Władysław Żakowicz
The extinction paradox, the difference of classical and quantum scattering cross-sections for the scattering of particles by a rigid sphere (σQ=2πa2=2σC for ka>>1), is analyzed in a simpler 2D model of a rigid cylindrical potential. Rigorous solutions of the Schrödinger equation for particle beams, including also finite width beams, are derived and employed in the description of the scattering process. The scattering particle fluxes, with a thorough treatment of the forward directions, are being studied. It is pointed out that for wide beams (w>>a) the scattered flux can reach the value determined by the quantum theory, provided that it is measured at distances R>>waλ. Moderately narrow beams, but also that the transverse width of beams of de Broglie's waves is small.
Acta Phys. Polon. A 101, 369 (2002)
Jun 23, 2001
May 10, 2001
Light rays and imaging in wave optics
Władysław Żakowicz
An interpretation of focusing and image formation on scattering of electromagnetic waves by a dielectric cylinder (a cylindrical lens) is proposed on the basis of the full Maxwell theory. It is centered on analysis of the behavior of integral curves of the Poynting vector here called wave rays. These wave rays cannot intersect so that the focusing and imaging spots are identified with regions of high flow concentration. Two-dimensional examples of wave rays and wave fronts in the scattering of plane and cylindrical electromagnetic waves as well as of Gaussian beams by a dielectric cylinder derived from rigorous solution of the Maxwell equations for incident waves perpendicular to and uniform along the scatterer are given. Their qualitative comparison with geometrical and diffraction approximations are provided. Fixed points and vortex structure of the Poynting flow are investigated. An example of (Gaussian-beam) scattering with transparent multiple internal reflections and multiple wave splitting is given.
Phys. Rev. E 64, 066610 (2001)
An interpretation of focusing and image formation on scattering of electromagnetic waves by a dielectric cylinder (a cylindrical lens) is proposed on the basis of the full Maxwell theory. It is centered on analysis of the behavior of integral curves of the Poynting vector here called wave rays. These wave rays cannot intersect so that the focusing and imaging spots are identified with regions of high flow concentration. Two-dimensional examples of wave rays and wave fronts in the scattering of plane and cylindrical electromagnetic waves as well as of Gaussian beams by a dielectric cylinder derived from rigorous solution of the Maxwell equations for incident waves perpendicular to and uniform along the scatterer are given. Their qualitative comparison with geometrical and diffraction approximations are provided. Fixed points and vortex structure of the Poynting flow are investigated. An example of (Gaussian-beam) scattering with transparent multiple internal reflections and multiple wave splitting is given.
Phys. Rev. E 64, 066610 (2001)
Apr 5, 2001
Fluctuations of ideal Bose-Einstein condensate
Mol. Phys. Rep. Suppl. 1(New Trends in Atomic Physics,Wolfgang Paul Colloquium in memoriam of Wolfgang Paul), 46 (2001)
M. Gajda, Z. Idziaszek, K. Rzążewski, and P. Navez
M. Gajda, Z. Idziaszek, K. Rzążewski, and P. Navez
Jan 19, 2001
Multi-mode description of an interacting Bose-Einstein condensate
Opt. Express 8, 92 (2001)
Krzysztof Goral, Mariusz Gajda, and Kazimierz Rzazewski
We study the equilibrium dynamics of a weakly interacting Bose-Einstein condensate trapped in a box. In our approach we use a semiclassical approximation similar to the description of a multi-mode laser. In dynamical equations derived from a full N-body quantum Hamiltonian we substitute all creation (and annihilation) operators (of a particle in a given box state) by appropriate c-number amplitudes. The set of nonlinear equations obtained in this way is solved numerically. We show that on the time scale of a few miliseconds the system exhibits relaxation -- reaches an equilibrium with populations of different eigenstates fluctuating around their mean values.
Krzysztof Goral, Mariusz Gajda, and Kazimierz Rzazewski
We study the equilibrium dynamics of a weakly interacting Bose-Einstein condensate trapped in a box. In our approach we use a semiclassical approximation similar to the description of a multi-mode laser. In dynamical equations derived from a full N-body quantum Hamiltonian we substitute all creation (and annihilation) operators (of a particle in a given box state) by appropriate c-number amplitudes. The set of nonlinear equations obtained in this way is solved numerically. We show that on the time scale of a few miliseconds the system exhibits relaxation -- reaches an equilibrium with populations of different eigenstates fluctuating around their mean values.
