The inverse problem for electromagnetic field produced by arbitrary altered charge distribution in dipole approximation is solved. The charge distribution is represented by its dipole moment. It is assumed that the spectral properties of magnetic field of the dipole are known. The position of the dipole and its Fourier components are considered as the unknown quantities. It is assumed that relative increments of amplitude and phase of magnetic field in the vicinity of the observation point are known. The derived results can be used for study of phenomena concerned with occurrence and variation of localized electric charge distribution, when the position and the dynamics of a localized source of electromagnetic field are to be defined.
Considerable time is often spent optimizing antennas to meet specific design metrics. Rarely, however, are the resulting antenna designs compared to rigorous physical bounds on those metrics. Here we study the performance of optimized planar meander line antennas with respect to such bounds. Results show that these simple structures meet the lower bound on radiation Q-factor (maximizing single resonance fractional bandwidth), but are far from reaching the associated physical bounds on efficiency. The relative performance of other canonical antenna designs is compared in similar ways, and the quantitative results are connected to intuitions from small antenna design, physical bounds, and matching network design.
We propose a novel approach to the inverse Ising problem which employs the recently introduced Density Consistency approximation (DC) to determine the model parameters (couplings and external fields) maximizing the likelihood of given empirical data. This method allows for closed-form expressions of the inferred parameters as a function of the first and second empirical moments. Such expressions have a similar structure to the small-correlation expansion derived by Sessak and Monasson, of which they provide an improvement in the case of non-zero magnetization at low temperatures, as well as in presence of random external fields. The present work provides an extensive comparison with most common inference methods used to reconstruct the model parameters in several regimes, i.e. by varying both the network topology and the distribution of fields and couplings. The comparison shows that no method is uniformly better than every other one, but DC appears nevertheless as one of the most accurate and reliable approaches to infer couplings and fields from first and second moments in a significant range of parameters.
The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem starting from initial conditions given using nothing more than the methods of synthetic geometry so close to Newtons approach. The method works with elliptic, parabolic and hyperbolic orbits; it can even be used to derive Rutherfords relation from which the scattering cross section can be easily evaluated. We think our discussion is both interesting and useful inasmuch as it serves to relate the initial conditions with the corresponding trajectories in a purely geometrical way uncovering in the process some seldom discussed interesting connections.
For an oscillating electric dipole in the shape of a small, solid, uniformly-polarized, spherical particle, we compute the self-field as well as the radiated electromagnetic field in the surrounding free space. The assumed geometry enables us to obtain the exact solution of Maxwells equations as a function of the dipole moment, the sphere radius, and the oscillation frequency. The self field, which is responsible for the radiation resistance, does not introduce acausal or otherwise anomalous behavior into the dynamics of the bound electrical charges that comprise the dipole. Departure from causality, a well-known feature of the dynamical response of a charged particle to an externally applied force, is shown to arise when the charge is examined in isolation, namely in the absence of the restraining force of an equal but opposite charge that is inevitably present in a dipole radiator. Even in this case, the acausal behavior of the (free) charged particle appears to be rooted in the approximations used to arrive at an estimate of the self-force. When the exact expression of the self-force is used, our numerical analysis indicates that the impulse-response of the particle should remain causal.
We propose a novel approach in a search for the neutron electric dipole moment (EDM) by taking advantage of signal amplification in a weak measurement, known as weak value amplification. Considering an analogy to the weak measurement that can measure the spin magnetic moment interaction, we examine an experimental setup with a polarized neutron beam through an external electric field with spatial gradient, where the signal is sensitive to the EDM interaction. In particular, a dedicated analysis of effects from impurities in pre- and post-selections is performed. We show that the weak value amplification occurs where the signal is enhanced by up to two orders of magnitude, and demonstrate a potential sensitivity of the proposed setup to the neutron EDM.