Linear Coupling Research Articles

Controlling energy conservation in quantum dynamics with independently moving basis functions: Application to multi-configuration Ehrenfest.

Application of the time-dependent variational principle to a linear combination of frozen-width Gaussians describing the nuclear wavefunction provides a formalism where the total energy is conserved. The computational downside of this formalism is that trajectories of individual Gaussians are solutions of a coupled system of differential equations, limiting implementation to serial propagation algorithms. To allow for parallelization and acceleration of the computation, independent trajectories based on simplified equations of motion were suggested. Unfortunately, within practical realizations involving finite Gaussian bases, this simplification leads to breaking the energy conservation. We offer a solution for this problem by using Lagrange multipliers to ensure the energy and normconservation regardless of basis function trajectories or basis completeness. We illustrate our approach within the multi-configurational Ehrenfest method considering a linear vibronic coupling model.

Matrix Product State Formulation of the MCTDH Theory in Local Mode Representations for Anharmonic Potentials.

The matrix product state formulation of the multiconfiguration time-dependent Hartree theory, MPS-MCTDH, reported previously [Kurashige, J. Chem. Phys. 2018, 19, 194114] is extended to realistic anharmonic potentials with n-mode representations beyond the linear vibronic coupling model. For realistic vibrational potentials, the local mode representation should give a more compact representation of the potentials, i.e., lowering the dimensionality of the entanglements, than the normal coordinates, and the MPS-MCTDH formulation should work more efficiently and maintain the accuracy with a small bond dimension of the MPS ansatz. In fact, it was confirmed that the use of the local coordinates made the interaction matrices diagonal dominant and the number of terms in the n-body expansion of the potentials was significantly reduced. The method was applied to the IR spectrum of the CH2O molecule, the zero-point energies, and the vibrational energy redistribution dynamics of polyenes C2nH2n+2. The results showed that the efficiency of the MPS-MCTDH method is significantly accelerated by the use of local coordinates even if the long-range interactions are included in the potential.

Vibronic resonance along effective modes mediates selective energy transfer in excitonically coupled aggregates.

We recently proposed effective normal modes for excitonically coupled aggregates that exactly transform the energy transfer Hamiltonian into a sum of one-dimensional Hamiltonians along the effective normal modes. Identifying physically meaningful vibrational motions that maximally promote vibronic mixing suggested an interesting possibility of leveraging vibrational-electronic resonance for mediating selective energy transfer. Here, we expand on the effective mode approach, elucidating its iterative nature for successively larger aggregates, and extend the idea of mediated energy transfer to larger aggregates. We show that energy transfer between electronically uncoupled but vibronically resonant donor-acceptor sites does not depend on the intermediate site energy or the number of intermediate sites. The intermediate sites simply mediate electronic coupling such that vibronic coupling along specific promoter modes leads to direct donor-acceptor energy transfer, bypassing any intermediate uphill energy transfer steps. We show that the interplay between the electronic Hamiltonian and the effective mode transformation partitions the linear vibronic coupling along specific promoter modes to dictate the selectivity of mediated energy transfer with a vital role of interference between vibronic couplings and multi-particle basis states. Our results suggest a general design principle for enhancing energy transfer through synergistic effects of vibronic resonance and weak mediated electronic coupling, where both effects individually do not promote efficient energy transfer. The effective mode approach proposed here paves a facile route toward four-wavemixing spectroscopy simulations of larger aggregates without severely approximating resonant vibronic coupling.

Holographic models of composite Higgs in the Veneziano limit. Part II. Fermionic sector

We continue our study of strongly-coupled, approximately scale-invariant gauge theories with a large number of flavours, which provide a suitable ultraviolet completion of the composite-Higgs scenario. We identify the requisite operators to realise partial compositeness of the Standard-Model fermions. In order to compute the spectrum of composite fermionic states, we extend the bottom-up holographic models, which we previously introduced to capture the main features of the non-perturbative dynamics in the Veneziano limit, by adding fermion fields in the bulk. We identify regions in parameter space where some fermionic bound states become light, depending in particular on the number of flavours, the operator scaling dimensions, and the bulk Yukawa couplings. We also observe a dense spectrum of states, when multi-scale dynamics is induced by a large backreaction of bulk scalars on the geometry. Adapting the formalism of the holographic Wilsonian renormalisation group, we study the linear coupling between the composite and elementary fermions, as a function of energy scale. We find that, in some circumstances, the associated operators are dangerously irrelevant: the renormalisation-group flow gives rise to a large linear coupling in the infrared, even when it is irrelevant from the point of view of the ultraviolet fixed point. We finally compute the partially composite spectrum, correlate it with the analysis of the flow, and assess the potential phenomenological implications, e.g. for the top-quark partners.

