Janowicz Maciej; Karakula Sylwia; Mostowski Jan
A characteristic function for spin systems is applied to investigate the dissipation and decoherence of one and two two-level atoms. Particular attention is devoted to the Schrödinger cat-like states of two two-level systems. It has been demonstrated that the decoherence time and the phase damping rate depend linearly on the number of degrees of freedom for the maximally entangled initial state. Use of various characteristic functions to describe the decoherence processes is advocated. Two realizations of the SU(2) group are discussed in this context. The first one is based on the homomorphism of SU(2) and the group of rotations, the second one takes as its basis the Schwinger coupled-boson representation of angular-momentum operators as well as the definition of the characteristic function provided by Scully and Wódkiewicz.
J. Phys. B vol. 39, 5199-5213 (2006) [2/3]
Nov 16, 2006
Comparison of Gain--Loss Asymmetry Behavior for Stocks and Indexes
Magdalena A. Zaluska-Kotur, Krzysztof Karpio, Arkadiusz Orlowski
Investment horizon approach has been used to analyze indexes of Polish stock market. Optimal time horizon for each return value is evaluated by fitting appropriate function form of the distribution. Strong asymmetry of gain--loss curves is observed for WIG index, whereas gain and loss curves look similar for WIG20 and for most stocks of individual companies. The gain--loss asymmetry for these data, measured by a coefficient, that we postulated before [submitted to {ITALIC Physica A}], has opposite sign to this for WIG index.
Acta Phys. Polonica B Vol. 37, No. 11
Investment horizon approach has been used to analyze indexes of Polish stock market. Optimal time horizon for each return value is evaluated by fitting appropriate function form of the distribution. Strong asymmetry of gain--loss curves is observed for WIG index, whereas gain and loss curves look similar for WIG20 and for most stocks of individual companies. The gain--loss asymmetry for these data, measured by a coefficient, that we postulated before [submitted to {ITALIC Physica A}], has opposite sign to this for WIG index.
Acta Phys. Polonica B Vol. 37, No. 11
Oct 8, 2006
Cellular automaton approach to electromagnetic wave propagation in dispersive media
M.W. Janowicz, J.M.A. Ashbourn, Arkadiusz Orłowski, Jan Mostowski
Extensions of Białynicki-Birula's cellular automaton are proposed for studies of the one-dimensional propagation of electromagnetic fields in Drude metals, as well as in both transparent, dispersive and lossy dielectrics. These extensions are obtained by representing the dielectrics with appropriate matter fields, such as polarization together with associated velocity fields. To obtain the different schemes for the integration of the resulting systems of linear partial differential equations, split-operator ideas are employed. Possible further extensions to two-dimensional propagation and for the study of left-handed materials are discussed. The stability properties of the cellular automaton treated as a difference scheme are analysed.
P. Roy. Soc. A - Math. Phy. vol. 462, 2927-2948 (2006) [3/4]
Extensions of Białynicki-Birula's cellular automaton are proposed for studies of the one-dimensional propagation of electromagnetic fields in Drude metals, as well as in both transparent, dispersive and lossy dielectrics. These extensions are obtained by representing the dielectrics with appropriate matter fields, such as polarization together with associated velocity fields. To obtain the different schemes for the integration of the resulting systems of linear partial differential equations, split-operator ideas are employed. Possible further extensions to two-dimensional propagation and for the study of left-handed materials are discussed. The stability properties of the cellular automaton treated as a difference scheme are analysed.
P. Roy. Soc. A - Math. Phy. vol. 462, 2927-2948 (2006) [3/4]
Sep 15, 2006
Hydrogen atom in phase space : the Wigner representation
Ludmiła Praxmeyer, Jan Mostowski and Krzysztof Wódkiewicz
We have found an effective method of calculating the Wigner function, being a quantum analogue of joint probability distribution of position and momentum, for bound states of nonrelativistic hydrogen atom. The formal similarity between the eigenfunctions of nonrelativistic hydrogen atom in the momentum representation and Klein-Gordon propagators has allowed the calculation of the Wigner function for an arbitrary bound state of the hydrogen atom. These Wigner functions for some low lying states are depicted and discussed.
