Procházení Acta Polytechnica. 2017, vol. 57, no. 6 dle data publikování
Zobrazují se záznamy 1-16 z 16
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FUNCTIONAL REALIZATIONS OF LIE ALGEBRAS AS NOETHER POINT SYMMETRIES OF SYSTEMS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)Functional realizations of Lie algebras are applied to the problem of determining Lie and Noether point symmetries of Lagrangian systems in N dimensions, particularly in the plane. This encompasses both the case of ... -
ALGEBRAIC DESCRIPTION OF SHAPE INVARIANCE REVISITED
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)We revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical ... -
RATIONALLY EXTENDED SHAPE INVARIANT POTENTIALS IN ARBITRARY D DIMENSIONS ASSOCIATED WITH EXCEPTIONAL Xm POLYNOMIALS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)Rationally extended shape invariant potentials in arbitrary D-dimensions are obtained by using point canonical transformation (PCT) method. The bound-state solutions of these exactly solvable potentials can be written in ... -
NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)We investigate spacing statistics for ensembles of various real random matrices where the matrix-elements have various Probability Distribution Function (PDF: f(x)) including Gaussian. For two modifications of 2 × 2 matrices ... -
ON THE COMMON LIMIT OF THE PT-SYMMETRIC ROSEN–MORSE II AND FINITE SQUARE WELL POTENTIALS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)Two PT-symmetric potentials are compared, which possess asymptotically finite imaginary components: the PT-symmetric Rosen-Morse II and the finite PT-symmetric square well potentials. Despite their different mathematical ... -
LAMBERT FUNCTION METHODs TO STUDY LASER DYNAMICS WITH TIME-DELAYED FEEDBACK
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)Time-delayed differential equations arise frequently in the study of nonlinear dynamics of lasers with optical feedback and because the analytical solution of such equations can be intractable, one resorts to numerical ... -
FURTHER GENERALISATIONS OF THE KUMMER-SCHWARZ EQUATION: ALGEBRAIC AND SINGULARITY PROPERTIES
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)The Kummer–Schwarz Equation, 2y'y'''− 3(y'')2 = 0, has a generalisation, (n − 1)y(n−2)y(n) − ny(n−1)2 = 0, which shares many properties with the parent form in terms of symmetry and singularity. All equations of the class ... -
CRYPTO-HERMITIAN APPROACH TO THE KLEIN–GORDON EQUATION
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)We explore the Klein-Gordon equation in the framework of crypto-Hermitian quantum mechanics. Solutions to common problems with probability interpretation and indefinite inner product of the Klein-Gordon equation are proposed. -
LIE ALGEBRA REPRESENTATIONS AND RIGGED HILBERT SPACES: THE SO(2) CASE
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)It is well known that related with the irreducible representations of the Lie group SO(2) we find a discrete basis as well a continuous one. In this paper we revisited this situation under the light of Rigged Hilbert ... -
ON THE SPECTRUM OF THE ONE-DIMENSIONAL SCHRÖDINGER HAMILTONIAN PERTURBED BY AN ATTRACTIVE GAUSSIAN POTENTIAL
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)We propose a new approach to the problem of finding the eigenvalues (energy levels) in the discrete spectrum of the one-dimensional Hamiltonian with an attractive Gaussian potential by using the well-known Birman-Schwinger ... -
SIMPLE MODELS OF THREE COUPLED PT -SYMMETRIC WAVE GUIDES ALLOWING FOR THIRD-ORDER EXCEPTIONAL POINTS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)We study theoretical models of three coupled wave guides with a PT-symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated ... -
ON SELF-SIMILARITIES OF CUT-AND-PROJECT SETS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)Among the commonly used mathematical models of quasicrystals are Delone sets constructed using a cut-and-project scheme, the so-called cut-and-project sets. A cut-and-project scheme (L,π1, π2) is given by a lattice L in Rs ... -
HIGHLY ACCURATE CALCULATION OF THE REAL AND COMPLEX EIGENVALUES OF ONE-DIMENSIONAL ANHARMONIC OSCILLATORS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)We draw attention on the fact that the Riccati-Padé method developed some time ago enables the accurate calculation of bound-state eigenvalues as well as of resonances embedded either in the continuum or in the discrete ... -
THE ANALYSIS OF IMAGES IN N-POINT GRAVITATIONAL LENS BY METHODS OF ALGEBRAIC GEOMETRY
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)This paper is devoted to the study of images in N-point gravitational lenses by methods of algebraic geometry. In the beginning, we carefully define images in algebraic terms. Based on the definition, we show that in this ... -
NON-UNITARY TRANSFORMATION OF QUANTUM TIME-DEPENDENT NON-HERMITIAN SYSTEMS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)We provide a new perspective on non-Hermitian evolution in quantum mechanics by emphasizing the same method as in the Hermitian quantum evolution. We first give a precise description of the non unitary transformation and ... -
NUMERICAL CALCULATION OF THE COMPLEX BERRY PHASE IN NON-HERMITIAN SYSTEMS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2017)We numerically investigate topological phases of periodic lattice systems in tight-binding description under the influence of dissipation. The effects of dissipation are effectively described by PT-symmetric potentials. ...