The split-operator pseudo-spectral method based on the fast Fourier transform (SO-FFT) is a fast and accurate method for the numerical solution of the time-dependent Schrödinger-like equations (TDSE). As well as other grid-based approaches, SO-FFT encounters a problem of the unphysical reflection of the wave function from the grid boundaries. Exterior complex scaling (ECS) is an effective method widely applied for the suppression of the unphysical reflection. However, SO-FFT and ECS have not been used together heretofore because of the kinetic energy operator coordinate dependence that appears in ECS applying. We propose an approach for the combining the ECS with SO-FFT for the purpose of the solution of TDSE with outgoing-wave boundary conditions. Also, we propose an effective ECS-friendly FFT-based preconditioner for the solution of the stationary Schrödinger equation by means of the preconditioned conjugate gradients method.

The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodical force is combined with a theoretical analysis by means of the quasi-harmonic reduction. Both two mechanisms of synchronization are demonstrated: capture of the phase and frequency of oscillations and suppression by an external signal. Classification of undamped oscillations in an autonomous system with a line of equilibria as a special kind of self-sustained oscillations is concluded due to the possibility to observe the effect of frequency-phase locking in the same system in the presence of an external influence. It is established that the occurrence of phase locking in the considered system continuously depends both on parameter values and initial conditions. The simultaneous dependence of synchronization area boundaries on the initial conditions and the parameter values is also shown.

The split-operator pseudo-spectral method based on the fast Fourier transform (SO-FFT) is a fast and accurate method for the numerical solution of the time-dependent Schrödinger-like equations (TDSE). As well as other grid-based approaches, SO-FFT encounters a problem of the unphysical reflection of the wave function from the grid boundaries. Exterior complex scaling (ECS) is an effective method widely applied for the suppression of the unphysical reflection. However, SO-FFT and ECS have not been used together heretofore because of the kinetic energy operator coordinate dependence that appears in ECS applying. We propose an approach for the combining the ECS with SO-FFT for the purpose of the solution of TDSE with outgoing-wave boundary conditions. Also, we propose an effective ECS-friendly FFT-based preconditioner for the solution of the stationary Schrödinger equation by means of the preconditioned conjugate gradients method.

We demonstrate how the pitchfork, transcritical and saddle-node bifurcations of steady states observed in dynamical systems with a finite number of isolated equilibrium points occur in systems with lines of equilibria. The exploration is carried out by using the numerical simulation and linear stability analysis applied to a model of a memristor-based oscillator. First, all the discussed bifurcation scenarios are considered in the context of systems including Chua's memristor with a piecewise-smooth characteristic. Then the memristor characteristic is changed to a function that is smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration. The presented results are obtained for electronic circuit models, but the considered bifurcation phenomena can be exhibited by systems with a line of equilibria of any nature.

Magnonics is a field of science that addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operations in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors that covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with Boolean digital data, unconventional approaches like neuromorphic computing, and the progress towards magnon-based quantum computing. The article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section is prepared by one or a group of authors and concludes with a brief description of the current challenges and the outlook of the further development of the research directions.

The paper deals with Sturm-Liouville-type operators with frozen argument of the form $\ell y:=-y''(x)+q(x)y(a),$ $y^{(\alpha)}(0)=y^{(\beta)}(1)=0,$ where $\alpha,\beta\in\{0,1\}$ and $a\in[0,1]$ is an arbitrary fixed rational number. Such nonlocal operators belong to the so-called loaded differential operators, which often appear in mathematical physics. We focus on the inverse problem of recovering the potential $q(x)$ from the spectrum of the operator $\ell.$ Our goal is two-fold. Firstly, we establish a deep connection between the so-called main equation of this inverse problem and Chebyshev polynomials of the first and the second kinds. This connection gives a new perspective method for solving the inverse problem. In particular, it allows one to completely describe all non-degenerate and degenerate cases, i.e. when the solution of the inverse problem is unique or not, respectively. Secondly, we give a complete and convenient description of iso-spectral potentials in the space of complex-valued integrable functions.

Electron-positron pair production by the superposition of two laser pulses with different frequencies and amplitudes is analyzed as a particular realization of the assisted dynamic Schwinger effect. It is demonstrated that, within a non-perturbative kinetic equation framework, an amplification effect is conceivable for certain parameters. When both pulses have wavelengths longer than the Compton wavelength, the residual net density of produced pairs is determined by the resultant field strength. The number of pairs starts to grow rapidly if the wavelength of the high-frequency laser component gets close to the Compton wavelength.

