Related papers: Benford's law and complex atomic spectra

We theoretically study the propagation of light through a cold atomic medium, where the effects of motion, laser intensity, atomic density, and polarization can all modify the properties of the scattered light. We present two different…

Atomic electrons are sensitive to the properties of the nucleus they are bound to, such as nuclear mass, charge distribution, spin, magnetization distribution, or even excited level scheme. These nuclear parameters are reflected in the…

The electronic properties of one-dimensional clusters of N atoms or molecules have been studied. The model used is similar to the Kronig-Penney model with the potential offered by each ion being approximated by an attractive delta function.…

Using a configuration interaction approach we study statistics of the dipole matrix elements (E1 amplitudes) between the 14 lower odd states with J=4 and 21st to 100th even states with J=4 in the Ce atom (1120 lines). We show that the…

We develop a field-nonlinear theory of sub-Doppler spectroscopy in a gas of two-level atoms, based on a self-consistent solution of the Maxwell-Bloch equations in the mean field and single-atom density matrix approximations. This makes it…

Ionic electro-active polymer (Nafion for example) can be used as sensor or actuator. To this end, a thin film of the water-saturated material is sandwiched between two electrodes. Water saturation causes a quasi-complete dissociation of the…

Shaped laser pulses are a powerful tool to induce population transfer between electronic molecular states, and time-dependent perturbation theory is suitable for a description of such a transfer in weak external fields. The application of…

We develop a theoretical framework for the diffusion of a single unconstrained species of atoms on a crystal lattice that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to…

There are two fair ways to distribute particles in boxes. The first way is to divide the particles equally between the boxes. The second way, which is calculated here, is to score fairly the particles between the boxes. The obtained power…

When the scattering length is proportional to the distance from the center of the system, two particles are shown to be trapped about the center. Furthermore, their spectrum exhibits discrete scale invariance, whose scale factor is…

Benford's law is often used as a support to critical decisions related to data quality or the presence of data manipulations or even fraud. However, many authors argue that conventional statistical tests will reject the null of data…

It is a common belief that in any environment where life is possible, life will be generated. Here it is suggested that the cause for a spontaneous generation of complex systems is probability driven processes. Based on equilibrium…

We give a short, self-contained, and elementary proof of the strong law of large numbers under a power law decay hypothesis for joint second moments. The result is related to the classical one by Lyons. However, we also provide a rate of…

Natural optical activity is the paradigmatic example of an effect originating in the weak spatial inhomogeneity of the electromagnetic field on the atomic scale. In molecules, such effects are well described by the multipole theory of…

The processes with three or more charged particles in the final state exhibit particular threshold behavior, as inferred by the famous Wannier law for (2e + ion) system. We formulate a general solution which determines the threshold…

We consider random permutations derived by sampling from stick-breaking partitions of the unit interval. The cycle structure of such a permutation can be associated with the path of a decreasing Markov chain on $n$ integers. Under certain…

We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…

We present a theory for rigorous quantum scattering calculations of probabilities for chemical reactions of atoms with diatomic molecules in the presence of an external electric field. The approach is based on the fully uncoupled basis set…

We consider a linearly polarized electromagnetic wave incident on an opaque screen with square aperture of edge a. An application of Faraday's law to a loop parallel to the screen, on the side away from the source, shows that the wave must…

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…