Higher-order Transitions Research Articles

A research of higher-order network emotional phase transitions

This paper explores the law of emotion transmission on the social Internet. By applying higher-order network theory, ER random networks are reconstructed and higher-order network structures with multiple interaction points are generated. The I-state of the SI model is extended to set up the propagation rules of emotions based on higher-order networks. Concepts such as sentiment recession rate are introduced to make sentiment propagate through different simplexes, so as to obtain the propagation rules of higher-order networks. Qualitative analysis of emotional changes during the propagation process verifies the phase transition phenomenon of emotions in the network. By comparing simulated results with actual data, we demonstrate the accuracy of our higher-order network-based emotion propagation model in reflecting real-world trends and outcomes. The study also explores the effects of factors such as the initial proportion of extreme emotions on emotion propagation. This study provides valuable insights into understanding the operation of complex systems and offers important implications for government predictions of opinion development.

Exploring transitions in finite-size Potts model: comparative analysis using Wang–Landau sampling and parallel tempering

Abstract This research provides a examination of transitions within the various-state Potts model in two-dimensional finite-size lattices. Leveraging the Wang–Landau sampling and parallel tempering, we systematically obtain the density of states, facilitating a comprehensive comparative analysis of the results. The determination of the third-order transitions location are achieved through a meticulous examination of the density of states using microcanonical inflection-point analysis. The remarkable alignment between canonical and microcanonical results for higher-order transition locations affirms the universality of these transitions. Our results further illustrate the universality of the robust and microcanonical inflection-point analysis of Wang–Landau sampling.

Extended Kataura plot of single-walled carbon nanotubes and on-demand fabrication of mixed-dimensional heterostructures

We present a comprehensive optical spectroscopic study on air-suspended single-walled carbon nanotubes (SWNTs) with diameters ranging from 1.7 nm to 3.4 nm and at higher-order optical transitions, a previously inaccessible regime. We establish an atlas of resonant radial breathing modes (RBMs) for more than 100 new SWNTs in this unknown regime, thus significantly extending the RBM dataset in Kataura plot and enhancing our knowledge of SWNTs. Additionally, we develop an innovative transfer technique for manipulating individual SWNTs of known chiralities (determined by optical spectroscopies) by integrating a polarization imaging technique with the conventional van der Waals (vdW) dry transfer. The unprecedented spatial and structural control of this technique enables a deterministic fabrication and integration of a variety of novel mixed-dimensional vdW heterostructures that were considered unachievable before. Our work significantly extends RBM dataset of SWNT Kataura plot and represents a huge advancement towards controlled fabrication and integration of mixed-dimensional vdW heterostructures encompassing one-dimensional vdW materials.

(Invited) Mie Resonant Silicon Nanosphere Nanoantenna for Fluorescence Enhancement

A nanoantenna is a device that manipulates light propagation and enhances light-matter interaction at the nanoscale. Integration of an emitter into a nanoantenna capable of increasing local density of photonic states at the emission wavelength results in the enhancement of the spontaneous emission rate (Purcell effect) and modifies the emission spectrum. A nanoantenna can also control the directionality and radiation pattern of an emitter. Traditionally, plasmonic nanoantennas made from gold or silver nanostructures supporting localized surface plasmon resonances had been the main stream of the nanoantenna research. Recently, high refractive index nanoparticles having low-order Mie resonances have been attracting attention as a new type of dielectric nanoantennas. Advantages of a dielectric nanoantenna compared to a plasmonic one are the smaller loss and the possession of magnetic type Mie resonances arising from light-induced displacement current. By properly controlling the overlap of the magnetic and electric multipole resonances, radiation patters of an emitter placed nearby can be tailored with high degree of freedom. Furthermore, magnetic-type Mie resonances can couple with higher-order optical transitions of an emitter such as a magnetic-dipole transition, and thus can enhance and control radiation from otherwise weak forbidden transitions.Recently, we have succeeded in producing perfectly spherical nanoparticles of crystalline silicon (Si) in 100-300 nm in diameters. These Si nanospheres exhibit the electric and magnetic multipole resonances at the optical frequency [1]. In this presentation, we first show scattering and absorption properties of the Mie resonant Si nanospheres. Especially, we show that solutions of size-purified Si nanospheres exhibit vivid structural color and the solutions can be used as structural color inks. We then show that the solutions can preserve helicity of incoming circularly-polarized light and can enhance local chiral fields around nanospheres [2, 3]. This property can be used to improve the sensitivity of enantiomer-selective chiral molecular sensing. We then show some examples of enhanced light-matter interaction by Si nanoparticles. These include enhancement of magnetic dipole transitions of an emitter by magnetic-type Mie resonances of Si nanospheres (magnetic Purcell effect) [4, 5], enhancement of excitation and emission processes of in-plane dipoles of monolayer transition metal dichalcogenides (TMDC) [6], and enhancement of a spin forbidden singlet-to-triplet absorption transition of a molecule by Si nanodisks [7, 8].

