On Cyclic Harmonic Oscillators

It is proven that the energy of a quantum mechanical harmonic oscillator with a generically time-dependent but cyclic frequency, $\omega_{0}(t_{0})= \omega_{0}(0)$, cannot decrease on the average if the system is originally in a stationary state, after the system goes through a full cycle. The energy exchange always takes place in the direction from the macroscopic system (environment) to the quantum microscopic system.Comment: Latex file, 14 pages, 3 figures, minor correction made in Section

on a rapidly converging iterative algorithm for diode parameter extraction from a single iv curve

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Numerical and analytical results for the two discs capacitor problem

In this paper, we study the two discs capacitor, for equal and different radii. The new results obtained allow a complete characterization of capacity coefficients and forces at short distances. An extensive numerical calculation confirms the theoretical results. The study shows the existence of a hierarchy in the divergent behaviour of the capacitance coefficients and this implies some unusual behaviour of the forces, strictly related to the dimensionality of the nearcontact zone between electrodes

Capacitance and forces for thick circular electrodes

Some new results are presented concerning the forces between two equal circular electrodes of finite thickness. For close electrodes different scenarios result, depending on the thickness and on the ratio of charges of the conductors. Attractive or repulsive forces can appear depending on the parameters and on the separation of the electrodes. The force between the electrodes can be non monotonic as a function of the distance and one or more equilibrium points can appear. A unified description of cylindrical systems using a high precision method based on a Galerkin expansion is given and we check our results with a quite accurate boundary element method (BEM)

Capacitance and forces for two square electrodes

A numerical and semi-analytical study of electrostatics of a system of two parallel square electrodes is focused on the behavior at short and large distances of the capacity coefficients and of the electrostatic forces between the plates. It is found, using a Boundary Element Method approach with a regular grid and an analytical treatment of the kernel matrix, a strict parallelism with the analogous system of two circular disks, in particular for the possibility of disentangle the divergences at short distances and the presence of a logarithmically divergent repulsive force, with the exception of electrodes with exactly opposite charges. With our semi-analytical approach, fully exploiting the symmetries of the problem and using very small subdomains, the capacitance coefficients of the two square capacitor are determined with a great accuracy, comparable with the best data available in the literature just for the capacitance of a single square