Harmonically Trapped Classical Gas under Critical Rotation

We study one- and two-dimensional systems of two interacting particles in a time dependent harmonic potential. In a case of one-dimensional geometry a frequency of the potential varies periodically, while in the two-dimen- sional case the harmonic potential rotates with a constant angular velocity. We show that depending on the driving frequency the distance between the particles can either explode or stay bound. Repulsive interaction can prevent the explosion, which seems quite counter-intuitive. Our work is related to Ecole Normale Superieure experiment and shows that the effect found there is purely classical.

Facts and Myths of Enigma: Breaking Stereotypes

Kris Gaj and Arkadiusz Orlowski

In spite of a relatively large number of publications about breakingEnigma by the Allies before and during the World War II, this subject remainsrelatively unknown not only to the general public, but also to peopleprofessionally involved in cryptological research. For example, the story ofEnigma is rarely a part of a modern textbook on cryptology or a modern courseon cryptography and network security. There exist multiple reasons for thissituation. First, there are still a few unresolved issues, resulting from conflictingreports, the lack of reliable sources, and a long period required for declassifyingdocuments related to any cryptological activity during the World War II.Secondly, the issue is highly political, and there is little consensus in weighingthe contribution of all involved countries. Thirdly, many contemporarycryptologists honestly believe that there is little to learn from the analysis of oldcryptosystems, because of the tremendous progress in theory and practice ofcryptography and a little similarity between old and modern ciphers. In thispaper we confront these opinions by presenting a look at the current state ofknowledge about cryptological methods and devices used to break Enigma. Weintroduce all major players involved in these activities, and we make an effortto weigh their original contributions. Finally, we show that the story of Enigmacan still provide contemporary cryptographers with many useful lessonsregarding the way of organizing and building any large-scale security system.

Lect. Notes Comput. Sci. vol. 2656, 106-122 (2003)

Classical properties of quantum scattering

Władysław Żakowicz

Quantum elastic potential scattering of a particle is re-examined taking into account exact solutions of the corresponding Schrödinger equation. In addition to the scattering of stationary plane waves and stationary finite-width wave beams, nonstationary wave packets having finite duration times are studied and some corresponding examples are presented. The role of interference between the scattered wave and the advancing incident beam is studied. Several two-dimensional scattering problems, involving axially symmetric, generic examples of nonuniform attractive and repulsive potentials, are discussed in more detail. This discussion concentrates on finding proper conditions when the solutions of the Schrödinger equation may resemble the corresponding solutions of the classical Newton equation. Examples are shown where such similarities occur.

J. Phys. A vol. 36, 4445-4464 (2003)

Interaction of an atom with a small dispersive and absorptive dielectric body

The paper analyzes the interaction of an atomic system with a quantum damped harmonic oscillator. Such an oscillator is the building block in the recently proposed models of bulk dielectrics and may also serve as a simple model of a small dielectric body. Dispersion and losses are taken into account by assuming the oscillator to be coupled to a zero-temperature reservoir consisting of an infinite system of other harmonic oscillators. The Green’s function of the atomic system is calculated perturbatively when coupled to the bath. The self-energy of the atomic electron is obtained by the partial resummation of perturbation diagrams, and thus energy-level shifts of both ground and excited states of the atom due to the presence of the oscillator are determined. Corrections to the decay rates are also obtained and analyzed as functions of the distance of the atom from the oscillator, and of the coupling of the oscillator to the reservoir.

Phys. Rev. A vol. 67, 063816-1-14 (2003) Claudia Eberlein and Maciej Janowicz

Collective diffusion of O/W(1 1 0) at high coverages: Monte Carlo simulations

Following our previously developed twin-spin model description of the equilibrium properties of the O/W(110) system we study its collective diffusion by means of a Monte Carlo dynamics. It is shown that the collective diffusion coefficient for our model has a different density dependence than this following from other models known in the subject literature. The essential feature of the model, responsible for its different dynamics, are the state dependent interactions. Further assumptions concerning interaction dependent barriers make our results comparable to the experimental data.

