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

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

Persistent Currents in Twisted Tori Made of Chiral Nanotubes

Mesoscopic metal rings can carry persistent currents driven by a constant magnetic field. The geometrical structure of a toroidal carbon nanotube can be characterized by four independent parameters. We derive the formula for persistent currents driven by a constant Bohm-Aharonov type of field perpendicular to the plane of the torus. The dependencies of the currents on the chirality, twist and circumference of the torus are discussed

Projektowanie rynków w oparciu o algorytmy kojarzenia

W pracy przedstawiono teorię stabilnego dopasowania algorytmu odroczonej akceptacji (AOA) oraz algorytmy TTC i TTCC wraz z ich zastosowaniami do np. kojarzenia uczelni i studentów, domów i właścicieli czy dawców i biorców nerek do przeszczepu. Dzięki tym algorytmom można projektować tzw. rynki kojarzenia, dla których optymalna alokacja dóbr jest możliwa bez wykorzystania mechanizmów finansowych charakterystycznych dla rynków towarowych. Omówiono właściwości algorytmów kojarzenia, m.in. ich stabilność, Pareto optymalność i odporność na manipulacje, oraz cechy algorytmu TTCC, dzięki którym krzyżowe transplantacje można zastąpić łańcuchowymi, co dzięki osiągnięciu głębszego rynku, pozwala na bardziej optymalne wykorzystanie nerek do przeszczepu

Collective phenomena in multiwall carbon nanotubes

Collective phenomena due to persistent currents in carbon multiwall nanotubes are studied. The formula for persistent currents minimising free energy and conditions for the stability of persistent currents in multiwall nanotubes in magnetic field are derived. Numerical calculations performer show the possibility of obtaining spontaneous currents in two optimal configurations: undoped armchair-only multiwall nanotubes up to 0.01 K, and zig-zag{chiral¡chiral{zig-zag multiwall nanotubes doped to {3.033 eV up to about 1 K. The latter configuration may exhibit also the diamagnetic expulsion of magnetic field, which according to our calculations can reach 20% of the external °ux

How Quantum Prisoner’s Dilemma Can Support Negotiations

Decision-making by the two negotiating parties is simulated by a prisoner’s dilemma game. The game is formulated in a quantum manner, where players strategies are unitary transformations of qubits built over the basis of opposite decision options. Quantum strategies are correlated through the mechanism of quantum entanglement and the result of the game is obtained by the collapse of the resulting transformed state. The range of strategies allowed for quantum players is richer than in case of a classical game and therefore the result of the game can be better optimized. On the other hand, the quantum game is save against eavesdropping and the players can be assured that this type of quantum arbitration is fair. We show that quantum prisoner’s dilemma has more favorable Nash equilibria than its classical analog and they are close to the Pareto optimal solutions. Some economical examples of utilizing quantum game Nash equilibria are proposed.This work was partially supported by the grant from Polish National Science Center DEC-2011/03/B/HS4/[email protected] of Physics, University of Silesia5(71)9010

Socio-cultural circumstances to establish university spin-off companies

The characteristics and behaviour of university spin-off activity is an important subject in economic and management studies literature. Such studies merit research because it is suggested that university innovations stimulate economies by spurring product development, by creating new industries, and by contributing to employment and wealth creation. For this reason, universities have come to be highly valued in terms of the socio-cultural potential of their research efforts. The aim of this paper is to offer a framework for consequences of university spinoff activity

Mutual inductance and selfinductance in mesoscopic systems

Th e role played by the magnetostatic interaction in mesoscopic multichannel systems is discussed . We show that the interaction of currents from different channels , when taken in the selfconsistent mean field approximation, leads to selfinductan ce terms in the Hamiltoni an pro ducing an internal magnetic flux. Such multichannel systems can exhibit spontaneous flux or flux expulsion. The dependence of these phenomena on the parameters of the system is discussed

On the possibility of spontaneous currents in mesoscopie systems

It is shown that a mesoscopic metallic system can exhibit a phase transition to a low temperature state with a spontaneous orbital current if it is sufficiently free of elastic defect scattering. The interaction among the electrons, which is the reason of the phase transition, is of the magnetic origin and it leads to an ordered state of the orbital magnetic moments