Acta Polytechnica. 2013, vol. 53, no. 3
Zobrazují se záznamy 1-12 z 12
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Non-Hermitian Star-shaped Quantum Graphs
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)A compact review is given, and a few new numerical results are added to the recent studies of the q-pointed one-dimensional star-shaped quantum graphs. These graphs are assumed endowedwith certain specific, manifestly ... -
Intervals in Generalized Effect Algebras and their Sub-generalized Effect Algebras
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)We consider subsets G of a generalized effect algebra E with 0∈G and such that every interval [0, q]G = [0, q]E ∩ G of G (q ∈ G , q ≠ 0) is a sub-effect algebra of the effect algebra [0, q]E. We give a condition on E and ... -
Inherited Properties of Effect Algebras Preserved by Isomorphisms
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)We show that isomorphism of effect algebras preserves properties of effect algebras derived from effect algebraic sum ? of elements. These are partial order, order convergence, order topology, existence of states and other ... -
Spectral Singularities do not Correspond to Bound States in the Continuum
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)We show that, contrary to a claim made in arXiv:1011.0645, the von Neumann-Winger bound states that lie in the continuum of the scattering states are fundamentally different from Naimark’s spectral singularities. -
Emmy Noether and Linear Evolution Equations
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have ... -
Stationary and Dynamical Solutions of the Gross-Pitaevskii Equation for a Bose-Einstein Condensate in a PT symmetric Double Well
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)We investigate the Gross-Pitaevskii equation for a Bose-Einstein condensate in a PT symmetric double-well potential by means of the time-dependent variational principle and numerically exact solutions. A one-dimensional ... -
Spectral Analysis of Schrödinger Operators with Unusual Semiclassical Behavior
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)In this paper we discuss several examples of Schrödinger operators describing a particle confined to a region with thin cusp-shaped ‘channels’, given either by a potential or by a Dirichlet boundary; we focus on cases when ... -
Weakly Ordered A-Commutative Partial Groups of Linear Operators Densely Defined on Hilbert Space
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)The notion of a generalized effect algebra is presented as a generalization of effect algebra for an algebraic description of the structure of the set of all positive linear operators densely defined on a Hilbert space ... -
The Two-dimensional Harmonic Oscillator on a Noncommutative Space with Minimal Uncertainties
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms ... -
Complex Covariance
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)According to some generalized correspondence principle the classical limit of a non-Hermitian quantum theory describing quantum degrees of freedom is expected to be the well known classical mechanics of classical degrees ... -
Generalized Continuity Equation for Quasi-Hermitian Hamiltonians
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)The continuity relation is generalized to quasi-Hermitian one-dimensional Hamiltonians. As an application we show that the reflection and transmission coefficients computed with the generalized current obey the conventional ... -
On the Solvability of Some Partial Differential Inequality
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2013)The Dulac criterion is a classical method for ruling out the existence of periodic solutions in planar differential equations. In this paper the applicability and therefore reversibility of this criterionis under consideration.