Quantum transport in nonlinear Rudner-Levitov models

Quantum transport in a class of nonlinear extensions of the Rudner-Levitov model is numerically studied in this paper. We show that the quantization of the mean displacement, which embodies the quantum coherence and the topological characteristics of the model, is markedly modified by nonlinearities. Peculiar effects such as a ``trivial-nontrivial'' transition and unidirectional long-range quantum transport are observed. These phenomena can be understood on the basis of the dynamic behavior of the effective hopping terms, which are time and position dependent, containing contributions of both the linear and nonlinear couplings.

Blinking coupling enhances network synchronization

This paper studies the synchronization of a network with linear diffusive coupling, which blinks between the variables periodically. The synchronization of the blinking network in the case of sufficiently fast blinking is analyzed by showing that the stability of the synchronous solution depends only on the averaged coupling and not on the instantaneous coupling. To illustrate the effect of the blinking period on the network synchronization, the Hindmarsh-Rose model is used as the dynamics of nodes. The synchronization is investigated by considering constant single-variable coupling, averaged coupling, and blinking coupling through a linear stability analysis. It is observed that by decreasing the blinking period, the required coupling strength for synchrony is reduced. It equals that of the averaged coupling model times the number of variables. However, in the averaged coupling, all variables participate in the coupling, while in the blinking model only one variable is coupled at any time. Therefore, the blinking coupling leads to an enhanced synchronization in comparison with the single-variable coupling. Numerical simulations of the average synchronization error of the network confirm the results obtained from the linear stability analysis.

Linear magnetoelastic coupling and magnetic phase diagrams of the buckled-kagomé antiferromagnet [Formula: see text

Single crystals of Cu_3Bi(SeO_3)_2O_2Cl were investigated using high-resolution capacitance dilatometry in magnetic fields up to 15 T. Pronounced magnetoelastic coupling is found upon evolution of long-range antiferromagnetic order at T_{mathrm {N}} = 26.4(3) K. Grüneisen analysis reveals moderate effects of uniaxial pressure on T_{mathrm {N}}, of 1.8(4) K/GPa, -0.62(15) K/GPa and 0.33(10) K/GPa for p parallel a, b, and c, respectively. Below 22 K Grüneisen scaling fails which implies the presence of competing interactions. The structural phase transition at T_{mathrm {S}} = 120.7(5) K is much more sensitive to uniaxial pressure than T_{mathrm {N}}, with strong effects of up to 27(3) K/GPa (p parallel c). Magnetostriction and magnetization measurements reveal a linear magnetoelastic coupling for Bparallel c below T_{mathrm {N}}, as well as a mixed phase behavior above the tricritical point around 0.4 T. An analysis of the critical behavior in zero-field points to three-dimensional (3D) Ising-like magnetic ordering. In addition, the magnetic phase diagrams for fields along the main crystalline axes are reported.

Tunable optical response and fast (slow) light in optomechanical system with phonon pump

We theoretically investigate the tunable optical response of a weak probe field in a single phonon mechanical driven cavity optomechanical system where an oscillating membrane acts as a mechanical mode. This membrane is also coupled to the optical cavity mode through both the linear optomechanical coupling (LOC) and the quadratic optomechanical coupling (QOC) simultaneously. An external single phonon mechanical driving field present in our scheme gives an additional coherence effect as well as its relative phase and intensity can control significantly the absorption (amplification) profile of the output probe field. We have also shown that the phase dispersion and group delay of the probe field can be controlled flexibly through both types of optomechanical coupling strengths as well as the mean number of thermal phonons. Our results provide a flexible and generalised route to control the light propagation in such kinds of complex cavity optomechanical systems with coherent mechanical excitation.

