Acta Polytechnica. 2014, vol. 54, no. 2
Now showing items 1-16 of 16
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STABILITY OF BOSE-EINSTEIN CONDENSATES IN A PT-SYMMETRIC DOUBLE-δ POTENTIAL CLOSE TO BRANCH POINTS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)A Bose-Einstein condensate trapped in a double-well potential, where atoms are incoupled to one side and extracted from the other, can in the mean-field limit be described by the nonlinear Gross-Pitaevskii equation (GPE) ... -
ON TWO WAYS TO LOOK FOR MUTUALLY UNBIASED BASES
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)Two equivalent ways of looking for mutually unbiased bases are discussed in this note. The passage from the search for d+1 mutually unbiased bases in Cd to the search for d(d+1) vectors in Cd2 satisfying constraint relations ... -
DIRAC AND HAMILTON
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)Dirac devised his theory of Quantum Mechanics and recognised that his operators resembled the canonical coordinates of Hamiltonian Mechanics. This gave the latter a new lease of life. We look at what happens to Dirac’s ... -
EXACT RENORMALIZATION GROUP FOR POINT INTERACTIONS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, ... -
TRACKING DOWN LOCALIZED MODES IN PT-SYMMETRIC HAMILTONIANS UNDER THE INFLUENCE OF A COMPETING NONLINEARITY
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)The relevance of parity and time reversal (PT)-symmetric structures in optical systems has been known for some time with the correspondence existing between the Schrödinger equation and the paraxial equation of diffraction, ... -
SEMICLASSICAL ASYMPTOTICS OF EIGENVALUES FOR NON-SELFADJOINT OPERATORS AND QUANTIZATION CONDITIONS ON RIEMANN SURFACES
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)This paper reports a study of the semiclassical asymptotic behavior of the eigenvalues of some nonself-adjoint operators that are important for applications. These operators are the Schrödinger operator with complex periodic ... -
EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)Exceptional points (EPs) determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the ... -
A SIMPLE DERIVATION OF FINITE-TEMPERATURE CFT CORRELATORS FROM THE BTZ BLACK HOLE
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)We present a simple Lie-algebraic approach to momentum-space two-point functions of two-dimensional conformal field theory at finite temperature dual to the BTZ black hole. Making use of the real-time prescription of AdS/CFT ... -
LAPLACE-RUNGE-LENZ VECTOR IN QUANTUM MECHANICS IN NONCOMMUTATIVE SPACE
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)The object under scrutiny is the dynamical symmetry connected with conservation of the Laplace-Runge-Lenz vector (LRL) in the hydrogen atom problem solved by means of noncommutative quantum mechanics (NCQM). The considered ... -
A DIFFERENTIAL INTEGRABILITY CONDITION FOR TWO-DIMENSIONAL HAMILTONIAN SYSTEMS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)We review, restate, and prove a result due to Kaushal and Korsch [Phys. Lett. A 276, 47 (2000)] on the complete integrability of two-dimensional Hamiltonian systems whose Hamiltonian satisfies a set of four linear second ... -
THE FLOQUET METHOD FOR PT-SYMMETRIC PERIODIC POTENTIALS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)By the general theory of PT-symmetric quantum systems, their energy levels are either real or occur in complex-conjugate pairs, which implies that the secular equation must be real. However, for periodic potentials it is ... -
ON THE REAL MATRIX REPRESENTATION OF PT-SYMMETRIC OPERATORS
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)We discuss the construction of real matrix representations of PT-symmetric operators. We show the limitation of a general recipe presented some time ago for non-Hermitian Hamiltonians with antiunitary symmetry and propose ... -
EIGENVALUE COLLISION FOR PT-SYMMETRIC WAVEGUIDE
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)We consider a model of a planar PT-symmetric waveguide and study the phenomenon of the eigenvalue collision under perturbation of the boundary conditions. This phenomenon was discovered numerically in previous works. The ... -
CAN ONE REALLY STUDY CHAOS ANALYTICALLY?
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)One generally thinks that chaos can be studied only numerically by aid of the computer. It is however suggested by the theorem of Sharkovskii and Li and Yorke that in Id continuous maps analytical studies are possible. How ... -
THE COUPLED-CLUSTER APPROACH TO QUANTUM MANY-BODY PROBLEM IN A THREE-HILBERT-SPACE REINTERPRETATION
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)The quantum many-body bound-state problem in its computationally successful coupled cluster method (CCM) representation is reconsidered. In conventional practice one factorizes the groundstate wave functions |Ψ) = eS |Φ) ... -
A BOSE-EINSTEIN CONDENSATE WITH PT-SYMMETRIC DOUBLE-DELTA FUNCTION LOSS AND GAIN IN A HARMONIC TRAP: A TEST OF RIGOROUS ESTIMATES
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2014)We consider the linear and nonlinear Schrödinger equation for a Bose-Einstein condensate in a harmonic trap with PT-symmetric double-delta function loss and gain terms. We verify that the conditions for the applicability ...
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