Related papers: Ermakov-Pinney equation for time-varying mass syst…
In this manuscript, we investigate the analytical solution of the time-dependent Schr\"odinger equation for a harmonic oscillator with time-dependent mass and frequency, coupled with angular-dependent potential energy by utilizing the Dunkl…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
We consider a system of seminlinear parabolic variational inequalities with time-dependent convex obstacles. We prove the existence and uniqueness of its solution. We also provide a stochastic representation of the solution and show that it…
A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
Ergodic parameters like the Lyapunov and the conditional exponents are global functions of the invariant measure, but the invariant measure itself contains more information. A more complete characterization of the dynamics by new families…
We extend the time-dependent variational principle to the setting of dissipative dynamics. This provides a locally optimal (in time) approximation to the dynamics of any Lindblad equation within a given variational manifold of mixed states.…
We propose a proof of convergence of an adaptive method used in molecular dynamics to compute free energy profiles. Mathematically, it amounts to studying the long-time behavior of a stochastic process which satisfies a non-linear…
We consider the time-dependent thermal pure quantum state method and introduce the efficient scheme to evaluate the change in physical quantities induced by the time-dependent perturbations, which has been proposed in our previous paper [H.…
We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schr\"odinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted…
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value…
Pesin's formula relates the entropy of a dynamical system with its positive Lyapunov exponents. It is well known, that this formula holds true for random dynamical systems on a compact Riemannian manifold with invariant probability measure…
This paper addresses the problem of frequency-weighted extended balanced truncation for discrete and continuous-time linear time-invariant plants. We show that the frequency-weighted discrete-time plant admits block-diagonal solutions to…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…
Based on the recent result that, if the masses of timelike fields are point-dependent fields themselves, the action of matter fields is conformal form-invariant in its standard form, and on the active and passive approaches to conformal…
We study a classical reparametrization-invariant system, in which ``time'' is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a…
We solve the Schr\"odinger equation with a position-dependent mass (PDM) charged particle interacted via the superposition of the Morse and Coulomb potentials and exposed to external magnetic and Aharonov-Bohm (AB) flux fields. The…
We prove time-dependent versions of Kingman's subadditive ergodic theorem, which can be used to study stochastic processes as well as propagation of solutions to PDE in time-dependent environments.
This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation…