Second-order Couplings Research Articles

Topological solitons in charge-[formula omitted] flux quantized state of Kagome superconductors

A recent Little-Parks experiment on the new Kagome superconductor CsV3Sb5 demonstrated resistance oscillation with a period of ϕ0/3=hc/6e. This observation of charge-6e flux quantization is effectively explained by a three-component Ginzburg–Landau (GL) model that incorporates second-order Josephson-type couplings. Here, we numerically solve the GL model to present stable topological solitons. We reveal the structures of these solitons, characterized by closed domain walls with attached vortices. We identify two types of domain walls. These solitons possess multiple flux quanta and exhibit a ringlike geometry. Furthermore, we present the characteristic magnetic field distributions of these solitons, enabling their identification in, e.g., scanning Hall probe and scanning SQUID experiments.

Effects of high-order interactions on synchronization of a fractional-order neural system

In this study, effects of high-order interactions on synchronization of the fractional-order Hindmarsh–Rose neuron models have been examined deeply. Three different network situations in which first-order coupling, high-order couplings and first-plus second-order couplings included in the neuron models, have been considered, respectively. In order to find the optimal values of the first- and high-order coupling parameters by minimizing the cost function resulted from pairwise and triple interactions, the particle swarm optimization algorithm is employed. It has been deduced from the numerical simulation results that the first-plus second-order couplings induce the synchronization with both reduced first-order coupling strength and total cost compared to the first-order coupled case solely. When the only first-order coupled case is compared with the only second-order coupled case, it is determined that the neural network with only second-order couplings involved could achieve synchronization with lower coupling strength and, as a natural result, lower cost. On the other hand, solely second- and first-plus second-order coupled networks give very similar results each other. Therefore, high-order interactions have a positive effect on the synchronization. Additionally, increasing the network size decreases the values of the both first- and high-order coupling strengths to reach synchronization. However, in this case, total cost should be kept in the mind. Decreasing the fractional order parameter causes slower synchronization due to the decreased frequency of the neural response. On the other hand, more synchronous network is possible with increasing the fractional order parameter. Thus, the neural network with higher fractional order as well as high-order coupled is a good candidate in terms of the neural synchronization.

Multibody Constraints in the Geometrically Nonlinear Intrinsic Formulation

Abstract The intrinsic formulation for geometrically nonlinear beam dynamics provides a compact and versatile description of slender beam-like structures. With nonlinearities limited to second-order couplings in the formulation, it has been an attractive choice in formulating nonlinear reduced-order models for dynamic analysis and control design in aeroelasticity problems involving large displacements and rotations. Owing to its rotation-free formalism, the intrinsic formulation has not been formulated to accommodate multibody constraints, limiting its use against multibody structures with kinematic constraints. This work aims to address such weakness as we present developments in introducing multibody constraints into the full and reduced-order intrinsic equations while still preserving the beneficial traits of the method. We describe the resolution of displacement-level constraints using index-1 approach and adaptation of constraint stabilization strategies to the intrinsic formulation using state projection. The numerical behavior of the full- and reduced-order implementations are assessed using test cases with large static and dynamic deformations with time-domain simulations to demonstrate validity of the approach.

A Discrete-Variable Local Diabatic Representation of Conical Intersection Dynamics.

Conical intersections (CIs) are ubiquitous in polyatomic molecules and are responsible for a wide range of phenomena in photochemistry and photophysics. Modeling the conical intersection dynamics with adiabatic electronic states is hindered by the divergence of the first- and second-order derivative couplings at CIs due to electronic degeneracy. We introduce and implement a novel diabatic representation for exact correlated electron-nuclear wave packet dynamics through conical intersections. It directly employs the adiabatic electronic states but avoids the singular first- and second-order derivative couplings and is robust to different gauge choices of the electronic wave function phases. The reference nuclear geometries defining the adiabatic electronic states are determined by a discrete-variable representation of the nuclear coordinates. The nonadiabatic effects are accounted for by the electronic overlap matrix instead of derivative couplings as in the adiabatic representation. Illustrated by a two-mode conical intersection model, this representation captures all nonadiabatic effects, including electronic transitions, electronic coherence, and geometric phases. Thus, this representation provides a singularity-free framework for modeling ab initio conical intersection wave packet dynamics.

