Surf. Sc. 507, 150 (2002)
ZAŁUSKA-KOTUR M. A., ŁUSAKOWSKI A., KRUKOWSKI S.,TURSKI Ł. A.
We study two-dimensional lattice gas with interaction dependent rates of the particle diffusion and desorption. We run Monte Carlo dynamics and study decay of harmonic perturbation of the profile. In the close to equilibrium, long-wavelength limit dynamics separate into desorption process, independent of the perturbation wave vector k, and proportional to k2 collective diffusion. In most cases both processes can be analyzed separately. We show that in some highly ordered systems, like (2 x 2) ordered structure of repulsive square lattice gas, one process can change characteristics of the other. We observe that the diffusion coefficient becomes slower when the desorption process is more rapid. This effect is even more visible in higher temperatures. As a result the measured activation energy of the diffusion process can be changed by the presence of the rapid desorption and adsorption processes even when system is close to equilibrium
Mar 12, 2002
Thermodynamics of an interacting trapped Bose-Einstein gas in the classical field approximation
Phys. Rev. A 66, 051602 (2002)
Krzysztof Góral, Mariusz Gajda and Kazimierz Rzążewski
We present a convenient technique describing the condensate in dynamical equilibrium with the thermal cloud, at temperatures close to the critical one. We show that the whole isolated system may be viewed as a single classical field undergoing nonlinear dynamics leading to a steady state. In our procedure it is the observation process and the finite detection time that allow for splitting the system into the condensate and the thermal cloud.
Krzysztof Góral, Mariusz Gajda and Kazimierz Rzążewski
We present a convenient technique describing the condensate in dynamical equilibrium with the thermal cloud, at temperatures close to the critical one. We show that the whole isolated system may be viewed as a single classical field undergoing nonlinear dynamics leading to a steady state. In our procedure it is the observation process and the finite detection time that allow for splitting the system into the condensate and the thermal cloud.
Jan 21, 2002
Center-of-mass motion in the many-body theory of Bose-Einstein condensates
Iwo Białynicki-Birula and Zofia Białynicka-Birula
The method of generating a family of new solutions starting from any wave function satisfying the nonlinear Schrödinger equation in a harmonic potential proposed recently [J. J. García-Ripoll, V. M. Pérez-García, and V. Vekslerchik, Phys. Rev. E 64, 056602 (2001)] is extended to the many-body theory of mutually interacting particles. Our method is based on a generalization of the displacement operator known in quantum optics, and results in the separation of the center-of-mass motion from the internal dynamics of many-body systems. The center-of-mass motion is analyzed for an anisotropic rotating trap and a region of instability for intermediate rotational velocities is predicted.
Phys. Rev. A 65, 063606 (2002)
The method of generating a family of new solutions starting from any wave function satisfying the nonlinear Schrödinger equation in a harmonic potential proposed recently [J. J. García-Ripoll, V. M. Pérez-García, and V. Vekslerchik, Phys. Rev. E 64, 056602 (2001)] is extended to the many-body theory of mutually interacting particles. Our method is based on a generalization of the displacement operator known in quantum optics, and results in the separation of the center-of-mass motion from the internal dynamics of many-body systems. The center-of-mass motion is analyzed for an anisotropic rotating trap and a region of instability for intermediate rotational velocities is predicted.
