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,
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
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.
Jun 27, 2003
Quantum approach to electromagnetic energy transfer between two dielectric bodies
Phys. Rev. A vol. 68, 043823-1-17 (2003) [b. af.]
Maciej Janowicz, Daniel Reddig, and Martin Holthaus
The problem of radiative heat transfer between two dielectric bodies is analyzed from the point of view of elementary quantum electrodynamics. The dielectric properties of the bodies are assumed to be linear, but dispersion and losses are allowed. Quantization of the electromagnetic field in inhomogeneous, dispersive, and lossy dielectrics is performed with the help of the Huttner-Barnett procedure. The electromagnetic energy flux is expressed through the expectation value of the Poynting vector. In order to compute the Poynting vector, two techniques suitable for nonequilibrium processes are employed: the Heisenberg equations of motion and the diagrammatic Keldysh procedure. They are shown to give identical final results. These quantum-mechanical calculations provide a solid basis for the further, mainly numerical, development of the theory of thermal scanning microscopy.
Maciej Janowicz, Daniel Reddig, and Martin Holthaus
The problem of radiative heat transfer between two dielectric bodies is analyzed from the point of view of elementary quantum electrodynamics. The dielectric properties of the bodies are assumed to be linear, but dispersion and losses are allowed. Quantization of the electromagnetic field in inhomogeneous, dispersive, and lossy dielectrics is performed with the help of the Huttner-Barnett procedure. The electromagnetic energy flux is expressed through the expectation value of the Poynting vector. In order to compute the Poynting vector, two techniques suitable for nonequilibrium processes are employed: the Heisenberg equations of motion and the diagrammatic Keldysh procedure. They are shown to give identical final results. These quantum-mechanical calculations provide a solid basis for the further, mainly numerical, development of the theory of thermal scanning microscopy.
Apr 28, 2003
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.
Mar 22, 2003
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)
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)
Feb 20, 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)
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)
Feb 4, 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
Phys. Rev. A vol. 67, 063816-1-14 (2003) Claudia Eberlein and Maciej Janowicz
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