Władysław Żakowicz
Time-dependent scattering of finite duration wave packets on a rigid cylinder is studied using exact solutions of the corresponding Schrödinger equation. The similarity between the time evolution of the total wavefunction and evolution of the corresponding classical ensemble of particles is exposed. Special attention is paid to a discussion of the differences between the total wavefunction dynamics and the dynamics of the scattered part of the wavefunction, the part which is commonly used for the evaluation of scattering cross-sections. This discussion emphasizes the necessity of using the total wavefunction in the description of scattering.
J. Phys. B: At. Mol. Opt. Phys. 37 L153-L159
Jan 5, 2004
Dec 26, 2003
Fluctuation dynamics of exchange rates on Polish financial market.
A. Orłowski, Z.R. Struzik, E. Syczewska and M.A. Załuska-Kotur
We show results of local fluctuation analysis, probability distributions, and fractional integration analysis for nominal exchange rates of the Polish zloty versus two foreign currencies (US dollar and German mark/euro). The results confirm the rapid change of the volatility pattern in August 1997. We compare the type of the fluctuation behavior before and after this date.
Physica A. 344, Issues 1-2,
We show results of local fluctuation analysis, probability distributions, and fractional integration analysis for nominal exchange rates of the Polish zloty versus two foreign currencies (US dollar and German mark/euro). The results confirm the rapid change of the volatility pattern in August 1997. We compare the type of the fluctuation behavior before and after this date.
Physica A. 344, Issues 1-2,
Dec 15, 2003
Application of the ultrametric distance to portfolio taxonomy. Critical approach and comparison with other methods
Urszula Skórnik-Pokarowska and Arkadiusz Orłowski
We calculate the ultrametric distance between the pairs of stocks that belong to the same portfolio. The ultrametric distance allows us to distinguish groups of shares that are related. In this way, we can construct a portfolio taxonomy that can be used for constructing an efficient portfolio. We also construct a portfolio taxonomy based not only on stock prices but also on economic indices such as liquidity ratio, debt ratio and sales profitability ratio. We show that a good investment strategy can be obtained by applying to the portfolio chosen by the taxonomy method the so-called Constant Rebalanced Portfolio.
Physica A. Vol. 344, Issues 1-2
We calculate the ultrametric distance between the pairs of stocks that belong to the same portfolio. The ultrametric distance allows us to distinguish groups of shares that are related. In this way, we can construct a portfolio taxonomy that can be used for constructing an efficient portfolio. We also construct a portfolio taxonomy based not only on stock prices but also on economic indices such as liquidity ratio, debt ratio and sales profitability ratio. We show that a good investment strategy can be obtained by applying to the portfolio chosen by the taxonomy method the so-called Constant Rebalanced Portfolio.
Physica A. Vol. 344, Issues 1-2
Nov 22, 2003
Nov 19, 2003
Two-photon Jaynes-Cummings model without rotating wave approximation
Maciej Janowicz and Arkadiusz Orłowski
The three-level atomic system interacting with one mode of the electromagnetic field in a Ξ-configuration is investigated. Effective Hamiltonians for two-photon processes without the rotating wave approximation are obtained by application of the perturbation method of multiple time scales. Some inaccuracies in the form of Hamiltonians of this type recently presented are pointed out and corrected.
A four-level Xi-system: Exact solvability and effective evolution operators via multiple scales
Properties of a four-level atomic system interacting with one and two modes of the electromagneticfield in a “Ξ”-configuration are investigated. By linearization of the Hamiltonians we show that the corresponding mathematical models are exactly solvable. To obtain simpler effective Hamiltonians the perturbative method of multiple scales is applied. The lowest-order corrections to the resulting effective evolution operators are also calculated.
Nov 5, 2003
Optimization of Directional Antennas in Two-Dimensional Artificial Dielectrics
M. Janowicz, M. Rusek and A. Orłowski
We investigate numerically the problem of optimization of directional characteristics of dipole antennas located inside, or in the vicinity of, photonic crystals or more general artificial dielectrics, made of very thin perfectly conducting wires. We concentrate on two-dimensional propagation. Simulated annealing is used to find the distribution of wires which optimizes the directional pattern. It is demonstrated that high directivity can be obtained for systems containing a very small number of elements provided that the size and shape of the unit cell as well as the position of the radiating source with respect to the crystal are optimized. Building up of the radiation pattern is also illustrated with the help of the wave-optical rays.
Acta Physica Polonica A Vol. 105 No. 3
We investigate numerically the problem of optimization of directional characteristics of dipole antennas located inside, or in the vicinity of, photonic crystals or more general artificial dielectrics, made of very thin perfectly conducting wires. We concentrate on two-dimensional propagation. Simulated annealing is used to find the distribution of wires which optimizes the directional pattern. It is demonstrated that high directivity can be obtained for systems containing a very small number of elements provided that the size and shape of the unit cell as well as the position of the radiating source with respect to the crystal are optimized. Building up of the radiation pattern is also illustrated with the help of the wave-optical rays.
Acta Physica Polonica A Vol. 105 No. 3
Aug 29, 2003
Vortex lines of the electromagnetic field
Iwo Bialynicki-Birula and Zofia Bialynicka-Birula
A new method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann–Silberstein vector is multiplied by a complex scalar function . Such a multiplication may lead to new solutions of the Maxwell equations only when the electromagnetic field is null, i.e. when both relativistic invariants vanish. In general, zeros of the function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.
Phys. Rev. A vol. 67, 062114-1-8 (2003)
A new method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann–Silberstein vector is multiplied by a complex scalar function . Such a multiplication may lead to new solutions of the Maxwell equations only when the electromagnetic field is null, i.e. when both relativistic invariants vanish. In general, zeros of the function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.
Phys. Rev. A vol. 67, 062114-1-8 (2003)
Aug 18, 2003
Chemical diffusion in an interacting lattice gas: Analytic theory and simple applications
Zbigniew W. Gortel and Magdalena A. Załuska-Kotur
A variational approach to microscopic kinetics of an interacting lattice gas is presented. It accounts for the equilibrium correlations in the system and allows one to derive an algebraic expression for the particle density (coverage) dependent chemical diffusion coefficient for a wide variety of interaction models. Detailed derivation is presented for a one dimensional case for which the results are compared with the results of Monte Carlo simulations. Generalization and an application to the simplest case of the two dimensional lattice gas is briefly described.
Phys. Rev. B 70, 125431 (2004)
A variational approach to microscopic kinetics of an interacting lattice gas is presented. It accounts for the equilibrium correlations in the system and allows one to derive an algebraic expression for the particle density (coverage) dependent chemical diffusion coefficient for a wide variety of interaction models. Detailed derivation is presented for a one dimensional case for which the results are compared with the results of Monte Carlo simulations. Generalization and an application to the simplest case of the two dimensional lattice gas is briefly described.
Phys. Rev. B 70, 125431 (2004)
Jul 28, 2003
Pair-correlation function of a metastable helium Bose-Einstein condensate
The pair-correlation function is one of the basic quantities to characterize the coherence properties of a Bose-Einstein condensate. We calculate this function in the experimentally important case of a zero temperature Bose-Einstein condensate in a metastable triplet helium state using the variational method with a pair-excitation ansatz. We compare our result with a pair-correlation function obtained for the hard-sphere potential with the same scattering length. Both functions are practically indistinguishable for distances greater than the scattering length. At smaller distances, due to interatomic interactions, the helium condensate shows strong correlations
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