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The Zeeman effect for hydrogen atom in twist-deformed space-time

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 Added by Marcin Daszkiewicz
 Publication date 2019
  fields
and research's language is English




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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.

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50 - Marcin Daszkiewicz 2018
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.
49 - Marcin Daszkiewicz 2018
In this article, we define two-particle system in Coulomb potential for twist-deformed space-time with spatial directions commuting to time-dependent function $f_{kappa_a}({t})$. 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 paper, we use the latest results of the ultra-high accuracy 1S-2S transition experiments in hydrogen atom to constrain the forms of the deformed dispersion relation in the nonrelativistic limit. For the leading correction of the nonrelativistic limit, the experiment sets a limit at an order of magnitude for the desired Planck-scale level, thereby providing another example of the Planck-scale sensitivity in the study of the dispersion relation in controlled laboratory experiments. And for the next-to-leading term, bound has two orders of magnitude away from the Planck scale, but it still amounts to the best limit, in contrast to previously obtained bound in the nonrelativistic limit from the cold-atom-recoil experiments.
67 - Marcin Daszkiewicz 2019
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.
70 - Marcin Daszkiewicz 2017
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 $kappa$, there appears chaos in the system for initial total energies $E_{0,{rm tot}}$ below the threshold $E_{0,{rm th}} = 1/6$.
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