Investigation of the optical properties of Pb1-xCdxTe films using spectroscopic ellipsometry

Using spectroscopic ellipsometry, we studied the optical properties of four Pb1-xCdxTe (0 ≤ x ≤ 0.20) films. The Pb1-xCdxTe films, deposited on silicon substrates using an electron-beam deposition technique, show a rock-salt structure, with their lattice constants decreasing as a function of Cd concentration. Ellipsometry measurements, which covered a wide spectral range between 0.1 eV to 4.1 eV, determined the index of refraction and the extinction coefficient of the films. As the Cd concentration increases from 0 % to 20 % in the Pb1-xCdxTe films, the index of refraction decreases by ∼10 %, across the entire energy range. Similarly, there seems to be a decrease in the extinction coefficient with the increase of Cd concentration. An oscillator model, depicting the optical functions of each Pb1-xCdxTe film, allowed us to obtain the band gap of each film which blue-shifts as the Cd concentration is increased. Besides the fundamental band gap, we recovered the higher-order electronic transitions that occur in the Brillouin zone of the Pb1-xCdxTe lattice.

Delocalization and higher-order topology in a nonlinear elastic lattice

Topological elastic waves provide novel and robust ways for manipulating mechanical energy transfer and information transmission, with potential applications in vibration control, analog computation, and more. Recently discovered higher-order topological insulators (HOTIs) with multidimensional and hierarchical edge states can further expand the capabilities of topological elastic waves. However, the effects of nonlinearity on elastic HOTIs remain elusive. In this paper, we propose a nonlinear elastic higher-order topological Kagome lattice. After briefly reviewing its linear properties, we explore the effects of nonlinearity on the higher-order band topology and topological states. To do this, we have developed a method to calculate approximate nonlinear modes in order to identify the bulk polarization and probe the higher-order topological phase in the nonlinear lattice. We find that nonlinearity induces unusual delocalization of topological corner states, band crossing, and higher-order topological phase transition. The delocalization reveals that intracell hardening nonlinearity leads to direct delocalization of topological corner states while intracell softening nonlinearity first enhances and then reduces localization. The nonlinear higher-order topological phase is amplitude dependent, and we demonstrate a transition from a trivial to a non-trivial phase, enabling amplitude induced topological corner and edge states. Additionally, this phase transition corresponds to the closing and reopening of the bandgap, accompanied by an unusual band crossing. By examining the band topology before and after the band crossing, we find that the bulk polarization becomes quantized with respect to amplitude and can predict higher-order topological phases in nonlinear lattices. The obtained results are expected to be beneficial for the development of tunable and robust elastic wave devices.

Calorimetric, optical and dielectric measurements on two Schiff's based liquid crystalline materials exhibiting multiple phase transitions.

We report high-resolution calorimetric, optical and dielectric studies on two Schiff's based liquid crystalline materials, 4O.5 and 5O.5, which exhibit multiple phase transitions. The study goes beyond the commonly studied isotropic-to-nematic (I-N) and nematic-to-smectic A (N-SmA) phase transitions and explores higher-order smectic phase transitions. The critical exponent, α values, for different phase transitions has been explored. For the I-N, N-SmA, SmA-SmC, SmC-SmF, SmF-CrG and SmB-CrG transitions, α values close to 0.5 and amplitude ratios A-/A+ ~ 1.6 and D-/D+ ~ 1 indicate a first-order nature. Notably, for the SmA-SmB transition, although α (≈ 0.64) is larger than the tricritical value of 0.5, A-/A+ ~ 1.2 and D-/D+ ~ 1, and the study reports an order parameter critical exponent (β) of 0.26 ± 0.002, which supports a tricritical nature for this transition. Importantly, the ratios of A-/A+ and D-/D+ are found to have similar values across all three-measurement methods, indicating consistency and agreement among these methods.

