The Canonical Form of the Rabi Hamiltonian

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.Comment: 17 pages, LaTeX, no figures, to appear in J.Math.Phy

Coherence of Currents in Mesoscopic Cylinders

The persistent currents driven by the pure Aharonov-Bohm type magnetic field in mesoscopic normal metal or semiconducting cylinders are studied. A two-dimensional (2D) Fermi surfaces are characterized by four parameters. Several conditions for the coherence and enhancement of currents are discussed. These results are then generalized to a three-dimensional (3D) thin-walled cylinder to show that under certain geometric conditions on the Fermi surface, a novel effect - the appearance of spontaneous currents is predicted.Comment: 17 pages, Latex, 8 figures available on request, to be published in Z.Physik

Thermal photon dispersion law and modified black-body spectra

Based on the postulate that photon propagation is governed by an SU(2) gauge principle we numerically compute the one-loop dispersion for thermalized photon propagation on the radiatively induced mass shell. Formerly, the dispersion was addressed by assuming $p^2=0$. While this approximation turns out to be excellent for temperatures $\le 2 T_{\tiny{CMB}}$ the exact result exhibits a much faster (power-like) shrinking of the gap in the black-body spectral intensity with rising temperature. Our previous statements on anomalous large-angle CMB temperature-temperature correlations, obtained in the approximation $p^2=0$, remain valid.Comment: v2: 13 pages, 6 figures; sec. 2.1. added to explain effective theory; references added; matches journal published versio

Radiative return at NLO and the measurement of the hadronic cross-section in electron-positron annihilation

Electron-positron annihilation into hadrons plus an energetic photon from initial state radiation allows the hadronic cross-section to be measured over a wide range of energies. The full next-to-leading order QED corrections for the cross-section for e^+ e^- annihilation into a real tagged photon and a virtual photon converting into hadrons are calculated where the tagged photon is radiated off the initial electron or positron. This includes virtual and soft photon corrections to the process e^+ e^- \to \gamma +\gamma^* and the emission of two real hard photons: e^+ e^- \to \gamma + \gamma + \gamma^*. A Monte Carlo generator has been constructed, which incorporates these corrections and simulates the production of two charged pions or muons plus one or two photons. Predictions are presented for centre-of-mass energies between 1 and 10 GeV, corresponding to the energies of DAPHNE, CLEO-C and B-meson factories.Comment: 13 pages, 15 figure

Gevrey class regularity for solutions of micropolar fluid equations

AbstractIn this paper we consider the solutions of micropolar fluid equations in space dimension two with periodic boundary condition. We show that the strong solutions are analytic in time with values in an appropriate Gevrey class of function, provided that external forces and moments are time-independent and are in a Gevrey class

Equitable distribution in a three players problem

Jazz band is a 3 player superadditive game in characteristic func- tion form. Three players have to divide the payoff they can get, while being in a grand coalition, provided their individual and duo coalitions payoffs are known. Assumptions of individual and collective rationality lead to the notion of the core of the game. We discuss offers that cannot readily be refused [OCRR] as the solutions of the game in case of an empty core, when duo coalitions are the best options but only for two out of three players. The experiment shows that even in case of an empty core the most probable results are three-way coalitions and the share of the weakest player usually exceeds his OCRR. The Shapley value is introduced and its fairness is discussed as it lies at the side of the core while, on the other hand, the nucleolus lies exactly at the center of the core. We conclude that, in spite of that, the Shapley value is the best candidate for a fair sharing solution of the jazz band game and other similar games as, opposite to the other values, it is dependent both on individual and duo coalitions payoffs

Numerical modeling of pure metal solidification using the one domain approach

Numerical modeling of pure metal solidification on the basis of the well-known Stefan model is rather difficult. The knowledge of temporary solidification front position and the local values of the solidification rate in the normal direction for time t are necessary in order to determine the new position of moving boundary for time t + ∆t. The problem is especially complicated for 2D and 3D tasks. The concept greatly simplifying the modeling of solidification process boils down to the introduction of the artificial region corresponding to the mushy zone sub-domain. For this region the substitute thermal capacity is defined and the mathematical model corresponds to the one domain approach. The artificial mushy zone appears owing to conventional enlargement of solidification point on a certain interval of temperature ∆T. The basic goal of the paper is the numerical analysis of the influence of the interval ∆T on the numerical solution simulating the thermal processes in the domain of the solidifying metal

Roses or bread? Anti-communist narration in feminist readings of Anna Świrszczyńska’s poetry

The article discusses the question of feminist interpretations of the poetry of Anna Świrszczyńska, one of the most recognized Polish poets of international renown, whose works and activity are often associated with a strong feminist worldview. Many interpreters of Świrszczyńska’s poetry did not focus enough on the origin of the poet’s feminist attitude, claiming that it was rather exceptional and rare for the period of the Polish People’s Republic. Contrary to the narration established by the interpreters of her poetry after 1989, I argue that Świrszczyńska’s feminist sensitivity was not an isolated and individual phenomenon, as it emerged in a time of increased women’s activity and the development of the socialist project for women’s equality deployed in Poland after 1945. I believe that both the political activity of communist women and the grassroots actions taken by the working-class women in the socialist state became the main factors in shaping Świrszczyńska’s feminist worldview. The Polish feminist narrative after 1989, however, due to its anti-communist approach to the problem of feminism in the Polish People’s Republic, did not include the history of the Polish left-wing women’s movement. This results from applying to the Polish history of women’s movements 1) liberal notions of feminist agency; 2) Western feminist theories devoid of Marxist paradigm; and 3) a normative definition of feminism understood only in terms of anti-systemic activity. By taking into account Świrszczyńska’s political and cultural activity, I emphasize the necessity of filling the gaps in the story of Polish women’s movement. Such a strategy is inevitably connected with the necessity of remodelling the genealogy of Polish feminism, redefining the notion of agency, and feminism itself