相关论文: Perturbation Theory for the Systems of Ordinary Li…
In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we…
We consider a linear differential system of Mathieu equations with periodic coefficients over periodic closed orbits and we prove that, arbitrarily close to this system, there is a linear differential system of Hamiltonian damped Mathieu…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
Perturbative Symmetry Approach is formulated in symbolic representation. Easily verifiable integrability conditions of a given equation are constructed in the frame of the approach. Generalisation for the case of non-local and non-evolution…
Perturbation theory is an important technique for reducing computational cost and providing physical insights in simulating quantum systems with classical computers. Here, we provide a quantum algorithm to obtain perturbative energies on…
This paper considers the use of singular perturbation approximations for general linear quantum systems where the system dynamics are described in terms of both annihilation and creation operators. Results that are related to the physical…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular…
This paper considers the use of singular perturbation approximations for a class of linear quantum systems arising in the area of linear quantum optics. The paper presents results on the physical realizability properties of the approximate…
We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our…
Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which evoked an explosion of applications with the blooming of atomic and subatomic physics. Even though PT is well-used today,…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
Perturbation theory (PT) is a powerful and commonly used tool in the investigation of closed quantum systems. In the context of open quantum systems, PT based on the Markovian quantum master equation is much less developed. The…
We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed Differential-Algebraic Equations, allowing the perturbation to contain a distributed and possibly infinite delay. Under suitable assumptions, the perturbed…
Linear equations with periodic coefficients describe the behavior of various dynamical systems. This studying is devoted to their applications to the planetary restricted three-body problem (RTBP). Here we consider the Laplace method for…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
This work introduces a methodology for generating linear operators that approximately represent nonlinear systems of perturbed ordinary differential equations. This is done through the application of classical perturbation theory via the…
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…