Coherent structures of elastoinertial instabilities in Taylor–Couette flows

We combine flow visualisation techniques and particle image velocimetry to experimentally investigate the higher-order transition to elastoinertial turbulence of Boger fluids ( $El = 0.11\unicode{x2013}0.34$ ) in Taylor–Couette flows. The observed route to turbulence is associated with the appearance of chaotic inflow jets, termed flame patterns, for increasing inertia, and stable structures of solitons, known as diwhirls, for decreasing inertia. We also report for the first time spatially and temporally resolved flow fields in the meridional plane for the three characteristic viscoelastic flow regimes (diwhirls, flame patterns and elastoinertial turbulence). We observe in all cases coherent structures of dynamically independent solitary vortex pairs. The stability of these coherent structures is jet-dominated and can be mainly ascribed to the high extension of the polymer chains in the inflow boundaries in the $r$ – $z$ plane. Solitary pairs are self-sustained when created through random events and do not split; instead, they merge when moving sufficiently close and annihilate when hoop stresses are not sufficient to sustain them. The highly localised and random events result in highly fluctuating, chaotic flow states. We estimate the decay exponent of spatial power spectral density, illustrating a universal scaling of $-2.5$ for elastoinertial turbulence. Based on our observations and in an effort to unify and combine precedent theories with our results, we suggest a mechanism for the origins of elastoinertial instabilities, accounting for both the effect of elasticity on the vortex formation and the effect of increasing/decreasing inertia on the flow dynamics.

An ab initio spectroscopic model of the molecular oxygen atmospheric and infrared bands.

We present a unified variational treatment of the magnetic dipole matrix elements, Einstein coefficients and line strength for general open-shell diatomic molecules in the general purpose diatomic code Duo. Building on previous work in which similar expressions for the electric quadrupole transitions were developed, we also present a complete ab initio spectroscopic model for the infrared, electric dipole-forbidden, spectrum of the 16O2 molecule. The model covers seven states, namely the X 3Σ-g, a 1Δg, b 1Σ+g, I 1Πg, II 1Πg, I 3Πg and II 3Πg states, for which 7 potential energy, 6 electronic angular momentum, 7 spin-orbit, and 14 quadrupole moment curves are calculated using ic-MRCI theory and an aug-cc-pV5Z basis set. These curves are diabatised to remove avoided crossings between the excited Π states, and the resultant properties are used to produce a line list for higher-order transitions of astrophysical interest.

Optimal parameterizing manifolds for anticipating tipping points and higher-order critical transitions.

A general, variational approach to derive low-order reduced models from possibly non-autonomous systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes more classical notions of invariant or slow manifolds when the breakdown of "slaving" occurs, i.e., when the unresolved variables cannot be expressed as an exact functional of the resolved ones anymore. The OPM provides, within a given class of parameterizations of the unresolved variables, the manifold that averages out optimally these variables as conditioned on the resolved ones. The class of parameterizations retained here is that of continuous deformations of parameterizations rigorously valid near the onset of instability. These deformations are produced through the integration of auxiliary backward-forward systems built from the model's equations and lead to analytic formulas for parameterizations. In this modus operandi, the backward integration time is the key parameter to select per scale/variable to parameterize in order to derive the relevant parameterizations which are doomed to be no longer exact away from instability onset due to the breakdown of slaving typically encountered, e.g., for chaotic regimes. The selection criterion is then made through data-informed minimization of a least-square parameterization defect. It is thus shown through optimization of the backward integration time per scale/variable to parameterize, that skilled OPM reduced systems can be derived for predicting with accuracy higher-order critical transitions or catastrophic tipping phenomena, while training our parameterization formulas for regimes prior to these transitions takes place.

4D potential energy surface of NCCN-H2 collision: Rotational dynamics by p-H2 and o-H2 at interstellar temperatures.

The rotational excitation rates of NCCN species are studied for its collision with hydrogen (H2) in temperatures ranging from 1 to 100K. Such collisions can occur in the interstellar medium with H2 in either para (p-) or ortho (o-) state, of which the p-H2 state can be approximated via its collision with He (using a scaling factor) or with a reduced rigid rotor-H2 surface (by averaging over various orientations of H2). In the current work, a four-dimensional (4D) abinitio potential energy surface (PES) is considered to study the collision dynamics of H2 in both p- and o-states and the results are compared with previous approximations. The 4D surface is constructed using the explicitly correlated coupled-cluster method CCSD(T)-F12b with the augmented triple zeta basis AVTZ and then fitted into an artificial neural networks (NN) model to augment the surface and account for missing data points. The radial coefficients are obtained from this NN fitted 4D PES via a least square fit over two spherical harmonics functions. The cross sections (σ) are computed using the close-coupling (CC) method (until 230 cm-1) for both p- and o-H2 collisions, and the rates are obtained by Boltzmann distribution over the translational energy of H2 until 100K. The o-H2 rates are found to be higher by 25%-30% and 10%-20% compared to the p-H2 rates for Δj = 2 and higher order transitions, respectively. The coupled-state/centrifugal sudden approximated rates are also computed and found to have deviations as large as 40% when compared to CC rates, thus making quantitative descriptions unreliable.

