相关论文: Approximate solutions to Mathieu's equation
The general solution of the homogeneous damped Mathieu equation in the analytical form, allowing its practical using in many applications, including superconductivity studies, without numerical calculations has been found.
Mathematical models related to some Josephson junctions are pointed out and attention is drawn to the solutions of certain initial boundary problems and to some of their estimates. In addition, results of rigorous analysis of the behaviour…
The quantum dynamics of a one-dimensional bosonic Josephson junction is studied by solving the time-dependent many-boson Schr\"odinger equation numerically exactly. Already for weak interparticle interactions and on short time scales, the…
Mathieu equation is widely used to study several natural phenomenon. In this paper, we show that replacing the sinusoid in the Mathieu equation with a phasor can lead to solutions that behave in a totally different way. Solutions of Mathieu…
Recently developed simple approach for the exact/approximate solution of Schrodinger equations with constant/position-dependent mass, in which the potential is considered as in the perturbation theory, is shown to be equivalent to the one…
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in…
We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we…
We study fermion-parity-changing quantum phase transitions (QPTs) in platform Josephson junctions. These QPTs, associated with zero-energy bound states, are rather widely observed experimentally. They emerge from numerical calculations…
One of the well-studied equations in the theory of ODEs is the Mathieu differential equation. A common approach for obtaining solutions is to seek solutions via Fourier series by converting the equation into an infinite system of linear…
The Mathisson equations under the Frenkel-Mathisson supplementary condition are studied in a Schwarzschild field. The choice of solutions, which describe the motions of the proper center of mass of a spinning test particle, is discussed,…
The Schwinger-Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the indepedent solutions which respectively…
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate…
Superconducting circuits comprising Josephson junctions have spurred significant research activity due to their promise to realize scalable quantum computers. Effective Hamiltonians for these systems have traditionally been derived assuming…
The Josephson effect is found to stem from the quantum behavior of massive photons existing in a superconducting medium. Accordingly, the Josephson coupling energy is found to be equal to the rest mass energy of these photons. The Josephson…
We derive an approximate analytic solution for a single fluxon in a double stacked Josephson junctions (SJJ's) for arbitrary junction parameters and coupling strengths. It is shown that the fluxon in a double SJJ's can be characterized by…
We prove some general results on the existence and uniqueness of solutions to the Liouville equation. Then, we discuss the sharpness and possible generalizations. Finally, we give several applications, arising in both mathematics and…
The square tight-binding model in a magnetic field leads to the almost-Mathieu operator which, for rational fields, reduces to a $q\times q$ matrix depending on the components $\mu$, $\nu$ of the wave vector in the magnetic Brillouinzone.…
We consider two problems arising in the study of the Schr\"odinger-Newton equations. The first is to find their Lie point symmetries. The second, as an application of the first, is to investigate an approximate solution corresponding to…
Two-fluxon state in an annular Josephson junction in the presence of external magnetic field is studied analytically, numerically and experimentally. We obtain an analytical expression for the potential of interaction between the fluxons…
The solution to Poisson's equation arise in many Markov chain and Markov jump process settings, including that of the central limit theorem, value functions for average reward Markov decision processes, and within the gradient formula for…