Phys. Rev. A 65, 063606 (2002)
Dec 2, 2001
Twin spin model of surface phase transitions in O/W(110)
Phys. Rev. B 65, 045404 (2002)
Magdalena A. Załuska-Kotur, Stanisław Krukowski, Zbigniew Romanowski, Łukasz A. Turski
A model describing surface phase transitions in an O/W(110) system is proposed. The model is based on the hourglass structure of adsorption sites of oxygen on tungsten surface. The hourglass structure of the site in the O/W(110) system has been confirmed by quantum mechanical density functional theory (DFT) calculations. The results of DFT calculations indicate that the saddle point at the center has the energy 0.2 eV higher than two symmetric minima. An essential ingredient of the model is the assumption that the interaction of O atom with the other O atom, located in nn site, lifts the degeneracy of the two energy minima, converting the hourglass structure of the adsorption site to a single state site. The O/W(110) adsorption model can be projected onto a system consisting of double spins distributed on a two-dimensional square lattice. The properly chosen two-body interactions in the square lattice double-spin system are capable of recovering all phase transitions that are observed in the O/W(110) system. Due to well known mapping between spin and the lattice gas systems, the proposed model can be used to describe multidomain structure in the O/W(110) system
Magdalena A. Załuska-Kotur, Stanisław Krukowski, Zbigniew Romanowski, Łukasz A. Turski
A model describing surface phase transitions in an O/W(110) system is proposed. The model is based on the hourglass structure of adsorption sites of oxygen on tungsten surface. The hourglass structure of the site in the O/W(110) system has been confirmed by quantum mechanical density functional theory (DFT) calculations. The results of DFT calculations indicate that the saddle point at the center has the energy 0.2 eV higher than two symmetric minima. An essential ingredient of the model is the assumption that the interaction of O atom with the other O atom, located in nn site, lifts the degeneracy of the two energy minima, converting the hourglass structure of the adsorption site to a single state site. The O/W(110) adsorption model can be projected onto a system consisting of double spins distributed on a two-dimensional square lattice. The properly chosen two-body interactions in the square lattice double-spin system are capable of recovering all phase transitions that are observed in the O/W(110) system. Due to well known mapping between spin and the lattice gas systems, the proposed model can be used to describe multidomain structure in the O/W(110) system
Nov 15, 2001
Statistical physics of Bose-Einstein condensation
Acta Phys. Polon. A 100, 7 Suppl.S. (2001)
M. Gajda and K. Rzążewski
We review a progress in understanding of statistical properties of a quantum degenerate Bose gas. We show how the Maxwell demon ensemble helps to compute fluctuations of the Bose--Einstein condensate of an ideal Bose gas according to the microcanonical ensemble. Then, we review a method of measuring these fluctuations. Using a soluble model of interacting Bose gas we also stress the importance of higher-order correlation functions. Finally, we review our novel computational method of studying an interacting Bose gas near its critical temperature.
M. Gajda and K. Rzążewski
We review a progress in understanding of statistical properties of a quantum degenerate Bose gas. We show how the Maxwell demon ensemble helps to compute fluctuations of the Bose--Einstein condensate of an ideal Bose gas according to the microcanonical ensemble. Then, we review a method of measuring these fluctuations. Using a soluble model of interacting Bose gas we also stress the importance of higher-order correlation functions. Finally, we review our novel computational method of studying an interacting Bose gas near its critical temperature.
Jul 26, 2001
Soluble model of interacting bosons trapped in harmonic potential: Quality of Bogoliubov approximation
M.A. Załuska-Kotur, M. Gajda and J. Mostowski
We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for a detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactly soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives a quite accurate description of the system in the limit of weak interactions.
Acta Phys. Polon. A 100, 485 (2001)
We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for a detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactly soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives a quite accurate description of the system in the limit of weak interactions.
Acta Phys. Polon. A 100, 485 (2001)
Motion of vortex lines in nonlinear wave mechanics
Iwo Białynicki-Birula and Zofia Białynicka-Birula
We extend our previous analysis of the motion of vortex lines [I. Bialynicki-Birula, Z. Bialynicka-Birula, and C. Śliwa, Phys. Rev. A 61, 032110 (2000)] from linear to a nonlinear Schrödinger equation with harmonic forces. We also argue that under certain conditions, the influence of the contact nonlinearity on the motion of vortex lines is negligible. The present analysis adds new weight to our previous conjecture that the topological features of vortex dynamics are to a large extent universal.
Phys. Rev. A 65, 014101 (2002)
We extend our previous analysis of the motion of vortex lines [I. Bialynicki-Birula, Z. Bialynicka-Birula, and C. Śliwa, Phys. Rev. A 61, 032110 (2000)] from linear to a nonlinear Schrödinger equation with harmonic forces. We also argue that under certain conditions, the influence of the contact nonlinearity on the motion of vortex lines is negligible. The present analysis adds new weight to our previous conjecture that the topological features of vortex dynamics are to a large extent universal.