Active-Set Identification with Complexity Guarantees of an Almost Cyclic 2-Coordinate Descent Method with Armijo Line Search

In this paper, it is established finite active-set identification of an almost cyclic 2-coordinate descent method for problems with one linear coupling constraint and simple bounds. First, general active-set identification results are stated for non-convex objective functions. Then, under convexity and a quadratic growth condition (satisfied by any strongly convex function), complexity results on the number of iterations required to identify the active set are given. In our analysis, a simple Armijo line search is used to compute the stepsize, thus not requiring exact minimizations or additional information.

Three-Dimensional Control Charts for Regulating Processes Described by a Two-Dimensional Normal Distribution

In the statistical management of processes in the initial phase, the stability of the technological process is determined based on the available samples. If the process is not stable, eliminating possible causes is brought into a statistically controlled position. At the same time, simple Shewhart control charts are used. In practice, some methods bring the process to a stable state (ISO standards, standards of various states). After the process has become stable, the boundaries of control charts are found for further management. Then, with the help of new samples, the process is managed. The article considers a process modeled by a two-dimensional normal distribution. New control charts have been found to check the normality and correlation of two-dimensional random variable components. The process is regulated using these charts, preserving the shape of the density of the individual components of the normal vector and linearity of these components. When constructing control charts, the Kolmogorov-Smirnov type agreement criterion and the Fisher criterion on the strength of the linear coupling of components were used. A concrete example shows the course of the introduction of these charts in production. The work results can be used in the initial phase of regulation and during the control check of the process under study. We used these control charts to assess product quality and quality control coming from the machine that produces the sleeves. It presents statistical methods for analyzing problems in factory practice and solutions for their elimination.

Effect of linewidth enhancement factor on the generation of optical vortices in a class-A degenerate cavity semiconductor laser.

The dynamical behavior of a one-dimensional ring array of lasers generated in a class-A degenerate cavity semiconductor laser is numerically investigated. The class-A behavior of the laser is obtained by considering a low-loss vertical external cavity surface emitting laser (VECSEL), in which a telescope and a mask allow us to control the geometry and the linear nearest-neighbour coupling between the lasers. The behavior of the lasers is simulated using coupled rate equations, taking the influence of the Henry factor into account. It is shown that the ring array of lasers exhibits multistability. Moreover, by comparison with a class-B semiconductor laser, it is proved that the class-A nature of the laser makes it more robust to the increase of the Henry factor when it comes to generating topological charge carrying arrays of lasers, thus opening new perspectives of application for such lasers.

Surface hopping dynamics in periodic solid-state materials with a linear vibronic coupling model.

We report a surface hopping approach in which the implemented linear vibronic coupling Hamiltonian is constructed and the electronic wavefunction is propagated in the reciprocal space. The parameters of the linear vibronic coupling model, including onsite energies, phonon frequencies, and electron-phonon couplings, are calculated with density-functional theory and density-functional perturbation theory and interpolated in fine sampling points of the Brillouin zone with maximally localized Wannier functions. Using this approach, we studied the relaxation dynamics of the photo-excited hot carrier in a one-dimensional periodic carbon chain. The results show that the completeness of the number of Hilbert space k points and the number of phonon q points plays an important role in the hot carrier relaxation processes. By calculating the relaxation times of hot carriers under different reciprocal space sampling and extrapolating with the stretched-compressed exponential function, the relaxation times of hot electrons and holes in the quasi-continuous energy band are obtained. By considering the feedback effect in the hopping processes and analyzing the time-dependent phonon energy in different normal modes, we found that the long-wave longitudinal optical phonons play a major role in the relaxation dynamics of hot electrons and holes. We, therefore, provided herein an efficient and accurate approach for modeling the photophysical processes in periodic solid-state material systems.

Altered linear coupling between stimulus-evoked blood flow and oxygen metabolism in the aging human brain.