Potential for Definitive Discovery of a 70 GeV Dark Matter WIMP with Only Second-Order Gauge Couplings

Potential for Definitive Discovery of a 70 GeV Dark Matter WIMP with Only Second-Order Gauge Couplings

Formula omitted] model reduction for diffusively coupled second-order networks by convex-optimization

This paper provides an H2 optimal scheme for reducing diffusively coupled second-order systems evolving over undirected networks. The aim is to find a reduced-order model that not only approximates the input–output mapping of the original system but also preserves crucial structures, such as the second-order form, asymptotically stability, and diffusive couplings. To this end, an H2 optimal approach based on a convex relaxation is used to reduce the dimension, yielding a lower order asymptotically stable approximation of the original second-order network system. Then, a novel graph reconstruction approach is employed to convert the obtained model to a reduced system that is interpretable as an undirected diffusively coupled network. Finally, the effectiveness of the proposed method is illustrated via a large-scale networked mass–spring–damper system.

Simulating two-dimensional dynamics within a large-size atomic spin

Encoding a dimension in the internal degree of freedom of an atom provides an interesting tool for quantum simulation, facilitating the realization of artificial gauge fields. We propose an extension of the synthetic dimension toolbox, making it possible to encode two dimensions within a large atomic spin. The protocol combines first- and second-order spin couplings, such that the spin projection $m$ and the remainder $r=m$ (mod 3) of its Euclidian division by 3 act as orthogonal coordinates on a synthetic cylinder. It is suited for an implementation with lanthanide atoms, which feature a large electronic spin and narrow optical transitions for applying the required spin couplings. This method is useful for simulating geometries with periodic boundary conditions, and engineering various types of topological systems evolving in high dimensions.

Hebbian Network of Kuramoto Oscillators with Second-Order Couplings for Binary Pattern Retrieve: II. Nonorthogonal Standard Patterns and Structural Stability

Hebbian Network of Kuramoto Oscillators with Second-Order Couplings for Binary Pattern Retrieve: II. Nonorthogonal Standard Patterns and Structural Stability

Dynamics near a conical intersection-A diabolical compromise for the approximations of ab initio multiple spawning.

Full multiple spawning (FMS) offers an exciting framework for the development of strategies to simulate the excited-state dynamics of molecular systems. FMS proposes to depict the dynamics of nuclear wavepackets by using a growing set of traveling multidimensional Gaussian functions called trajectory basis functions (TBFs). Perhaps the most recognized method emanating from FMS is the so-called ab initio multiple spawning (AIMS). In AIMS, the couplings between TBFs-in principle exact in FMS-are approximated to allow for the on-the-fly evaluation of required electronic-structure quantities. In addition, AIMS proposes to neglect the so-called second-order nonadiabatic couplings and the diagonal Born-Oppenheimer corrections. While AIMS has been applied successfully to simulate the nonadiabatic dynamics of numerous complex molecules, the direct influence of these missing or approximated terms on the nonadiabatic dynamics when approaching and crossing a conical intersection remains unknown to date. It is also unclear how AIMS could incorporate geometric-phase effects in the vicinity of a conical intersection. In this work, we assess the performance of AIMS in describing the nonadiabatic dynamics through a conical intersection for three two-dimensional, two-state systems that mimic the excited-state dynamics of bis(methylene)adamantyl, butatriene cation, and pyrazine. The population traces and nuclear density dynamics are compared with numerically exact quantum dynamics and trajectory surface hopping results. We find that AIMS offers a qualitatively correct description of the dynamics through a conical intersection for the three model systems. However, any attempt at improving the AIMS results by accounting for the originally neglected second-order nonadiabatic contributions appears to be stymied by the hermiticity requirement of the AIMS Hamiltonian and the independent first-generation approximation.

A Dark Matter WIMP That Can Be Detected and Definitively Identified with Currently Planned Experiments

A recently proposed dark matter WIMP (weakly interacting massive particle) has only second-order couplings to gauge bosons and itself. As a result, it has small annihilation, scattering, and creation cross-sections, and is consequently consistent with all current experiments and the observed abundance of dark matter. These cross-sections are, however, still sufficiently large to enable detection in experiments that are planned for the near future, and definitive identification in experiments proposed on a longer time scale. The (multi-channel) cross-section for annihilation is consistent with thermal production and freeze-out in the early universe, and with current evidence for dark matter annihilation in analyses of the observations of gamma rays by Fermi-LAT and antiprotons by AMS-02, as well as the constraints from Planck and Fermi-LAT. The cross-section for direct detection via collision with xenon nuclei is estimated to be slightly below 10−47 cm2, which should be attainable by LZ and Xenon nT and well within the reach of Darwin. The cross-section for collider detection via vector boson fusion is estimated to be ∼1 fb, and may be ultimately attainable by the high-luminosity LHC; definitive collider identification will probably require the more powerful facilities now being proposed.

