Nuclear Physics Institute of Czech Republic

Prague, Czech Republic

Nuclear Physics Institute of Czech Republic

Prague, Czech Republic
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Znojil M.,Nuclear Physics Institute of Czech Republic
Annals of Physics | Year: 2015

Discrete multiparametric 1D quantum well with PT-symmetric long-range boundary conditions is proposed and studied. As a nonlocal descendant of the square well families endowed with Dirac (i.e.,Hermitian) and with complex Robin (i.e.,non-Hermitian but still local) boundary conditions, the model is shown characterized by the survival of solvability in combination with an enhanced spectral-design flexibility. The solvability incorporates also the feasibility of closed-form constructions of the physical Hilbert-space inner products rendering the time-evolution unitary. © 2015 Elsevier Inc.


Jakubsky V.,Nuclear Physics Institute of Czech Republic
Annals of Physics | Year: 2013

Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2×2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of the Hamiltonian that close centrally extended s o (3) , s o (2, 1) or oscillator algebra. The algebraic framework is used in construction of physically interesting solvable models described by the (2 + 1) dimensional Dirac equation. It is applied in description of open-cage fullerenes where the energies and wave functions of low-energy charge-carriers are computed. The potential algebras are also used in construction of shape-invariant, one-dimensional Dirac operators. We show that shape-invariance of the first-order operators is associated with the N = 4 nonlinear supersymmetry which is represented by both local and nonlocal supercharges. The relation to the shape-invariant non-relativistic systems is discussed as well. © 2013 Elsevier Inc.


It is known that the practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians H ≠ H † requires an efficient reconstruction of an ad hoc Hilbert-space metric Θ = Θ (H) which would render the time-evolution unitary. Once one considers just the N-dimensional matrix toy models H = H (N), the matrix elements of Θ (H) may be defined via a coupled set of N2 polynomial equations. Their solution is a typical task for computer-assisted symbolic manipulations. The feasibility of such a model-completion construction is illustrated here via a discrete square well model H = p2 + V endowed with a k-parametric close-to-the-boundary interaction V. The model is shown to possess (possibly, multiply degenerate) exceptional points marking the phase transitions which are attributable, due to the exact solvability of the model at any N < ∞, to the loss of the regularity of the metric. In the parameter-dependence of the energy spectrum near these singularities one encounters a broad variety of alternative, topologically non-equivalent scenarios. © 2013 Elsevier Inc.


Znojil M.,Nuclear Physics Institute of Czech Republic
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2015

Abstract In a way paralleling the recently accepted non-Hermitian version of quantum mechanics in its Schrödinger representation (working often with the innovative and heuristically productive concept of PT-symmetry), it is demonstrated that it is also possible to construct an analogous non-Hermitian version of quantum mechanics in its Heisenberg representation. © 2015 Elsevier B.V.


Shevchenko N.V.,Nuclear Physics Institute of Czech Republic
Nuclear Physics A | Year: 2012

We calculated the 1s level shifts and widths of kaonic deuterium, corresponding to accurate results on near-threshold antikaon-deuteron scattering. The Lippmann-Schwinger eigenvalue equation with a strong K --d and Coulomb potentials was solved. The two-body K --d potentials reproduce the near-threshold elastic amplitudes of K -d scattering obtained from the three-body Alt-Grassberger-Sandhas equations with the coupled channels using two versions of the K̄N-πσ potentials. The new K̄N-πσ potentials reproduce the very recent SIDDHARTA data on kaonic hydrogen, experimental data on K -p scattering and have one- or two-pole versions of theΛ(1405) resonance. © 2012 Elsevier B.V.


Shevchenko N.V.,Nuclear Physics Institute of Czech Republic
Physical Review C - Nuclear Physics | Year: 2012

We investigated the dependence of the K -d scattering length on models of the K̄N interaction with one or two poles for the Λ(1405) resonance. The K̄NN-πΣN system is described by coupled-channel Faddeev equations in Alt-Grassberger-Sandhas form. Our new two-body K̄N-πΣ potentials reproduce all existing experimental data on K -p scattering and kaonic hydrogen atom characteristics. New models of the ΣN-ΛN interaction were also constructed. Comparison with several approximations, usually used for scattering length calculations, was performed. © 2012 American Physical Society.


Znojil M.,Nuclear Physics Institute of Czech Republic
Annals of Physics | Year: 2012

A discrete N-level alternative to the popular imaginary cubic oscillator is proposed and studied. As usual, the unitarity of evolution is guaranteed by the introduction of an ad hoc, Hamiltonian-dependent inner-product metric, the use of which defines the physical Hilbert space and renders the Hamiltonian (with real spectrum) observable. Due to the simplicity of our model of dynamics the construction of the set of eligible metrics is shown tractable by non-numerical means which combine the computer-assisted algebra with the extrapolation and/or perturbation techniques. © 2012 Elsevier Inc.


Znojil M.,Nuclear Physics Institute of Czech Republic
Journal of Physics A: Mathematical and Theoretical | Year: 2014

A new Hermitizable quantum model is proposed in which the bound-state energies are real and given as roots of an elementary trigonometric expression while the wave function components are expressed as superpositions of two Chebyshev polynomials. As an N-site lattice version of square well with complex Robin-type two-parametric boundary conditions the model is unitary with respect to the Hilbert space metric Θ which becomes equal to the most common Dirac's metric Θ(Dirac) = I in the conventional textbook Hermitian-Hamiltonian limit. This metric is constructed in closed form at all N = 2, 3, .... © 2014 IOP Publishing Ltd.


Sauli V.,Nuclear Physics Institute of Czech Republic
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2014

The purpose of this paper is twofold. The first purpose is to find a fully Poincaré invariant solution of the Bethe-Salpeter equation (BSE) for excited quarkonia; however, the second, in fact, major focus is on the relevance of the space-time metric choice and its impact on the correct description of the ground and all excited states. For the first time, we compare the BSE solutions defined independently with the Euclidean and Minkowski metric. For this purpose, the BSE is conventionally defined and solved in Euclidean space with two versions of the propagator: the bare propagator and the confined form of the quark propagator with complex conjugated poles. In both considered cases, there is unexpected doubling of the spectrum when comparing to the experiments as well as to the solutions of the Schrödinger equation. The quark propagator with complex conjugated singularities allows us to find the BSE solution directly in Minkowski momentum space as well. We find the Minkowski space solution for confining theories is not only numerically accessible but provides a reliable albeit not yet completely satisfactory description of the ground and excited meson states. © 2014 American Physical Society.


Znojil M.,Nuclear Physics Institute of Czech Republic
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2010

An N-level quantum model is proposed in which the energies are represented by an N-plet of zeros of a suitable classical orthogonal polynomial. The family of Gegenbauer polynomials G(n,a,x) is selected for illustrative purposes. The main obstacle lies in the non-Hermiticity (aka crypto-Hermiticity) of Hamiltonians H ≠ H†. We managed to (i) start from elementary secular equation G(N,a,E n) = 0, (ii) keep our H, in the nearest-neighbor-interaction spirit, tridiagonal, (iii) render it Hermitian in an ad hoc, nonunique Hilbert space endowed with metric Θ ≠ I, (iv) construct eligible metrics in closed forms ordered by increasing nondiagonality, and (v) interpret the model as a smeared N-site lattice. © 2010 The American Physical Society.

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