The dynamically assisted pair creation (Schwinger effect) is considered for the superposition of two periodic electric fields acting a finite time interval. We find a strong enhancement by orders of magnitude caused by a weak field with a frequency being a multitude of the strong-field frequency. The strong low-frequency field leads to shell structures which are lifted by the weaker high-frequency field. The resonance type amplification refers to a new, monotonously increasing mode, often hidden in some strong oscillatory transient background which disappears during the smoothly switching off the background fields, thus leaving a pronounced residual shell structure in phase space.

The report presents the results of using the nonperturbative kinetic approach to describe the excitation of plasma oscillations in a graphene monolayer. As examples the constant electric field as well as an electric field of short high-frequency pulses are considered. The dependence of the induced conduction and polarization currents characteristics on the pulse intensity, pulse duration, and polarization is investigated. The characteristics of secondary electromagnetic radiation resulting from the alternating currents is investigated. The nonlinear response to the external electric field characterizes graphene as an active medium. Qualitative agreement is obtained with the existing experimental result of measurements of currents in constant electric fields and radiation from graphene in the case of excitation by means of the infrared and optical pulses.

Atrial fibrillation (AF) is the most prevalent arrhythmia and is associated with a five-fold increase in stroke risk. Many individuals with AF go undetected. These individuals are often asymptomatic. There are ongoing debates on whether mass screening for AF is to be recommended. However, there is incentive in performing screening for specific at risk groups such as individuals suspected of sleep-disordered breathing where an important association between AF and obstructive sleep apnea (OSA) has been demonstrated. We introduce a new methodology leveraging digital biomarkers and recent advances in artificial intelligence (AI) for the purpose of mass AF diagnosis. We demonstrate the value of such methodology in a large population sample at risk of sleep disordered breathing. Four databases, totaling n=3,088 patients and p=26,913 hours of ECG raw data were used. Three of the databases (n=125, p=2,513) were used for training a machine learning model in recognizing AF events from beat-to-beat interval time series. The visit 1 of the sleep heart health study database (SHHS1, n=2,963, p=24,400) consists of overnight polysomnographic (PSG) recordings, and was considered as the test set. In SHHS1, expert inspection identified a total of 70 patients with a prominent AF rhythm. Model prediction on the SHHS1 showed an overall Se=0.97,Sp=0.99,NPV=0.99,PPV=0.67 in classifying individuals with or without prominent AF. PPV was non-inferior (p=0.03) for individuals with an apnea-hypopnea index (AHI) > 15 versus AHI < 15. Over 22% of correctly identified prominent AF rhythm cases were not documented as AF in the SHHS1. Individuals with prominent AF can be automatically diagnosed from an overnight single channel ECG recording, with an accuracy unaffected by the presence of OSA. AF detection from overnight ECG recording revealed a large proportion of undiagnosed AF and may enhance the phenotyping of OSA.

It is shown that nonlocal coupling provides for controlling the collective noise-induced dynamics in the regime of stochastic resonance. This effect is demonstrated by means of numerical simulation on an example of coupled overdamped bistable oscillators. In particular, it has been established that increasing the coupling radius and coupling strength allows to enhance or to suppress the effect of stochastic resonance which is reflected in the evolution of the dependence of the signal-to-noise ratio (SNR) on the noise intensity for varying coupling parameters. Nonlocal coupling is considered as an intermediate option between local and global (pairwise or higher-order interactions) coupling topologies which are also discussed in the context of the stochastic resonance control.

The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the constituents is decisive and the spatial and the momentum distribution of one electron depends on those of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. Here, we implement an imaging scheme which visualizes correlations between electrons by coincident detection of the reaction fragments after high energy photofragmentation. With this technique, we examine the H2 two-electron wave function in which electron-electron correlation beyond the mean-field level is prominent. We visualize the dependence of the wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging. Our study paves the way for future time resolved correlation imaging at FELs and laser based X-ray sources.

We consider Lagrange interpolation on the set of finitely many intervals. This problem is closely related to the least deviating polynomial from zero on such sets. We will obtain lower and upper estimates for the corresponding Lebesgue constant. The case of two intervals of equal lengths is simpler, and an explicit construction for two non-symmetric intervals will be given only in a special case.