Atomic Lifetimes of Astrophysical Interest in Ions of Fe

Multiply charged ions of iron dominate the EUV spectrum of the solar corona. For the interpretation of such spectra, data on both the atomic structure and the transition rate are essential, most of which are provided by theory and computation. The wavelengths of observed spectra are used to test the predicted energy level structure, while the line intensities depend on level lifetimes and branch fractions. A number of electric dipole and higher-order transition rates have been measured over the years in the laboratory, mostly by beam-foil spectroscopy, at heavy-ion storage rings, and at various ion traps. In this paper, the state of the knowledge base on level lifetimes in all ions of Fe is assessed, and the problems of further progress are outlined.

Unified characterization for higher-order topological phase transitions

Unified characterization for higher-order topological phase transitions

Corner states in photonic higher-order Dirac semimetals

The introduction of higher-order topological insulators featuring topological corner states has been an extremely active topic for the generation of confined modes. Recent studies show that corner states are not an exclusive feature of topological insulators but can also exist as bound states in the continuum (BIC). This suggests that corner states may exist in different topological phases that exhibit a higher-order character, beyond the conventional bulk-edge correspondence. In this paper, we show that corner states can appear in a higher-order Dirac semimetal phase of a two-dimensional photonic lattice. Such a lattice displays a dispersion relationship with a fourfold degeneracy, which serves to induce a higher-order topological phase transition, leaving a Dirac point between two edge bands. Just as Dirac modes exist in regular lattice defects, the nonconventional bulk-edge-corner correspondence leads to corner states in the Dirac semimetal phase. Notably, the induced corner state exhibits an algebraic decay characteristic of long-range interactions, predicted by the massless Dirac equation. The analysis of the field profile and quality factors indicates that the state is not a BIC, but rather a corner-Dirac state. We show that if the photonic lattice does not present a higher-order phase transition the existence of the corner-Dirac state does not arise. The results obtained in this paper indicate that corner states can exist throughout the entire topological phase transition process, even in the semimetal phase, and pave the way to generate light-matter interactions with such a photonic bath.

3D simulations of ultrasonic waves in plates using the scaled boundary finite element method and high-order transition elements

It can be difficult to efficiently model ultrasonic waves in 3D structures, especially when the computational model needs to account for complex geometries. This contribution presents a solution based on the Scaled Boundary Finite Element Method (SBFEM). It is a numerical tool suitable for elastodynamic problems. A space-tree discretisation, namely quad-trees, is used. This technique allows the decomposition of an image into quadrilaterals or quads, which are extruded to generate the 3D plate geometry. In particular, small quads resolve regions with discontinuities, allowing them to represent fine details in the structure. Moreover, this meshing technique allows for exploiting cell similarities, making the calculation procedure more efficient. The space-tree discretisations are generated from a high-resolution image containing all the information about damaged regions or boundary conditions. The resulting SBFEM polyhedral domains employ transition elements to ensure correct coupling between cells of different sizes. The analytical solution of a cylindrical scatterer serves as a reference to validate the proposed approach. Other examples also demonstrate the validity of the methodology and its flexibility.

Exploring quantum phase transitions by the cross derivative of the ground state energy

In this work, the cross derivative of the Gibbs free energy, initially proposed for phase transitions in classical spin models (Chen et al 2020 Phys. Rev. B 101 165123), is extended for quantum systems. We take the spin-1 XXZ chain with anisotropies as an example to demonstrate its effectiveness and convenience for the Gaussian-type quantum phase transitions therein. These higher-order transitions are very challenging to determine by conventional methods. From the cross derivative with respect to the two anisotropic strengths, a single valley structure is observed clearly in each system size. The finite-size extrapolation of the valley depth shows a perfect logarithmic divergence, signaling the onset of a phase transition. Meanwhile, the critical point and the critical exponent for the correlation length are obtained by a power-law fitting of the valley location in each size. The results are well consistent with the best estimations in the literature. Its application to other quantum systems with continuous phase transitions is also discussed briefly.