Neural-vascular coupling (NVC) is the process by which oxygen and nutrients are delivered to metabolically active neurons by blood vessels. Murine models of NVC disruption have revealed its critical role in healthy neural function. We hypothesized that, in humans, aging exerts detrimental effects upon the integrity of the neural-glial-vascular system that underlies NVC. To test this hypothesis, calibrated functional magnetic resonance imaging (cfMRI) was used to characterize age-related changes in cerebral blood flow (CBF) and oxygen metabolism during visual cortex stimulation. Thirty-three younger and 27 older participants underwent cfMRI scanning during both an attention-controlled visual stimulation task and a hypercapnia paradigm used to calibrate the blood-oxygen-level-dependent signal. Measurement of stimulus-evoked blood flow and oxygen metabolism permitted calculation of the NVC ratio to assess the integrity of neural-vascular communication. Consistent with our hypothesis, we observed monotonic NVC ratio increases with increasing visual stimulation frequency in younger adults but not in older adults. Age-related changes in stimulus-evoked cerebrovascular and neurometabolic signal could not fully explain this disruption; increases in stimulus-evoked neurometabolic activity elicited corresponding increases in stimulus-evoked CBF in younger but not in older adults. These results implicate age-related, demand-dependent failures of the neural-glial-vascular structures that comprise the NVC system.

Optical properties of para‐oligophenylenes: A case study of electronic absorption spectrum and relaxation dynamics of terphenyl

AbstractWe present a detailed quantitative description of vibronic‐coupling effects on the singlet photophysics of para‐oligophenylenes. Four energetically close‐lying singlet states (S1, S2, S3, and S4) are taken into consideration to interpret the first UV/Vis absorption band of these molecules. As a representative example, the energetics of those four states are evaluated for para‐terphenyl by performing extensive electronic structure calculations within the linear vibronic coupling framework. We obtain absorption spectral profiles by wavepacket propagation technique using the multi‐configuration time‐dependent Hartree method. Computed spectral profiles are in accord with the experiment. A minor electronic population transfer to upper states on a timescale of 10 fs is observed, suggesting the excited‐state nonadiabatic behavior of the molecule. Our findings necessitate the experimental validation of the role of higher states in the spectroscopy and dynamics of photoexcited para‐oligophenylenes.

How the Interplay among Conformational Disorder, Solvation, Local, and Charge-Transfer Excitations Affects the Absorption Spectrum and Photoinduced Dynamics of Perylene Diimide Dimers: A Molecular Dynamics/Quantum Vibronic Approach.

In this contribution we present a mixed quantum-classical dynamical approach for the computation of vibronic absorption spectra of molecular aggregates and their nonadiabatic dynamics, taking into account the coupling between local excitations (LE) and charge-transfer (CT) states. The approach is based on an adiabatic (Ad) separation between the soft degrees of freedom (DoFs) of the system and the stiff vibrations, which are described by the quantum dynamics (QD) of wave packets (WPs) moving on the coupled potential energy surfaces (PESs) of the LE and CT states. These PESs are described with a linear vibronic coupling (LVC) Hamiltonian, parameterized by an overlap-based diabatization on the grounds of time-dependent density functional theory computations. The WPs time evolution is computed with the multiconfiguration time-dependent Hartree method, using effective modes defined through a hierarchical representation of the LVC Hamiltonian. The soft DoFs are sampled with classical molecular dynamics (MD), and the coupling between the slow and fast DoFs is included by recomputing the key parameters of the LVC Hamiltonians, specifically for each MD configuration. This method, named Ad-MD|gLVC, is applied to a perylene diimide (PDI) dimer in acetonitrile and water solutions, and it is shown to accurately reproduce the change in the vibronic features of the absorption spectrum upon aggregation. Moreover, the microscopic insight offered by the MD trajectories allows for a detailed understanding of the role played by the fluctuation of the aggregate structure on the shape of the vibronic spectrum and on the population of LE and CT states. The nonadiabatic QD predicts an extremely fast (∼50 fs) energy transfer between the two LEs. CT states have only a moderate effect on the absorption spectrum, despite the fact that after photoexcitation they are shown to acquire a fast and non-negligible population, highlighting their relevance in dictating the charge separation and transport in PDI-based optical devices.

