相关论文: Approximate solutions to Mathieu's equation

Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…

The stationary Josephson effect in a system of ballistic graphene is studied in the framework of quasiclassical Green's function theory. Reflecting the ultimate two-dimensionality of graphene, a Josephson junction involving a graphene sheet…

The invariance for the equation of fast diffusion in the 2D coordinate space has been proved, and its reduction to the 1D (with respect to the spatial variable) analog is demonstrated. On the basis of these results, new exact…

While teaching a course on integral equations, I noticed that a straightforward combination of Neumann series and Fourier series for the resolvent (or the solution) of an integral equation has good approximation qualities. This short…

Using the path integral approach, we provide an explicit derivation of the equation for the phase boundary for quantum Josephson junction arrays with offset charges and non-diagonal capacitance matrix. For the model with nearest neighbor…

Any time-dependent solution of Schr\"{o}dinger equation may be always correlated to a solution of Hamilton equations or to a statistical combination of their solutions; only the set of corresponding solutions is somewhat smaller (due to…

The Mathieu functions are used to solve analytically some problems in elliptical cylinder coordinates. A computational toolbox was implemented in Matlab. Since the notation and normalization for Mathieu functions vary in the literature, we…

We extend the scattering theory of the Josephson effect to include a coupling of the Josephson junction to a gapless electron reservoir in the normal state. By opening up the system with a quasiparticle escape rate $1/\tau$, the…

When an Approximation Theorist looks at well-posed PDE problems or operator equations, and standard solution algorithms like Finite Elements, Rayleigh-Ritz or Trefftz techniques, methods of fundamental or particular solutions and their…

Recently, an approximated solution of the Einstein equations for a rotating body whose mass effects are negligible with respect to the rotational ones has been derived by Tartaglia. At first sight, it seems to be interesting because both…

Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…

While Fourier's law is empirically confirmed for many substances and over an extremely wide range of thermodynamic parameters, a convincing microscopic derivation still poses difficulties. With current machines the solution of Newton's…

The Schr\"odinger equation is universally accepted due to its excellent predictions aligning with observed results within its defined conditions. Nevertheless, it does not seem to possess the simplicity of fundamental laws, such as Newton's…

The dc Josephson effect is considered from the thermodynamic point of view. Universal thermodynamic equations, relating both bound and continuum contributions to the Josephson current with the normal electron scattering amplitudes are…

The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of…

The classical problem of the Josephson junction of arbitrary length W in the presence of externally applied magnetic fields (H) and transport currents (J) is reconsidered from the point of view of stability theory. In particular, we derive…

The Josephson current in a diffusive superconductor/ferromagnet/superconductor junction with precessing magnetization is calculated within the quasiclassical theory of superconductivity. When the junction is phase-biased, a stationary…

In probability theory, how to approximate the solution of a stochastic differential equation is an important topic. In Watanabe's classical textbook, by an approximation of the Wiener process, solutions of approximated equations converge to…

Several noteworthy properties of the differential equation utilized for the modeling of Josephson junctions are considered. The explicit representation of the monodromy transform of the space of its solutions is given. In case of positive…

Starting from the general Lindhard theory describing the partition of particles energy in materials between ionisation and displacements, analytical approximate solutions have been derived, for media containing one and more atomic species,…