arXiv subjects
Publications and source records attributed to Marcin Daszkiewicz.
In this article we provide three new twist-deformed Newtonian Schwarzschild-(Anti-)de Sitter models. They are defined on the Lie-algebraically as well as on the canonically noncommutative space-times respectively. Particularly we find the corresponding Hamiltonian functions and the proper equations of motion. The relations between the models are discussed as well.
In this article we find the Zeeman corrections for hydrogen atom in the case of twist-deformed space-time. Particularly, we derive the corresponding orbital and spin $\hat{g}$-factors as well as we notice, that the second one of them remains undeformed.
In this article we discus the energy-momentum conservation principle for two-particle system in the case of canonically and Lie-algebraically twist-deformed Galilei Hopf algebra. Particularly, we provide consistent with the coproducts energy and momentum addition law as well as its symmetric with respect the exchange of particles counterpart. Besides, we show that the vanishing of total fourmomentum for two Lie-algebraically deformed kinematical models leads to the discret values of energies and momenta only in the case of the symmetrized addition rules.
Recently, there has been provided two chaotic models based on the twist-deformation of classical Henon-Heiles system. First of them has been constructed on the well-known, canonical space-time noncommutativity, while the second one on the Lie-algebraically type of quantum space, with two spatial directions commuting to classical time. In this article, we find the direct link between mentioned above systems, by synchronization both of them in the framework of active control method. Particularly, we derive at the canonical phase-space level the corresponding active controllers as well as we perform (as an example) the numerical synchronization of analyzed models.
In this article, we define two-particle system in Coulomb potential for twist-deformed space-time with spatial directions commuting to time-dependent function $f_{κ_a}({t})$. Particularly, we provide the proper Hamiltonian function and further, we rewrite it in terms of commutative variables. Besides, we demonstrate, that for small values of deformation parameters, the obtained in the perturbation framework, first-ordered corrections for ground Helium energy are equal to zero. In such a way we show, that nontrivial impact of space-time noncommutativity appears only at the second order of the quantum-mechanical correction expansion.
In this article we provide the noncommutative Sprott models. We demonstrate, that effectively, each of them is described by system of three complex, ordinary and nonlinear differential equations. Apart of that, we find for such modified models the corresponding (noncommutative) jerk dynamics as well as we study numerically as an example, the deformed Sprott-A system.
In this article, we define the Pauli Hamiltonian function for twist-deformed N-enlarged Newton-Hooke space-time provided in article [12]. Further, we derive its energy spectrum, i.e., we find the corresponding eigenvalues as well as the proper eigenfunctions.
In this article we synchronize by active control method all 19 identical Sprott systems provided in paper [10]. Particularly, we find the corresponding active controllers as well as we perform (as an example) the numerical synchronization of two Sprott-A models.
In this article we provide the Henon-Heiles system defined on Lie-algebraically deformed nonrelativistic space-time with the commutator of two spatial directions proportional to time. Particularly, we demonstrate that in such a model the total energy is not conserved and for this reason the role of control parameter is taken by the initial energy value $E_{0,{\rm tot}} = E_{\rm tot}(t=0)$. Besides, we show that in contrast with the commutative case, for chosen values of deformation parameter $κ$, there appears chaos in the system for initial total energies $E_{0,{\rm tot}}$ below the threshold $E_{0,{\rm th}} = 1/6$.
In this article we provide canonically deformed classical Henon-Heiles system. Further we demonstrate that for proper value of deformation parameter $θ$ there appears chaos in the model.
In this article, we investigate the impact of twisted space-time on the photoelectric effect, i.e., we derive the $θ$-deformed threshold frequency. In such a way we indicate that the space-time noncommutativity strongly enhances the photoelectric process.
In this article we formally investigate the impact of twisted space-time on black-body radiation phenomena, i.e. we derive the $θ$-deformed Planck distribution function as well as we perform its numerical integration to the $θ$-deformed total radiation energy. In such a way we indicate that the space-time noncommutativity very strongly damps the black-body radiation process. Besides we provide for small parameter $θ$ the twisted counterparts of Rayleigh-Jeans and Wien distributions respectively.
The three quantum groups dual to the generalized twist deformed Poincare Hopf algebras are provided with use of FRT procedure. Their Galilean counterparts are obtained by nonrelativistic contraction scheme.
We derive the energy levels for oscillator model defined on the twisted N-enlarged Newton-Hooke space-time, i.e., we find time-dependent eigenvalues and corresponding time-dependent eigenstates. We also demonstrate that for a particular choice of deformation parameters of phase space the above spectrum can be identified with the time-dependent Landau one.
We investigate the Kerr black hole defined on canonically deformed space-time. Particulary, we find the corresponding event horizon, the ergosphere, the temperature and the entropy of such deformed object.
The coherent states for twist-deformed oscillator model provided in article [1] are constructed. Besides, it is demonstrated that the energy spectrum of considered model is labeled by two quantum numbers - by so-called main and azimutal quantum numbers respectively.
We define the model of hydrogen atom for twist-deformed acceleration-enlarged Newton-Hooke space-time. Further, using time-dependent perturbation theory, we find in first step of iteration procedure the solution of corresponding Schroedinger equation as well as the probability of transition between two different energy-eigenstates.
We compare two ways of force terms generating in the model of nonrelativistic particle moving in the presence of constant field force $\vec{F}$. First of them uses the twist-deformed N-enlarged Newton-Hooke quantum space-times while the second one incorporates the Coriolis transformations of classical space. Particularly, we find the conditions for which the both treatments provide the same force terms. The presented investigations are performed by analogy to the schemes and ideas proposed in paper [1].