Ejection Energy of Photoelectrons in Strong Field Ionization

We show that zero ejection energy of the photoelectrons is classically impossible for hydrogen-like ions, even when field ionization occurs adiabatically. To prove this we transform the basic equations to those describing two 2D anharmonic oscillators. The same method yields an alternative way to derive the anomalous critical field of hydrogen-like ions. The analytical results are confirmed and illustrated by numerical simulations. PACS Number: 32.80.RmComment: 7 pages, REVTeX, postscript file including the figures is available at http://www.physik.th-darmstadt.de/tqe/dieter/publist.html or via anonymous ftp from ftp://tqe.iap.physik.th-darmstadt.de/pub/dieter/publ_I_pra_pre.ps, accepted for publication in Phys. Rev.

The Zipf law for random texts with unequal probabilities of occurrence of letters and the Pascal pyramid

We model the generation of words with independent unequal probabilities of occurrence of letters. We prove that the probability $p(r)$ of occurrence of words of rank $r$ has a power asymptotics. As distinct from the paper published earlier by B. Conrad and M. Mitzenmacher, we give a brief proof by elementary methods and obtain an explicit formula for the exponent of the power law.Comment: 4 page

Fictitious Level Dynamics: A Novel Approach to Spectral Statistics in Disordered Conductors

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form factor in two ways. First, describing the dynamics using a Fokker-Planck equation, we make a physically motivated decoupling, obtaining the spectral correlations in terms of the quantum return probability. Second, from an identity which we derive between two- and three-particle correlation functions, we make a mathematically controlled decoupling to obtain the same result. We also calculate weak localization corrections to this result, and show for two dimensional systems (which are of most interest) that corrections vanish to three-loop order.Comment: 35 pages in REVTeX format including 10 postscript figures; to be published in a special issue (on Topics in Mesoscopic Physics) of the Journal of Mathematical Physics, October 199

Crossover from diffusive to strongly localized regime in two-dimensional systems

We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean conductance, g, in agreement with the strong version of the single-parameter scaling hypothesis. The distribution seems to change drastically at a critical value very close to one. For conductances larger than this critical value, the distribution is roughly Gaussian while for smaller values it resembles a log-normal distribution. The two distributions match at the critical point with an often appreciable change in behavior. This matching implies a jump in the first derivative of the distribution which does not seem to disappear as system size increases. We have also studied 1/g corrections to the skewness to quantify the deviation of the distribution from a Gaussian function in the diffusive regime.Comment: 4 pages, 4 figure