Conformational Analysis of [60]PCBM via Second-Order Proton NMR Spin-Spin Coupling Effects.

The 1H NMR spectrum of phenyl C61 butyric acid methyl ester ([60]PCBM) was recorded at high resolution (600 MHz). All of the 1H resonances expected of the Cs-symmetric molecule were observed. The spin-spin couplings in the 1H NMR spectrum were not as expected at first order. Instead, the effects of AA'BB'-type second-order couplings were clearly observed for the protons attached to both ester carbons C3 and C4, which were analyzed in terms of seven coupling constants. This indicates that there is no free rotation of the σ bonds of the alkyl chain in the ester group, although rotation becomes free at a larger distance from the fullerene bridge carbon (C61). The 1H NMR results further indicated that there is a 1:6:1 population ratio of the three staggered conformers (gauche:anti:gauche') about the ester group C3-C4 bond. These results may aid in the understanding of the morphological interactions between [60]PCBM and its surroundings in condensed-phase organic electronic devices such as organic and perovskite photovoltaics.

Stability in a Hebbian Network of Kuramoto Oscillators with Second-Order Couplings for Binary Pattern Retrieve

We study the stability of an oscillatory associative memory network consisting of $N$ coupled Kuramoto oscillators with applications in binary pattern retrieve. In this model, the coupling function...

A generalized theoretical framework for the description of spin decoupling in solid-state MAS NMR: Offset effect on decoupling performance.

We present a generalized theoretical framework that allows the approximate but rapid analysis of residual couplings of arbitrary decoupling sequences in solid-state NMR under magic-angle spinning conditions. It is a generalization of the tri-modal Floquet analysis of TPPM decoupling [Scholz et al., J. Chem. Phys. 130, 114510 (2009)] where three characteristic frequencies are used to describe the pulse sequence. Such an approach can be used to describe arbitrary periodic decoupling sequences that differ only in the magnitude of the Fourier coefficients of the interaction-frame transformation. It allows a ∼100 times faster calculation of second-order residual couplings as a function of pulse sequence parameters than full spin-dynamics simulations. By comparing the theoretical calculations with full numerical simulations, we show the potential of the new approach to examine the performance of decoupling sequences. We exemplify the usefulness of this framework by analyzing the performance of commonly used high-power decoupling sequences and low-power decoupling sequences such as amplitude-modulated XiX (AM-XiX) and its super-cycled variant SC-AM-XiX. In addition, the effect of chemical-shift offset is examined for both high- and low-power decoupling sequences. The results show that the cross-terms between the dipolar couplings are the main contributions to the line broadening when offset is present. We also show that the SC-AM-XIX shows a better offset compensation.

Discrete gap solitons in binary positive-negative index nonlinear waveguide arrays with strong second-order couplings.

We report on the existence and properties of discrete gap solitons in zigzag arrays of alternating waveguides with positive and negative refractive indices. The zigzag quasi-one-dimensional configuration of the waveguide array introduces strong next-to-nearest neighbor interaction in addition to nearest neighbor coupling. Effective diffraction can be controlled both in size and in sign by the value of the next-to-nearest neighbor coupling coefficient and can even be canceled completely. In the regime where instabilities occur, we found different families of discrete solitons bifurcating from the gap edges of the linear spectrum. We show that both staggered and unstaggered discrete solitons can become highly localized states near the zero diffraction points even for low powers. Stability analysis has shown that the soliton solutions are stable over a wide range of parameters and can exist in focusing, defocusing, and even in an alternating focusing-defocusing array.

Why Do Mixed Quantum-Classical Methods Describe Short-Time Dynamics through Conical Intersections So Well? Analysis of Geometric Phase Effects.

