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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. Source

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. Source

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. Source

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. Source

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. Source

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