Origin of Mass. Mass and Mass-Energy Equation from Classical-Mechanics Solution

We establish the classical wave equation for a particle formed of a massless oscillatory elementary charge generally also traveling, and the resulting electromagnetic waves, of a generally Doppler-effected angular frequency \w, in the vacuum in three dimensions. We obtain from the solutions the total energy of the particle wave to be \eng=\hbarc\w, 2\pi \hbarc being a function expressed in wave-medium parameters and identifiable as the Planck constant. In respect to the train of the waves as a whole traveling at the finite velocity of light $c$, \eng=mc^2 represents thereby the translational kinetic energy of the wavetrain, m=\hbarc\w/c^2 being its inertial mass and thereby the inertial mass of the particle. Based on the solutions we also write down a set of semi-empirical equations for the particle's de Broglie wave parameters. From the standpoint of overall modern experimental indications we comment on the origin of mass implied by the solution.Comment: 13 pages, no figure. Augmented introductio

Scattering of coherent states on a single artificial atom

In this work we theoretically analyze a circuit QED design where propagating quantum microwaves interact with a single artificial atom, a single Cooper pair box. In particular, we derive a master equation in the so-called transmon regime, including coherent drives. Inspired by recent experiments, we then apply the master equation to describe the dynamics in both a two-level and a three-level approximation of the atom. In the two-level case, we also discuss how to measure photon antibunching in the reflected field and how it is affected by finite temperature and finite detection bandwidth.Comment: 18 pages, 7 figure

Coherent current transport in wide ballistic Josephson junctions

We present an experimental and theoretical investigation of coherent current transport in wide ballistic superconductor-two dimensional electron gas-superconductor junctions. It is found experimentally that upon increasing the junction length, the subharmonic gap structure in the current-voltage characteristics is shifted to lower voltages, and the excess current at voltages much larger than the superconducting gap decreases. Applying a theory of coherent multiple Andreev reflection, we show that these observations can be explained in terms of transport through Andreev resonances.Comment: 4 pages, 4 figure