J. Phys. A vol. 39, 14143-14151 (2006) [1/3]
We have found an effective method of calculating the Wigner function, being a quantum analogue of joint probability distribution of position and momentum, for bound states of nonrelativistic hydrogen atom. The formal similarity between the eigenfunctions of nonrelativistic hydrogen atom in the momentum representation and Klein-Gordon propagators has allowed the calculation of the Wigner function for an arbitrary bound state of the hydrogen atom. These Wigner functions for some low lying states are depicted and discussed.
J. Phys. A vol. 39, 14143-14151 (2006) [1/3]
May 5, 2006
Classification of zero-energy resonances by dissociation of Feshbach molecules
Thomas M. Hanna, Krzysztof Góral, Emilia Witkowska, and Thorsten Köhler
We study the dissociation of Feshbach molecules by a magnetic field sweep across a zero-energy resonance. In the limit of an instantaneous magnetic field change, the distribution of atomic kinetic energy can have a peak indicating dominance of the molecular closed-channel spin configuration over the entrance channel. The extent of this dominance influences physical properties such as stability with respect to collisions, and so the readily measurable presence or absence of the corresponding peak provides a practical method of classifying zero-energy resonances. Currently achievable ramp speeds, e.g., those demonstrated by Dürr [Phys. Rev. A 70, 031601 (2005)], are fast enough to provide magnetic field changes that may be interpreted as instantaneous. We study the transition from sudden magnetic field changes to asymptotically wide, linear ramps. In the latter limit, the predicted form of the atomic kinetic energy distribution is independent of the specific implementation of the two-body physics, provided that the near-resonant scattering properties are properly accounted for.
Phys. Rev. A vol. 74, 023618 - 1-10 (2006) [1/4]
We study the dissociation of Feshbach molecules by a magnetic field sweep across a zero-energy resonance. In the limit of an instantaneous magnetic field change, the distribution of atomic kinetic energy can have a peak indicating dominance of the molecular closed-channel spin configuration over the entrance channel. The extent of this dominance influences physical properties such as stability with respect to collisions, and so the readily measurable presence or absence of the corresponding peak provides a practical method of classifying zero-energy resonances. Currently achievable ramp speeds, e.g., those demonstrated by Dürr [Phys. Rev. A 70, 031601 (2005)], are fast enough to provide magnetic field changes that may be interpreted as instantaneous. We study the transition from sudden magnetic field changes to asymptotically wide, linear ramps. In the latter limit, the predicted form of the atomic kinetic energy distribution is independent of the specific implementation of the two-body physics, provided that the near-resonant scattering properties are properly accounted for.
Phys. Rev. A vol. 74, 023618 - 1-10 (2006) [1/4]
Apr 29, 2006
Statics and dynamics of Bose-Einstein condensates in double square well potentials
E. Infeld, P. Ziń, J. Gocałek, and M. Trippenbach
We treat the behavior of Bose-Einstein condensates in double square well potentials of both equal and different depths. For even depth, symmetry preserving solutions to the relevant nonlinear Schrödinger equation are known, just as in the linear limit. When the nonlinearity is strong enough, symmetry breaking solutions also exist, side by side with the symmetric one. Interestingly, solutions almost entirely localized in one of the wells are known as an extreme case. Here we outline a method for obtaining all these solutions for repulsive interactions. The bifurcation point at which, for critical nonlinearity, the asymmetric solutions branch off from the symmetry preserving ones is found analytically. We also find this bifurcation point and treat the solutions generally via a Josephson junction model. When the confining potential is in the form of two wells of different depth, interesting phenomena appear. This is true of both the occurrence of the bifurcation point for the static solutions and also of the dynamics of phase and amplitude varying solutions. Again a generalization of the Josephson model proves useful. The stability of solutions is treated briefly.
