Piotr Łukasiewicz and Arkadiusz Orłowski
The results showing relationships between distributions of individual incomes and incomes of two-earners households are presented. It is shown that individual incomes are very well described by Dagum's distributions. Income distributions in two quite different countries (USA and Poland) are studied for comparison. Obtained results show very striking and interesting differences.
Physica A Vol. 344, 1-2
Aug 23, 2004
Aug 20, 2004
Application of bootstrap to detecting chaos in financial time series
Katarzyna Brzozowska-Rup and Arkadiusz Orłowski
A moving blocks bootstrap procedure is used to investigate the dynamics of nominal exchange rates and the return rates of the US Dollar against the Polish Zloty. The problem if these financial time series exhibit chaotic behavior is undertaken. A possibility of detecting the presence of a positive Lyapunov exponent is studied.
Physica A. 344, 1-2
A moving blocks bootstrap procedure is used to investigate the dynamics of nominal exchange rates and the return rates of the US Dollar against the Polish Zloty. The problem if these financial time series exhibit chaotic behavior is undertaken. A possibility of detecting the presence of a positive Lyapunov exponent is studied.
Physica A. 344, 1-2
Jul 22, 2004
Classical-field approximation for cold weakly interacting bosons without free parameters
Łukasz Zawitkowski, Mirosław Brewczyk, Mariusz Gajda and Kazimierz Rzążewski
The classical-field approximation to cold weakly interacting bosons allows for a unified treatment of condensed and uncondensed parts of the system. Until now, however, the quantitative predictions were limited by a dependence of the results on a grid chosen for numerical implementation of the method. In this paper, we propose replacing this unphysical ambiguity by an additional postulate: the temperature of the gas at thermal equilibrium should be the same as that of an ideal Bose gas with the same fraction of condensed atoms. As it turns out, with this additional assumption, nearly all atoms are within the classical fields, thus the method applies to the whole system.
Phys. Rev. A 70, 033614 (2004)
The classical-field approximation to cold weakly interacting bosons allows for a unified treatment of condensed and uncondensed parts of the system. Until now, however, the quantitative predictions were limited by a dependence of the results on a grid chosen for numerical implementation of the method. In this paper, we propose replacing this unphysical ambiguity by an additional postulate: the temperature of the gas at thermal equilibrium should be the same as that of an ideal Bose gas with the same fraction of condensed atoms. As it turns out, with this additional assumption, nearly all atoms are within the classical fields, thus the method applies to the whole system.
Phys. Rev. A 70, 033614 (2004)
May 17, 2004
Temperature-dependent Bogoliubov approximation in the classical field approach to weakly interacting Bose gases.
Mirosław Brewczyk, Peter Borowski, Mariusz Gajda and Kazimierz Rzążewski
A classical field approximation to the finite temperature microcanonical thermodynamics of weakly interacting Bose gases is applied to the idealized case of atoms confined in a box with periodic boundary conditions. The whole isolated system is described by a set of classical amplitudes. We show that if the system is in equilibrium the classical amplitudes follow the equipartition theorem which allows us to assign a unique temperature to each given energy state. We also analyse the spectral properties of classical amplitudes and obtain nonperturbative results for the chemical potential as well as temperature-dependent Bogoliubov frequencies and their damping rates. Where available, we make comparison with the analytical estimates of these quantities.
J. Phys. B: At. Mol. Opt. Phys. 37 2725-2738
A classical field approximation to the finite temperature microcanonical thermodynamics of weakly interacting Bose gases is applied to the idealized case of atoms confined in a box with periodic boundary conditions. The whole isolated system is described by a set of classical amplitudes. We show that if the system is in equilibrium the classical amplitudes follow the equipartition theorem which allows us to assign a unique temperature to each given energy state. We also analyse the spectral properties of classical amplitudes and obtain nonperturbative results for the chemical potential as well as temperature-dependent Bogoliubov frequencies and their damping rates. Where available, we make comparison with the analytical estimates of these quantities.
J. Phys. B: At. Mol. Opt. Phys. 37 2725-2738
May 7, 2004
Dynamics of Argon Clusters in an Intense Laser Pulse: Bloch-Like Hydrodynamic Model
M. Rusek and A. Orłowski
The dynamics of small (≤55 atoms) argon clusters ionized by an intense, infrared, femtosecond laser pulse is studied using a Bloch-like hydrodynamic model. Evolution of both free electrons and ions formed in the cluster explosion process is examined. Oscillations of the electron cloud in a rare-gas atomic cluster are described as a motion of a fluid obeying Bloch-like hydrodynamic equations. Our theoretical approach includes all possible ionization mechanisms: tunnel (or field) ionization both by an external laser field, and by an internal field due to the space-charge distribution inside the cluster, as well as electron-impact (or collisional) ionization. The results of our simulations are compared both with experimental findings and with predictions of other theoretical models.
Acta Phys. Polonica A, Vol. 106 No 1
The dynamics of small (≤55 atoms) argon clusters ionized by an intense, infrared, femtosecond laser pulse is studied using a Bloch-like hydrodynamic model. Evolution of both free electrons and ions formed in the cluster explosion process is examined. Oscillations of the electron cloud in a rare-gas atomic cluster are described as a motion of a fluid obeying Bloch-like hydrodynamic equations. Our theoretical approach includes all possible ionization mechanisms: tunnel (or field) ionization both by an external laser field, and by an internal field due to the space-charge distribution inside the cluster, as well as electron-impact (or collisional) ionization. The results of our simulations are compared both with experimental findings and with predictions of other theoretical models.
Acta Phys. Polonica A, Vol. 106 No 1
Apr 14, 2004
Soliton Trains in Bose-Fermi Mixtures
T. Karpiuk, M. Brewczyk, S. Ospelkaus-Schwarzer, K. Bongs, M. Gajda, and K. Rzążewski
We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.
Phys. Rev. Let.Vol. 93 Issue 10
We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.
Phys. Rev. Let.Vol. 93 Issue 10
Mar 30, 2004
Explosion of Atom Clusters in a Free-Electron Intense Laser Pulse
M. Rusek and A. Orłowski
The explosion of rare-gas atomic clusters induced by short, intense X-ray pulses generated by a free-electron laser is studied. A numerical approach for an explicitly time-dependent description of small to medium size clusters in 3D is developed within the Thomas--Fermi model. 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.
Acta Phys. Polonica A, Vol.105 No. 5
The explosion of rare-gas atomic clusters induced by short, intense X-ray pulses generated by a free-electron laser is studied. A numerical approach for an explicitly time-dependent description of small to medium size clusters in 3D is developed within the Thomas--Fermi model. 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.
Acta Phys. Polonica A, Vol.105 No. 5
Mar 18, 2004
Jan 5, 2004
Scattering of plane wave packets by a rigid cylinder: a contribution to the quantum scattering theory
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
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
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