The effective mass approximation is analysed in a nonperturbative kinetic theory approach to strong field excitations in graphene [1,2]. This problem is highly actual for the investigation of quantum radiation from graphene [3], where the collision integrals in the photon kinetic equation are rather complicated functionals of the distribution functions of the charge carriers. These functions are needed in the explicit analytical definition as solutions of the kinetic equations for the electron-hole excitations. In the present work it is shown that the suggested approach is rather effective in a certain range of parameters for the pulse of an external electromagnetic field. For example, the applicability condition of the approximation in the case of a harmonic field is \hbar \omega^2 / (\sqrt{2} e E_0 v_F) &lt; 1, were $v_F$ is the Fermi velocity. In the standard massive quantum electrodynamics the usability of the analogical approximation is very narrow.

The generation of quantum-correlated pulse pairs in a dispersion modulated birefringent fiber is considered. The photon-number correlations and squeezing are studied using linearized quantum fluctuation theory. Two models of the pulse propagation in an optical fiber are used. The first model is based on the Manakov equations, and the second one is based on the coupled nonlinear Schrodinger equations with differential group delay and birefringence terms. In the Manakov model the correlated pulse pairs can be generated using splitting of a second-order soliton and inelastic collision of two fundamental solitons. The interpulse correlations depends on the modulation period of the fiber dispersion. In the model of the coupled nonlinear Schrodinger equations the correlated pulse pair can be produced using pulse splitting due to polarization mode dispersion. The pulses have orthogonal polarization states. This allows the pulses to be separated into two different channels using a polarization beam splitter. The interpulse correlation depends on the interplay between polarization mode dispersion and polarization instability.

This research investigates the complex spatiotemporal behaviors of Chialvo neuron maps under the influence of Levy noise on three different network topologies that is a ring network, a two dimensional lattice affected by electromagnetic flux, and a delayed coupled lattice. On the ring structure, we show that adding non uniform Levy noise induces the formation of new collective dynamics like standing and traveling waves. The frequency and type of these emergent patterns depend sensitively on the intrinsic excitability parameter and the noise intensity, revealing new pathways to control synchronization behavior through noise modulation. In the 2D lattice network, we show that electromagnetic flux and noise together induce a diverse range of behaviors, from synchronized waves to desynchronized states. Most strikingly, spiral wave chimeras emerge under moderate noise, with coherent and incoherent regions coexisting, highlighting the fine balance between external forcing and stochastic perturbations. Finally, upon introducing delay in the lattice structure, the system displays a rich variety of dynamical regimes such as labyrinth patterns, rotating spirals, and target waves whose stability and transitions are greatly affected by both delay and coupling strength.

The features of vacuum particle creation in an external classical field are studied for simplest external field models in $3 + 1$ dimensional QED. The investigation is based on a kinetic equation that is a nonperturbative consequence of the fundamental equations of motion of QED. The observed features of the evolution of the system apply on the qualitative level also for systems of other nature and therefore are rather general. Examples from cosmology and condensed matter physics illustrate this statement. The common basis for the description of these systems are kinetic equations for vacuum particle creation belonging to the class of integro-differential equations of non-Markovian type with fastly oscillating kernel. This allows to characterize processes of this type as belonging to the class of field induced phase transitions.

Based on methods of numerical simulation, the constructive role of nonlocal coupling is demonstrated in the context of wavefront propagation observed in an ensemble of overdamped bistable oscillators. Firstly, it is shown that the wavefront propagation can be controlled, i.e. accelerated or slowed down, by varying the strength and radius of nonlocal interactions. This applies to both deterministic and stochastic wavefront propagation. Secondly, nonlocal interactions are found to facilitate preservation of spatial domains and fronts being totally destroyed due to the action of noise in the case of local coupling. In addition, a new finding concerning the action of additive noise is reported: it is shown that additive noise is capable of accelerating front propagation if the local dynamics involves asymmetry.

Typically, the period-doubling bifurcations exhibited by nonlinear dissipative systems are observed when varying systems' parameters. In contrast, the period-doubling bifurcations considered in the current research are induced by changing the initial conditions whereas parameter values are fixed. Thus, the studied bifurcations can be classified as the period-doubling bifurcations without parameters. Moreover, we show a cascade of the period-doubling bifurcations without parameters resulting in transition to deterministic chaos. The explored effects are demonstrated by means of numerical modelling on an example of a modified Anishchenko-Astakhov self-oscillator where the ability to exhibit bifurcations without parameters is associated with the properties of a memristor. Finally, we compare the dynamics of the ideal-memristor-based oscillator with the behaviour of a model taking into account the memristor forgetting effect.