Phys. Rev. E 74, 026610 (2006)
We treat the behavior of Bose-Einstein condensates in double square well potentials of both equal and different depths. For even depth, symmetry preserving solutions to the relevant nonlinear Schrödinger equation are known, just as in the linear limit. When the nonlinearity is strong enough, symmetry breaking solutions also exist, side by side with the symmetric one. Interestingly, solutions almost entirely localized in one of the wells are known as an extreme case. Here we outline a method for obtaining all these solutions for repulsive interactions. The bifurcation point at which, for critical nonlinearity, the asymmetric solutions branch off from the symmetry preserving ones is found analytically. We also find this bifurcation point and treat the solutions generally via a Josephson junction model. When the confining potential is in the form of two wells of different depth, interesting phenomena appear. This is true of both the occurrence of the bifurcation point for the static solutions and also of the dynamics of phase and amplitude varying solutions. Again a generalization of the Josephson model proves useful. The stability of solutions is treated briefly.
Phys. Rev. E 74, 026610 (2006)
Apr 5, 2006
Kinetic lattice gas model of collective diffusion in a one-dimensional system with long-range repulsive interactions
Magdalena A. Zauska-Kotur, Zbigniew W. Gortel
Collective diffusion is investigated within the kinetic lattice gas model for systems of particles in one dimension with repulsive long-range interactions which are known to result in a staircaselike phase diagram with an infinite sequence of incompressible crystalline phases separated one from another by unstable compressible liquidlike phases. Using a recently proposed [Gortel and Zauska-Kotur, Phys. Rev. B 70, 125431 (2004)] variational method, an analytic expression for the particle density dependence of the diffusion coefficient is derived in which commonly postulated static and kinetic factors are unambiguously identified. It is shown that while the static factor exhibits singular coverage dependence due to a sharp drop of compressibility when the system enters a crystalline phase, the kinetic factor may substantially modify this behavior. Depending on details of the activated state interactions controlling the migration kinetics the diffusion coefficient may also be singular or, at another extreme, it may be a continuously smooth function of density. In view of these observations recent results on efficient low temperature self-reorganization through devil's staircase phases in the dense Pb/Si(111)-× are discussed.
Phys. Rev. B vol. 74, 045405 - 1-16 (2006) [1/2]
Collective diffusion is investigated within the kinetic lattice gas model for systems of particles in one dimension with repulsive long-range interactions which are known to result in a staircaselike phase diagram with an infinite sequence of incompressible crystalline phases separated one from another by unstable compressible liquidlike phases. Using a recently proposed [Gortel and Zauska-Kotur, Phys. Rev. B 70, 125431 (2004)] variational method, an analytic expression for the particle density dependence of the diffusion coefficient is derived in which commonly postulated static and kinetic factors are unambiguously identified. It is shown that while the static factor exhibits singular coverage dependence due to a sharp drop of compressibility when the system enters a crystalline phase, the kinetic factor may substantially modify this behavior. Depending on details of the activated state interactions controlling the migration kinetics the diffusion coefficient may also be singular or, at another extreme, it may be a continuously smooth function of density. In view of these observations recent results on efficient low temperature self-reorganization through devil's staircase phases in the dense Pb/Si(111)-× are discussed.
Phys. Rev. B vol. 74, 045405 - 1-16 (2006) [1/2]
Mar 20, 2006
Decoherence of entangled states in two-mode cavities
Janowicz M., Orłowski A.
Decoherence of the Schrödinger-cat states in two-mode cavities are discussed. The cat states are assumed to be produced by the measurement of the energy of a three-level atom which have passed through the cavity. The evolution of the field density matrix is obtained from the Lindblad form of the dissipater at zero temperature. It is shown that the decoherence time of the two-mode cat states critically depends on the degree of entanglement. Implications for decoherence of entanglement in the macroscopic scales are discussed.
J. Phys. B vol. 39, 1763-1771 (2006) [2/2]
Decoherence of the Schrödinger-cat states in two-mode cavities are discussed. The cat states are assumed to be produced by the measurement of the energy of a three-level atom which have passed through the cavity. The evolution of the field density matrix is obtained from the Lindblad form of the dissipater at zero temperature. It is shown that the decoherence time of the two-mode cat states critically depends on the degree of entanglement. Implications for decoherence of entanglement in the macroscopic scales are discussed.
