On the quantum chromatic number of a graph.
On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section
On the quasi-classical limit of the total scattering cross-section in nonrelativistic quantum mechanics
On the relative fundamental solutions for a second order differential operator on the Heisenberg group
Let Hₙ be the (2n+1)-dimensional Heisenberg group, let p,q ≥ 1 be integers satisfying p+q=n, and let , where X₁,Y₁,...,Xₙ,Yₙ,T denotes the standard basis of the Lie algebra of Hₙ. We compute explicitly a relative fundamental solution for L.
On the relativistic calculation of the Lamb shift
A relativistic calculation of the Lamb shift, using the classical field created by the Dirac transition currents, is proposed.
On the renormalization group iteration of a two-dimensional hierarchical non-linear -model
On the role of the normalization factors and of the pseudo-metric in crypto-Hermitian quantum models.
On the Scattering Matrix for N-Particle Hamiltonians
On the scattering theory for quantum dynamical semigroups
On the second order absolute differentiation
In this paper the authors compare two different approaches to the second order absolute differentiation of a fibered manifold (one of them was studied by the authors [Arch. Math., Brno 33, 23-35 (1997; Zbl 0910.53014)]. The main goal is the extension of one approach to connections on functional bundles of all smooth maps between the fibers of two fibered manifolds over the same base (we refer to the book “Natural Operations in Differential Geometry” [Springer, Berlin (1993; Zbl 0782.53013)] I. Kolar,...
On the second quantisation of Hilbert-Schmidt processes
On the semi-classical approximation of the solution of the Heisenberg equation with spin
On the set representation of an orthomodular poset
Let P be an orthomodular poset and let B be a Boolean subalgebra of P. A mapping s:P → ⟨0,1⟩ is said to be a centrally additive B-state if it is order preserving, satisfies s(a') = 1 - s(a), is additive on couples that contain a central element, and restricts to a state on B. It is shown that, for any Boolean subalgebra B of P, P has an abundance of two-valued centrally additive B-states. This answers positively a question raised in [13, Open question, p. 13]. As a consequence one obtains a somewhat...
On the set-theoretical Yang-Baxter equation.
On the simplicial structure of some Weil bundles
The author considers the problem to give explicit descriptions for several types of bundles on smooth manifolds, naturally related with the bundle of -dimensional velocities, or -jets. In fact, this kind of bundles are very natural objects in differential geometry, mechanics and Lagrangian dynamics. For this the author considers Weil bundles that arose from Weil algebras. If a suitable combinatorial data is provided by a simplicial coloured structure, then the author describes the corresponding...
On the singular spectrum for adiabatic quasiperiodic Schrödinger operators.
On the spectrum and eigenfunctions of the Schrödinger operator with Aharonov–Bohm magnetic field.
On the spectrum of a discrete non-Hermitian quantum system.
On the spectrum of Robin Laplacian in a planar waveguide
We consider the Laplace operator in a planar waveguide, i.e. an infinite two-dimensional straight strip of constant width, with Robin boundary conditions. We study the essential spectrum of the corresponding Laplacian when the boundary coupling function has a limit at infinity. Furthermore, we derive sufficient conditions for the existence of discrete spectrum.
On the state complexity of semi-quantum finite automata
Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata. This paper shows three results of such a type that are stronger in some sense than other ones because (a) they deal with models of quantum finite automata with very little quantumness (so-called semi-quantum one- and two-way finite automata); (b) differences, even comparing with probabilistic...