a closed symplectic manifold (M,ω): namely, the topological counterpart of the flux homomorphism. Using ...metrics arising from the decomposition of closed 1-forms with respect to an arbitrary linear section S, we generalize the construction of the group of strong symplectic homeomorphisms. The flux homomorphism for symplectomorphisms is extended to a surjective group homomorphism Sω0 on the group of S-homeomorphisms. We prove that the kernel of Sω0 is path connected, coincides with the subgroup Hameo(M,ω) of all Hamiltonian homeomorphisms and investigate the discreteness of the corresponding flux group SΓω. Later on, without appealing to any lifting map, we give an alternative proof of a result from the classical flux geometry saying that any smooth symplectic isotopy in Ham(M,ω) is a Hamiltonian isotopy. Furthermore under some hypothesis, we prove that any S-topological isotopy in Hameo(M,ω) is a continuous Hamiltonian isotopy. We also proved that any S-topological isotopy with trivial flux is homotopic to a continuous Hamiltonian isotopy, relatively to fixed endpoints.
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