Zobrazeno 1 - 10
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pro vyhledávání: '"Znojil, Miloslav"'
Autor:
Znojil, Miloslav
In spite of its unbroken ${\cal PT}-$symmetry, the popular imaginary cubic oscillator Hamiltonian $H^{(IC)}=p^2+{\rm i}x^3$ does not satisfy all of the necessary postulates of quantum mechanics. The failure is due to the ``intrinsic exceptional point
Externí odkaz:
http://arxiv.org/abs/2411.12501
Autor:
Znojil, Miloslav
Publikováno v:
Phys. Lett. A 523 (2024) 129782
In the framework of quasi-Hermitian quantum mechanics it is shown that a weakening of the isotropy of the Hilbert-space geometry can help us to enlarge the domain of the parameters at which the evolution is unitary. The idea is tested using a simplif
Externí odkaz:
http://arxiv.org/abs/2408.02491
Autor:
Znojil, Miloslav
Via elementary examples it is demonstrated that the singularities of classical physics (sampled by the Big Bang in cosmology) need not necessarily get smeared out after quantization. It is proposed that the role of quantum singularities can be played
Externí odkaz:
http://arxiv.org/abs/2407.14672
Autor:
Znojil, Miloslav
Publikováno v:
Symmetry-Basel 16 (2024), 629
Quantum mechanics of unitary systems is considered in quasi-Hermitian representation. In this framework the concept of perturbation is found counterintuitive, for three reasons. The first one is that in this formalism we are allowed to change the phy
Externí odkaz:
http://arxiv.org/abs/2405.02032
Publikováno v:
Symmetry 16, 860 (2024)
Time and again, non-conventional forms of Lagrangians with non-quadratic velocity dependence have found attention in the literature. For one thing, such Lagrangians have deep connections with several aspects of nonlinear dynamics including specifical
Externí odkaz:
http://arxiv.org/abs/2403.18801
Autor:
Znojil, Miloslav
Publikováno v:
Physica Scripta 99 (2024) 035250
Non-stationary version of unitary quantum mechanics formulated in non-Hermitian (or, more precisely, in hiddenly Hermitian) interaction-picture representation is illustrated via an elementary $N$ by $N$ matrix Hamiltonian $H(t)$ mimicking a 1D-box sy
Externí odkaz:
http://arxiv.org/abs/2401.10682
Autor:
Znojil, Miloslav
Publikováno v:
Symmetry 16 (2024) 0027
A new generalization of the Calogero's rational ($A_N$) many-body quantum model is proposed and studied. The key innovation lies in an asymmetrization of the Calogero's two-body interaction. In the generalized model the exact solvability is preserved
Externí odkaz:
http://arxiv.org/abs/2312.13667
Autor:
Lechtenfeld, Olaf, Znojil, Miloslav
Publikováno v:
J. Phys.: Conf. Ser. 2667 (2023) 012036
In the conventional Schr\"{o}dinger's formulation of quantum mechanics the unitary evolution of a state $\psi$ is controlled, in Hilbert space ${\cal L}$, by a Hamiltonian $\mathfrak{h}$ which must be self-adjoint. In the recent, ``quasi-Hermitian''
Externí odkaz:
http://arxiv.org/abs/2308.15043
Autor:
Znojil, Miloslav
Publikováno v:
Symmetry 15 (2023) 1596 (13pp)
A $(K+1)-$plet of non-Hermitian and time-dependent operators (say, $\Lambda_j(t)$, $j=0,1,\ldots,K$) can be interpreted as the set of observables characterizing a unitary quantum system. What is required is the existence of a self-adjoint and, in gen
Externí odkaz:
http://arxiv.org/abs/2308.07609