Phys. Rev. A 65, 014101 (2002)
Jul 3, 2001
Spontaneous Emission by Atoms in Simple Environments
Władysław Żakowicz
Spontaneous radiation by atoms in the presence of the planar dielectric--vacuum interface, planar dielectric waveguides and cylindrical dielectric waveguides are discussed in the frame of cavity quantum electrodynamics in full analogy with that in free space. However, quantization of the electromagnetic field should be based on the modes appropriate to the selected space structure. These quantizations are usually based on incoming waves. However, the discussion of the angular intensity pattern of spontaneous emission can be simplified if the quantization is based on outgoing modes. Using these outgoing photons the angular emission radiation pattern has been obtained from a straightforward application of the perturbative method of the quantum radiation theory. Adding a contribution of the waveguiding photons attached to the waveguides (when they are present) the total emission of the spontaneous radiation and excitation decay rates of atoms radiating in these systems have been derived.
Acta Phys. Polon. A 101, 119 (2002)
Spontaneous radiation by atoms in the presence of the planar dielectric--vacuum interface, planar dielectric waveguides and cylindrical dielectric waveguides are discussed in the frame of cavity quantum electrodynamics in full analogy with that in free space. However, quantization of the electromagnetic field should be based on the modes appropriate to the selected space structure. These quantizations are usually based on incoming waves. However, the discussion of the angular intensity pattern of spontaneous emission can be simplified if the quantization is based on outgoing modes. Using these outgoing photons the angular emission radiation pattern has been obtained from a straightforward application of the perturbative method of the quantum radiation theory. Adding a contribution of the waveguiding photons attached to the waveguides (when they are present) the total emission of the spontaneous radiation and excitation decay rates of atoms radiating in these systems have been derived.
Acta Phys. Polon. A 101, 119 (2002)
Jun 28, 2001
Chemical surface diffusion analysis by the time evolution of density profiles. The Monte Carlo simulations
Vacuum 63, 127 (2001)
M. A. Zauska-Kotura, A. Usakowskia, S. Krukowski, Z. Romanowskic and . A. Turski
We present two methods of the Monte Carlo analysis of the chemical diffusion processes on solid surfaces. First method is based on the analysis of the decay of sinusoidal adsorbate density perturbations; the second one uses the Boltzmann–Matano procedure applied to the step-like density profile. The usefulness of both these methods is shown on extraction of the chemical diffusion coefficient from the numerical results.We have applied our two methods to various realizations of 2D lattice gas systems, simulating diffusion of adsorbate on surfaces of crystal having hexagonal symmetry of adsorption sites. In particular we were interested in the dependence of the diffusion process on strength and sign of the interactions of the jumping adatom at its activated state. We have compared systems with the same equilibrium properties (same ordered and disordered phase structure) and different interaction-dependent barriers for attractive and repulsive forces.
M. A. Zauska-Kotura, A. Usakowskia, S. Krukowski, Z. Romanowskic and . A. Turski
We present two methods of the Monte Carlo analysis of the chemical diffusion processes on solid surfaces. First method is based on the analysis of the decay of sinusoidal adsorbate density perturbations; the second one uses the Boltzmann–Matano procedure applied to the step-like density profile. The usefulness of both these methods is shown on extraction of the chemical diffusion coefficient from the numerical results.We have applied our two methods to various realizations of 2D lattice gas systems, simulating diffusion of adsorbate on surfaces of crystal having hexagonal symmetry of adsorption sites. In particular we were interested in the dependence of the diffusion process on strength and sign of the interactions of the jumping adatom at its activated state. We have compared systems with the same equilibrium properties (same ordered and disordered phase structure) and different interaction-dependent barriers for attractive and repulsive forces.
Jun 23, 2001
On the extinction paradox
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)
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)
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