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We devise a three-parameter random search strategy to obtain accurate estimates of the large-coupling amplitude and exponent of an observable from its divergent Taylor expansion, known to some desired order. The endeavor exploits the power…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more…
The dynamical law obeyed by the one-dimensional physical systems in the scale relativity approach is reduced to a Riccati nonlinear differential equation. Applied to the harmonic oscillator potential, we show that such an approach permits…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
We study a system of stochastically forced infinite-dimensional coupled harmonic oscillators. Although this system formally conserves energy and is not explicitly dissipative, we show that it has a nontrivial invariant probability measure.…
A nonpolynomial one-dimensional quantum potential representing an oscillator, that can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is…
We derive approximate expressions for the amplitude decay of harmonic oscillations weakly damped by the simultaneous action of three different damping forces: force of constant magnitude, force linear in velocity, and force quadratic in…
A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions…
Multiple scale techniques are well-known in classical mechanics to give perturbation series free from resonant terms. When applied to the quantum anharmonic oscillator, these techniques lead to interesting features concerning the solution…
The small and large scale problem of various passive vector models with anisotropic forcing is considered by solving exactly the equation for the pair correlation function. Emphasis is placed in the phenomena of anomalous scaling and the…
It is studied the symmetry restoration in a theory of a self-interacting charged scalar field at finite temperature and in the presence of an external magnetic field. The effective potential is evaluated nonperturbatively through the…
In order to investigate the reliability of the classical approximation for non-perturbative real time correlation functions at finite temperature we study the two-point correlator for the anharmonic oscillator. For moderately large times…
We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency $\Omega$ is chosen to scale with the order as…
A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in…
High harmonics have emerged as a powerful ultrafast probe of phonon dynamics and electron-phonon interactions in solids, with most studies focusing on odd harmonics. Here, in a pump-probe setup with variable delay, we theoretically…
Power system oscillations are a significant concern for system operators, a problem that has grown due to the interconnection of inverter-based resources. To address this issue, various methods have been proposed to locate the sources of…
Factorization method is developed for a family of discretely spiked harmonic oscillators. Two sets of intertwining and ladder operators are presented to algebraically generate eigenstates with energies isomorphic to those of the ordinary…
We apply the effective potential analytic continuation (EPAC) method to one-dimensional asymmetric potential systems to obtain the real time quantum correlation functions at various temperatures. Comparing the EPAC results with the exact…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…