Forbidden activation levels in a non-stationary tunneling process

Tunneling in the presence of an opaque barrier, part of which varies in time, is investigated numerically and analytically in one dimension. Clearly, due to the varying barrier a tunneling particle experiences spectral widening. However, in the case of strong perturbations, the particles' activation to certain energies is avoided. We show that this effect occurs only when the perturbation decays faster than 1/t^2.Comment: 4pages,2 figures (Revtex

Universal Mortality Law, Life Expectancy and Immortality

Well protected human and laboratory animal populations with abundant resources are evolutionary unprecedented, and their survival far beyond reproductive age may be a byproduct rather than tool of evolution. Physical approach, which takes advantage of their extensively quantified mortality, establishes that its dominant fraction yields the exact law, and suggests its unusual mechanism. The law is universal for all animals, from yeast to humans, despite their drastically different biology and evolution. It predicts that the universal mortality has short memory of the life history, at any age may be reset to its value at a significantly younger age, and mean life expectancy extended (by biologically unprecedented small changes) from its current maximal value to immortality. Mortality change is rapid and stepwise. Demographic data and recent experiments verify these predictions for humans, rats, flies, nematodes and yeast. In particular, mean life expectancy increased 6-fold (to "human" 430 years), with no apparent loss in health and vitality, in nematodes with a small number of perturbed genes and tissues. Universality allows one to study unusual mortality mechanism and the ways to immortality

The quantum group, Harper equation and the structure of Bloch eigenstates on a honeycomb lattice

The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of homogeneous magnetic field. Provided the magnetic flux per unit hexagon is rational of the elementary flux, the one-particle Hamiltonian is expressed in terms of the generators of the quantum group $U_q(sl_2)$. Employing the functional representation of the quantum group $U_q(sl_2)$ the Harper equation is rewritten as a systems of two coupled functional equations in the complex plane. For the special values of quasi-momentum the entangled system admits solutions in terms of polynomials. The system is shown to exhibit certain symmetry allowing to resolve the entanglement, and basic single equation determining the eigenvalues and eigenstates (polynomials) is obtained. Equations specifying locations of the roots of polynomials in the complex plane are found. Employing numerical analysis the roots of polynomials corresponding to different eigenstates are solved out and the diagrams exhibiting the ordered structure of one-particle eigenstates are depicted.Comment: 11 pages, 4 figure

Synthetic Gauge Fields for Vibrational Excitations of Trapped ions

The vibrations of a collection of ions in a microtrap array can be described in terms of hopping phonons. We show theoretically that the vibrational couplings may be tailored by using a gradient of the microtrap frequencies, together with a periodic driving of the trapping potential. These ingredients allow us to induce effective gauge fields on the vibrational excitations, such that phonons mimic the behavior of charged particles in a magnetic field. In particular, microtrap arrays are ideally suited to realize the famous Aharonov-Bohm effect, and observe the paradigmatic edge states typical from quantum-Hall samples and topological insulators.Comment: replaced with published versio