Papers by Frantisek Ruzicka
Hilbert Space Inner Products for -symmetric Su-Schrieffer-Heeger Models
International Journal of Theoretical Physics, Feb 12, 2015
A Su-Schrieffer-Heeger model with added PT-symmetric boundary term is studied in the framework of... more A Su-Schrieffer-Heeger model with added PT-symmetric boundary term is studied in the framework of pseudo-hermitian quantum mechanics. For two special cases λ=0 and γ=0, a complete set of pseudometrics P(k) is constructed in closed form. When complemented with a condition of positivity, the pseudometrics determine all the physical inner products of the considered model.
One of the less well understood ambiguities of quantization is emphasized to result from the... more One of the less well understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians. This leads to the double-valued Hamiltonians reminiscent of a supersymmetry-related partners. Two eligible elementary nonlinear models are shown to admit a feasible quantization along these lines.
Three classes of finite-dimensional models of quantum systems exhibiting spectral degeneracies ca... more Three classes of finite-dimensional models of quantum systems exhibiting spectral degeneracies called quantum catastrophes are described in detail. Computer-assisted symbolic manipulation techniques are shown unexpectedly efficient for the purpose.
The realization of a genuine phase transition in quantum mechanics requires that at least one of ... more The realization of a genuine phase transition in quantum mechanics requires that at least one of the Kato's exceptional-point parameters becomes real. A new family of finite-dimensional and time-parametrized quantum-lattice models with such a property is proposed and studied. All of them exhibit, at a real exceptional-point time t=0, the Jordan-block spectral degeneracy structure of some of their observables sampled by Hamiltonian H(t) and site-position Q(t). The passes through the critical instant t=0 are interpreted as schematic simulations of non-equivalent versions of the Big-Bang-like quantum catastrophes.
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Papers by Frantisek Ruzicka