86 citations · 1k across the 58 of their papers we have counts for
13 papers · 1 filter
Translational dynamics of diatomic molecule in magnetic quadrupole trap
Yurij Yaremko, Maria Przybylska, Andrzej J. Maciejewski
We study the translational motions of homonuclear diatomic molecules prepared in their electronic states, deeply bound vibrational states, and rotational states of well-def…
Non-integrability of the -body problem
Andrzej J. Maciejewski, Maria Przybylska, Thierry Combot
We prove that the classical planar -body problem when restricted to a common level of the energy and the angular momentum is not integrable except in the case when both values o…
Destructive relativity
Maria Przybylska, Wojciech Szumiński, Andrzej J. Maciejewski
Relativistic Hamiltonian equations describing a motion of a point mass in an arbitrary homogeneous potential are considered. For the first time, the necessary integrability conditi…
The geodesic flow of the BGPP metric is Liouville integrable
Andrzej J. Maciejewski, Maria Przybylska, Galliano Valent
We prove that the geodesics equations corresponding to the BGPP metric are integrable in the Liouville sense. The symmetry of the model allows to reduce…
Non-integrability of the Kepler and the two-body problem on the Heisenberg group
Tomasz Stachowiak, Andrzej J. Maciejewski
The analog of the Kepler system defined on the Heisenberg group introduced by Montgomery and Shanbrom in [Fields Inst. Commun., Vol. 73, Springer, New York, 2015, 319-342, arXiv:12…
An exactly solvable system from quantum optics
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak
We investigate a generalisation of the Rabi system in the Bargmann-Fock representation. In this representation the eigenproblem of the considered quantum model is described by a sy…
Comment on "Solvability of the two-photon Rabi Hamiltonian"
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak
An implicit formula for the spectrum of the two-photon Rabi model was presented by Travenec in Phys. Rev. A 85, 043805 (2012) in analogy to the method of Braak [Phys. Rev. Lett. 10…
Analytical method of spectra calculations in the Bargmann representation
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak
We formulate a universal method for solving an arbitrary quantum system which, in the Bargmann representation, is described by a system of linear equations with one independent var…
Full spectrum of the Rabi model
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak
It is shown that in the Rabi model, for an integer value of the spectral parameter , in addition to the finite number of the classical Judd states there exist infinitely many po…
How to calculate spectra of Rabi and related models
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak
We show how to use properly the Bargmann space of entire functions in the analysis of the Rabi model. We are able to correct a serious error in recent papers on the topic and devel…
The Poisson equations in the nonholonomic Suslov problem: Integrability, meromorphic and hypergeometric solutions
Yuri Fedorov, Andrzej J. Maciejewski, Maria Przybylska
We consider the problem of integrability of the Poisson equations describing spatial motion of a rigid body in the classical nonholonomic Suslov problem. We obtain necessary condit…
Global integrability of cosmological scalar fields
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak +1
We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois gr…
Non-integrability of the problem of a rigid satellite in gravitational and magnetic fields
Andrzej J. Maciejewski, Maria Przybylska
In this paper we analyse the integrability of a dynamical system describing the rotational motion of a rigid satellite under the influence of gravitational and magnetic fields. In…