Probing the classical field approximation-thermodynamics and decaying vortices

Harry Schmidt, Krzysztof Góra, Filip Floegel, Mariusz Gajda and Kazimierz Rzazewski

We review our version of the classical field approximation to the dynamics of a finite-temperature Bose gas. In the case of a periodic box potential, we investigate the role of the high-momentum cut-off, essential in the method. In particular, we show that the cut-off going to the infinity limit describes the particle number going to infinity with the scattering length going to zero. In this weak-interaction limit, the relative population of the condensate tends to unity. We also show that the cross-over energy, at which the probability distribution of the condensate occupation changes its character, grows with a growing scattering length. In the more physical case of the condensate in the harmonic trap we investigate the dissipative dynamics of a vortex. We compare the decay time and the velocities of the vortex with the available analytic estimates.

J. Opt. B: Quantum Semiclass. Opt. vol. 5, S1-S7 (2003)

Scattering of sulfur ions carbon: Classical-trajectory Monte Carlo results

We analyze classically the scattering of sulfur ions by carbon using the classical-trajectory Monte Carlo method. It is assumed that the scatterer and scattered nuclei are coupled to each other as well as to all electrons, but there is no coupling between electrons themselves. To initialize the state of both atoms, quasiexact energies are used that are obtained from the Dirac-Fock method. Effective charges are used to partially take into account the intra-atomic interactions between electrons. We concentrate on the cross sections for production of vacancies in the K and L shells and capture of electrons to K, L, and M shells of the sulfur ions. The dependence of these cross sections on the energy of the projectile sulfur ions and on the initial charge states of these ions is analyzed. Our results will be helpful in the interpretation of x-ray spectra from highly ionized fast sulfur projectiles passing through a carbon foil.

Phys. Rev. A vol. 67, 012713-1-10 (2003) Slabkowska, Katarzyna, Polasik Marek, Janowicz Maciej

Mesoscopic models of oxygen migration on the Ru(001) surface

Phys. Rev. B 66, 165418 (2002)

Magdalena A. Załuska-Kotur, Zbigniew W. Gortel, and Robert Teshima

Atomic migration within the organized oxygen overlayers on the basal plane of Ru(001) is modeled within phenomenological mesoscopic model accounting for all possible atomic jumps within the adsorbate and capable of accessing several time scales in the migration kinetics. Experimentally observed diffusion and trapping of the isolated oxygen vacancy within the 3O(2×2) overlayer at coverage θ=3/4 are accounted for. The comparison with experiment is used to propose values of parameters for interactions between an atom adsorbed at a hcp site and another one temporarily at some of the neighboring bridge sites. The modeling is extended to the O(2×2) overlayer at θ=1/4 and it is shown that for this structure a competing diffusion channel exists which breaks down the equivalence of the atomic migration behavior between the organized θ=1/4 and θ=3/4 overlayers. For both overlayers simplified effective models are formulated, free of unobservable metastable configurations and unobservable time scales. Considerations for the ideal O(2×1) rowlike overlayer at θ=1/2 confirm that occasional jumps of the oxygen atoms to one side of the rows should be observable in the STM images for this overlayer in contrast to the θ=1/4 and 3/4 overlayers for which an excess atom or a vacancy, respectively, are necessary to initiate observable atomic migration processes.

Graphical examples of geometrical and wave optics

Władysław Żakowicz

A simple method of the description of optical pulses of finite dimensions and finite duration time is presented. The pulses are given by superpositions of the known analytical as well as numerical solutions of the Maxwell equations. The examples show optical properties of scattering in detail. In the general case the wide pulses split in the scattering processes. The description of these phenomena requires a full wave approach. The pulses (or their fragments) that do not split but move smoothly through the optical system (or its fragment) may be described with the help of the geometrical optics theory.

Acta Phys. Polon. B 33, 2059 (2002)

Collective diffusion in a twin-spin model of O/W (110)

Following our previously developed twin-spin model description of the equilibrium properties of the O/W(110) system we study its collective diffusion by means of a Monte Carlo dynamics. It is shown that the collective diffusion coefficient for our model has a different density dependence than this following from other models known in the subject literature. The essential feature of the model, responsible for its different dynamics, are the state dependent interactions. Further assumptions concerning interaction dependent barriers make our results comparable to the experimental data.

Phys. Rev. B vol. 67, 155406-1-7 (2003) Magdalena A. Zaluska-Kotur, Stanislaw Krukowski, Lukasz A. Turski