Jan 10, 2001
Ionization of hydrogen atoms by intense vacuum ultraviolet radiation
J. Phys. B 34, 2245 (2001)
Jaroslaw Bauer, Lukasz Plucinski, Bernard Piraux, Robert Potvliege, Mariusz Gajda and Jacek Krzywinski
We study the ionization of hydrogen atoms by an intense pulsed beam of photons with energies of 17 or 50 eV. The work is motivated by the demonstration of the free-electron laser (FEL) action at the DESY Laboratory. The parameters chosen for the incident field are in the regime accessible by the FEL. Ionization yields are obtained within three different approaches, namely the strong-field approximation, the Floquet method and a numerical solution of the time-dependent Schrödinger equation. A marked stabilization effect for 50 eV photons is shown.
Jaroslaw Bauer, Lukasz Plucinski, Bernard Piraux, Robert Potvliege, Mariusz Gajda and Jacek Krzywinski
We study the ionization of hydrogen atoms by an intense pulsed beam of photons with energies of 17 or 50 eV. The work is motivated by the demonstration of the free-electron laser (FEL) action at the DESY Laboratory. The parameters chosen for the incident field are in the regime accessible by the FEL. Ionization yields are obtained within three different approaches, namely the strong-field approximation, the Floquet method and a numerical solution of the time-dependent Schrödinger equation. A marked stabilization effect for 50 eV photons is shown.
Nov 9, 2000
On coherence of Bose fields
Mariusz Gajda, Magdalena Zaluska-Kotur, and Jan Mostowski
We study a system of interacting bosons at zero temperature in an atomic trap. Using wave function that models the ground state of interacting bosons we examine the concepts of the order parameter, off-diagonal order and coherence of the system. We suggest that the coherence length becomes much smaller than the size of the system if the number of trapped particles exceeds a certain limit. This behavior is related to the unavoidable existence of two different length scales -- one determined by the external potential and the second one depending on the two-body forces.
Opt. Express 8, 106 (2001)
We study a system of interacting bosons at zero temperature in an atomic trap. Using wave function that models the ground state of interacting bosons we examine the concepts of the order parameter, off-diagonal order and coherence of the system. We suggest that the coherence length becomes much smaller than the size of the system if the number of trapped particles exceeds a certain limit. This behavior is related to the unavoidable existence of two different length scales -- one determined by the external potential and the second one depending on the two-body forces.
Opt. Express 8, 106 (2001)
Oct 5, 2000
Correlations in financial time series: established versus emerging markets
Eur. Phys. J. B 20, 527 (2001)
M. Beben and A. Orłowski
Long-time correlations in both well-developed and emerging market indexes are studied. The Hurst exponent as well as detrended fluctuations analysis (DFA) are used as technical tools. Some features that seem to be specific for developing markets are discovered and briefly discussed.
M. Beben and A. Orłowski
Long-time correlations in both well-developed and emerging market indexes are studied. The Hurst exponent as well as detrended fluctuations analysis (DFA) are used as technical tools. Some features that seem to be specific for developing markets are discovered and briefly discussed.
Jul 12, 2000
Squeezing of electromagnetic field in a cavity by electrons in Trojan states
Piotr Kochański, Zofia Bialynicka-Birula, and Iwo Bialynicki-Birula
The notion of the Trojan state of a Rydberg electron, introduced by I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly [Phys. Rev. Lett. 73, 1777 (1994)] is extended to the case of an electromagnetic field quantized in a cavity. The shape of the electronic wave packet describing the Trojan state is practically the same as in the previously studied externally driven system. The fluctuations of the quantized electromagnetic field around its classical value exhibit strong squeezing. The emergence of Trojan states in the cylindrically symmetrical system is attributed to spontaneous symmetry breaking.
Phys. Rev. A 63, 013811 (2001)
The notion of the Trojan state of a Rydberg electron, introduced by I. Bialynicki-Birula, M. Kaliński, and J. H. Eberly [Phys. Rev. Lett. 73, 1777 (1994)] is extended to the case of an electromagnetic field quantized in a cavity. The shape of the electronic wave packet describing the Trojan state is practically the same as in the previously studied externally driven system. The fluctuations of the quantized electromagnetic field around its classical value exhibit strong squeezing. The emergence of Trojan states in the cylindrically symmetrical system is attributed to spontaneous symmetry breaking.
Phys. Rev. A 63, 013811 (2001)
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