Selective high-order resonance in asymmetric plasmonic nanostructures stimulated by vortex beams.

Orbital angular momentum (OAM) of light has the potential to induce high-order transitions of electrons in atoms by compensating for the OAM required. However, due to the dark spot situating at the focal center of the OAM beam, high-order transitions are typically weak. In this study, we demonstrate efficient and selective high-order resonances in symmetric and asymmetric plasmonic nanoparticles that are comparable in size to the waist radius of the OAM beam. In a symmetric nanoparticle configured with a complete nanoring lying on the focal center, there is a pure high-order resonance obeying the law of conservation of angular momentum during the interaction between OAM light and the nanosystem. In an asymmetric nanoparticle configured with an complete ring off the beam center or a splitting nanoring, there are multiple resonances whose resonance orders are influenced by the ring's geometry, position, orientation, and photon OAM. Thus, high-order resonances in the symmetric and asymmetric plasmonic nanostructures are selectively stimulated using vortex beams. Our results may help to understand and control OAM-involved light-material interactions of asymmetric nanosystems.

Combining experiments on luminescent centres in hexagonal boron nitride with the polaron model and ab initio methods towards the identification of their microscopic origin.

The two-dimensional material hexagonal boron nitride (hBN) hosts luminescent centres with emission energies of ∼2 eV which exhibit pronounced phonon sidebands. We investigate the microscopic origin of these luminescent centres by combining ab initio calculations with non-perturbative open quantum system theory to study the emission and absorption properties of 26 defect transitions. Comparing the calculated line shapes with experiments we narrow down the microscopic origin to three carbon-based defects: C2CB, C2CN, and VNCB. The theoretical method developed enables us to calculate so-called photoluminescence excitation (PLE) maps, which show excellent agreement with our experiments. The latter resolves higher-order phonon transitions, thereby confirming both the vibronic structure of the optical transition and the phonon-assisted excitation mechanism with a phonon energy ∼170 meV. We believe that the presented experiments and polaron-based method accurately describe luminescent centres in hBN and will help to identify their microscopic origin.

Ethanol-Induced Condensation and Decondensation in DNA-Linked Nanoparticles: A Nucleosome-like Model for the Condensed State

Inspired by the conventional use of ethanol to induce DNA precipitation, ethanol condensation has been applied as a routine method to dynamically tune "bond" lengths (i.e., the surface-to-surface distances between adjacent nanoparticles that are linked by DNA) and thermal stabilities of colloidal crystals involving DNA-linked nanoparticles. However, the underlying mechanism of how the DNA bond that links gold nanoparticles changes in this class of colloidal crystals in response to ethanol remains unclear. Here, we conducted a series of all-atom molecular dynamic (MD) simulations to explore the free energy landscape for DNA condensation and decondensation. Our simulations confirm that DNA condensation is energetically much more favorable under 80% ethanol conditions than in pure water, as a result of ethanol's role in enhancing electrostatic interactions between oppositely charged species. Moreover, the condensed DNA adopts B-form in pure water and A-form in 80% ethanol, which indicates that the higher-order transition does not affect DNA's conformational preferences. We further propose a nucleosome-like supercoiled model for the DNA condensed state, and we show that the DNA end-to-end distance derived from this model matches the experimentally measured DNA bond length of about 3 nm in the fully condensed state for DNA where the measured length is 16 nm in water. Overall, this study provides an atomistic understanding of the mechanism underlying ethanol-induced condensation and water-induced decondensation, while our proposed nucleosome-like model allows the design of new strategies for interpreting experimental studies of DNA condensation.

Fracton critical point at a higher-order topological phase transition

The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. Here we demonstrate that the existence of a two-dimensional topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. We present a theory of this quantum critical point (QCP) driven by the fluctuations and percolation of the domain walls between a HOTI and a trivial Mott insulator region. Due to the spinon zero modes that decorate the rough corners of the domain walls, the fluctuations of the phase boundaries trigger a spinon-dipole hopping term with fracton dynamics. Hence we find that the QCP is characterized by a critical dipole liquid theory with subsystem U(1) symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement: $Lln(L)$. Using the density matrix renormalization group method, we analyze the dipole stiffness together with the structure factor at the QCP, which provides strong evidence of a critical dipole liquid with a Bose surface, UV-IR mixing, and a dispersion relation $\ensuremath{\omega}={k}_{x}{k}_{y}.$