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
Dec 15, 2003
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
Jul 17, 2003
Probing Anderson localization of light via decay rate statistics
We have studied the distribution of resonance widths P(Γ) in one-, two-, and three-dimensional multiple light scattering systems. P(Γ) should follow a universal power law P(Γ)∼Γ-1 in the localized regime as confirmed by extensive numerical calculations. This behavior can be interpreted as an unambiguous signature of exponential Anderson localization of light in open systems.
Jul 2, 2003
Cluster explosion in an intense laser pulse
Radiation Physics and Chemistry 68, 273 (2003)
Marian Rusek, Hervé Lagadecb and Thomas Blenskib
This manuscript addresses a hot topic in the field of cluster physics: the explosion of rare-gas atomic clusters induced by short, intense laser pulses. Within the Thomas–Fermi model we have developed an numerical approach for an explicitly time-dependent description of small to medium size clusters in 3D. Such an approach, though strongly simplified in comparison to fully quantum-mechanical schemes, is nevertheless expected to yield a qualitatively correct description of the electronic and ionic dynamics of these systems, at a much lower computational cost.
Marian Rusek, Hervé Lagadecb and Thomas Blenskib
This manuscript addresses a hot topic in the field of cluster physics: the explosion of rare-gas atomic clusters induced by short, intense laser pulses. Within the Thomas–Fermi model we have developed an numerical approach for an explicitly time-dependent description of small to medium size clusters in 3D. Such an approach, though strongly simplified in comparison to fully quantum-mechanical schemes, is nevertheless expected to yield a qualitatively correct description of the electronic and ionic dynamics of these systems, at a much lower computational cost.
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