A Fourth-order Dielectric Narrow-band Bandpass Filter Using Coaxial Resonator

In this paper, a compact fourth-order dielectric bandpass filter is proposed. The filter adopts the mode of linear coupling and is composed of four coaxial resonators and two coupling slots, which are fed by two probes, and the four coaxial resonators are resonated to form a passband. The resonant frequency can be controlled by the radius and height of the resonators, and the inter-cavity coupling is controlled by the width of the coupling windows formed by the coupling slots. At last, the simulation results of the filter show that the filter has narrow bandwidth and good in-band matching performance and out-of-band suppression.

Trapping wave fields in an expulsive potential by means of linear coupling

We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly coupled components, with the confining harmonic-oscillator (HO) potential acting upon one component and an expulsive anti-HO potential acting upon the other. The systems can be implemented in optical and BEC dual-core waveguides. In the 1D linear system, codimension-one solutions are found in an exact form for the ground state (GS) and dipole mode (the first excited state). Generic solutions are produced by means of the variational approximation and are found in a numerical form. Exact codimension-one solutions and generic numerical ones are also obtained for the GS and vortex states in the 2D system (the exact solutions are found for all values of the vorticity). Both the trapped and antitrapped components of the bound states may be dominant ones, in terms of the norm. The localized modes may be categorized as bound states in continuum, as they coexist with delocalized ones. The 1D states, as well as the GS in 2D, are weakly affected and remain stable if the self-attractive or repulsive nonlinearity is added to the system. The self-attraction makes the vortex states unstable against splitting, while they remain stable under the action of the self-repulsion.

Optical response of the Leggett mode in multiband superconductors in the linear response regime

We study optical responses of Leggett modes in multiband superconductors in the linear response regime. The Leggett mode is a collective mode unique to multiband superconductors that arises from relative phase fluctuations of superconducting orders for different bands. We use the Ginzburg-Landau (GL) description to study the collective modes in multiband systems. We find that multiband superconductors generally allow a linear coupling between the Leggett mode and external electric fields due to the presence of a cross term between different components of superconducting orders in the GL theory. The presence of a linear coupling for the Leggett mode is in sharp contrast with the absence of that for Higgs (amplitude) modes in single-band superconductors that only support nonlinear optical responses such as third harmonic generation (THG). We further confirm such a linear coupling in multiband superconductors by a more microscopic description based on a diagrammatic approach. We study the collective modes within the random phase approximation (RPA) and compute their contribution to the linear optical conductivity. These findings suggest a new route to observe the Leggett mode by optical absorption.

Neuromorphic Behaviors of the 4-Lobe Chua Corsage Memristor

Neuromorphic computing plays an important role in brain-inspired computers, which can solve complex problems with higher efficiency and lower energy. As a promising candidate of neuromorphic devices, a locally active memristor has the ability to emulate complex neuromorphic functions, which has the potential to implement large-scale hardware spiking neural networks to unleash the efficiency and intelligence of the brain. In this paper, we analyze the characteristics of the locally active 4-lobe Chua corsage memristor (CCM) using small-signal equivalent circuits. In addition, we design a CCM-based third-order neuron circuit and illustrate its rich neuromorphic behaviors near the edge of chaos, such as self-sustained oscillation, periodic spiking, chaos, transient chaos, resting states, burst-number adaption, spike latency, and refractory period. Furthermore, collective behaviors such as exotic chimera states (e.g. coherent and incoherent patterns) have been observed in the ring neural network made of third-order memristive neurons with linear and nonlocal coupling.

Revealing the vibronic coupling effects in the size-dependent optical properties of cycloparaphenylene dications

We explain the visible and near-infrared optical properties of low-lying singlet excited states (S and S) of [5]-, [7]- and [9]cycloparaphenylene dications (CPPs). A narrow energy gap (<150 cm) separates these states at the Franck–Condon point of the individual molecule. The energy gap increases upon increasing the molecular size. Consequently, [5]CPP possesses highly overlapping S and S absorption bands. The overlap between these bands decreases and the resulting composite spectrum appears broader, particularly for [9]CPP. Theoretical spectra generated using quantum wavepacket calculations within the linear vibronic coupling approach match well with the experiment. Our findings reveal near-degenerate S and S minima, highlighting the relevance of both these states while assigning experimental fluorescence emission properties of CPPs.