Adequate simulation of nonadiabatic dynamics through conical intersection requires accounting for a nontrivial geometric phase (GP) emerging in electronic and nuclear wave functions in the adiabatic representation. Popular mixed quantum-classical (MQC) methods, surface hopping and Ehrenfest, do not carry a nuclear wave function to be able to incorporate the GP into nuclear dynamics. Surprisingly, the MQC methods reproduce ultrafast interstate crossing dynamics generated with the exact quantum propagation so well as if they contained information about the GP. Using two-dimensional linear vibronic coupling models we unravel how the MQC methods can effectively mimic the most significant dynamical GP effects: (1) compensation for repulsive diagonal second-order nonadiabatic couplings and (2) transfer enhancement for a fully cylindrically symmetric component of a nuclear distribution.

Photon-number correlations in waveguide lattices with second order coupling

We introduce second-order coupling into the transport and coupling of photons in waveguide lattices. Second-order coupling, as well as high-order couplings, can be significant in long, compact or some special lattices, and is important for large-scale quantum circuits. Photon-number correlations with various amounts of second-order couplings are calculated. Some distinctive and interesting effects arise, and these are helpful for our comprehension of quantum walks in waveguide lattices.

Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation

We propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the Born-Oppenheimer and fully nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies in situations where other criteria, such as the energy gap criterion or the extent of population transfer, fail. We further propose to estimate this quantum fidelity efficiently with a generalization of the dephasing representation to multiple surfaces. Two variants of the multiple-surface dephasing representation (MSDR) are introduced, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics (LMFD). The LMFD can be interpreted as the Ehrenfest dynamics of an ensemble of nuclear trajectories, and has been used previously in the nonadiabatic semiclassical initial value representation. In addition to propagating an ensemble of classical trajectories, the MSDR requires evaluating nonadiabatic couplings and solving the Schrödinger (or more generally, the quantum Liouville-von Neumann) equation for a single discrete degree of freedom. The MSDR can be also used in the diabatic basis to measure the importance of the diabatic couplings. The method is tested on three model problems introduced by Tully and on a two-surface model of dissociation of NaI.

Describing spatiotemporal couplings in ultrashort pulses using coupling coefficients

Three coupling coefficients are defined to describe spatiotemporal coupling in ultrashort pulses. With these coupling coefficients, the first-order spatiotemporal couplings of Gaussian pulse and beam are described analytically. Also, the first-order and the second-order spatiotemporal couplings caused by angular dispersion elements are studied using these coupling coefficients. It can be shown that these coupling coefficients are dimensionless and normalized, and readily indicate the severity of spatiotemporal coupling.

Second-order nonadiabatic couplings from time-dependent density functional theory: Evaluation in the immediate vicinity of Jahn-Teller/Renner-Teller intersections

For a rigorous quantum simulation of nonadiabatic dynamics of electrons and nuclei, knowledge of not only the first-order but also the second-order nonadiabatic couplings (NACs) is required. Here, we propose a method to efficiently calculate the second-order NAC from time-dependent density functional theory (TDDFT), on the basis of the Casida ansatz adapted for the computation of first-order NAC, which has been justified in our previous work and can be shown to be valid for calculating second-order NAC between ground state and singly excited states within the Tamm-Dancoff approximation. Test calculations of the second-order NAC in the immediate vicinity of Jahn-Teller and Renner-Teller intersections show that calculation results from TDDFT, combined with modified linear response theory, agree well with the prediction from the Jahn-Teller/Renner-Teller models. Contrary to the diverging behavior of the first-order NAC near all types of intersection points, the Cartesian components of the second-order NAC are shown to be negligibly small near Renner-Teller glancing intersections, while they are significantly large near the Jahn-Teller conical intersections. Nevertheless, the components of the second-order NAC can cancel each other to a large extent in Jahn-Teller systems, indicating the background of neglecting the second-order NAC in practical dynamics simulations. On the other hand, it is shown that such a cancellation becomes less effective in an elliptic Jahn-Teller system and thus the role of second-order NAC needs to be evaluated in the rigorous framework. Our study shows that TDDFT is promising to provide accurate data of NAC for full quantum mechanical simulation of nonadiabatic processes.

Describing second-order spatiotemporal couplings in ultrashort pulses using correlation coefficient

A second-order correlation coefficient is defined to estimate the severity of second-order spatiotemporal couplings. The correlation coefficient is scale invariant, normalized, dimensionless, etc. Using this correlation coefficient, the spatial chirp of ultrashort pulsed Gaussian beams is studied. It can be shown that the spatial chirp of ultrashort pulsed Gaussian beams depends on the pulse width, spectrum shape, and local frequency shift characteristics, and different types of ultrashort pulsed Gaussian beams exhibit different second-order spatiotemporal couplings characteristics.