J. Phys. B vol. 39, 1763-1771 (2006) [2/2]
Feb 3, 2006
Exponential beams of electromagnetic radiation
Iwo Bialynicki-Birula and Zofia Bialynicka-Birula
We show that in addition to well known Bessel, Hermite-Gauss, and Laguerre-Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of rho. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, but unlike Bessel beams they have a finite energy per unit beam length. The analysis of these beams is greatly simplified by an extensive use of the Riemann-Silberstein vector and the Whittaker representation of the solutions of the Maxwell equations in terms of just one complex function. The connection between the Bessel beams and the exponential beams is made explicit by constructing the exponential beams as wave packets of Bessel beams.
J. Phys. B vol. 39, 5545-5553 (2006) [1/2]
We show that in addition to well known Bessel, Hermite-Gauss, and Laguerre-Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of rho. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, but unlike Bessel beams they have a finite energy per unit beam length. The analysis of these beams is greatly simplified by an extensive use of the Riemann-Silberstein vector and the Whittaker representation of the solutions of the Maxwell equations in terms of just one complex function. The connection between the Bessel beams and the exponential beams is made explicit by constructing the exponential beams as wave packets of Bessel beams.
J. Phys. B vol. 39, 5545-5553 (2006) [1/2]
Jan 15, 2006
Anderson Localization of Electromagnetic Waves in Dielectric Media: Model Studies
Rusek M., Orłowski A.
Anderson localization of electromagnetic waves in random arrays of dielectric cylinders confined within a planar metallic waveguide is studied. The disordered dielectric medium is modeled by a system of randomly distributed 2D electric dipoles. An effective theoretical approach based on the method of images is developed. A clear distinction between isolated localized waves (which exist in finite media) and the band of localized waves (which appears only in the limit of the infinite medium) is presented. The Anderson transition emerging in the limit of an infinite medium is observed both in finite size scaling analysis of transmission and in the properties of the spectra of some random matrices. The sound physical interpretation of the obtained results suggests deeper insight into the existing experimental and theoretical work.
Acta Phys. Pol. A vol. 109 (1), 109-119 (2006) [KK, 2/2]
Anderson localization of electromagnetic waves in random arrays of dielectric cylinders confined within a planar metallic waveguide is studied. The disordered dielectric medium is modeled by a system of randomly distributed 2D electric dipoles. An effective theoretical approach based on the method of images is developed. A clear distinction between isolated localized waves (which exist in finite media) and the band of localized waves (which appears only in the limit of the infinite medium) is presented. The Anderson transition emerging in the limit of an infinite medium is observed both in finite size scaling analysis of transmission and in the properties of the spectra of some random matrices. The sound physical interpretation of the obtained results suggests deeper insight into the existing experimental and theoretical work.
Acta Phys. Pol. A vol. 109 (1), 109-119 (2006) [KK, 2/2]
Jan 14, 2006
Formation of soliton trains in Bose-Einstein condensates by temporal Talbot effect
K. Gawryluk, M. Brewczyk, M. Gajda and J, Mostowski
We study the formation of matter-wave soliton trains in Bose–Einstein condensates confined in a box-like potential. We find that the generation of 'real' solitons understood as multipeak structures undergoing elastic collisions is possible if the condensate is released from the box into the harmonic trap only within well-defined time intervals. When the box-like potential is switched off outside the existing time windows, the number of peaks in a train changes resembling missing solitons observed in recent experiment (Strecker et al 2002 Nature 417 150). Our findings indicate that a new way of generating soliton trains in condensates through the temporal, matter-wave Talbot effect is possible.
J. Phys. B: At. Mol. Opt. Phys. 39 No 1
We study the formation of matter-wave soliton trains in Bose–Einstein condensates confined in a box-like potential. We find that the generation of 'real' solitons understood as multipeak structures undergoing elastic collisions is possible if the condensate is released from the box into the harmonic trap only within well-defined time intervals. When the box-like potential is switched off outside the existing time windows, the number of peaks in a train changes resembling missing solitons observed in recent experiment (Strecker et al 2002 Nature 417 150). Our findings indicate that a new way of generating soliton trains in condensates through the temporal, matter-wave Talbot effect is possible.
J. Phys. B: At. Mol. Opt. Phys. 39 No 1
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