Borisov, D. I.; Zezyulin, D. A. On perturbation of thresholds in essential spectrum under coexistence of virtual level and spectral singularity. (English) Zbl 07822057 Russ. J. Math. Phys. 31, No. 1, 60-78 (2024). MSC: 81Qxx 35Bxx 35Jxx PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{D. A. Zezyulin}, Russ. J. Math. Phys. 31, No. 1, 60--78 (2024; Zbl 07822057) Full Text: DOI
Borisov, D. I.; Zezyulin, D. A. Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields. (English) Zbl 07801086 Ann. Phys. 459, Article ID 169498, 17 p. (2023). MSC: 81-XX 35-XX PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{D. A. Zezyulin}, Ann. Phys. 459, Article ID 169498, 17 p. (2023; Zbl 07801086) Full Text: DOI arXiv
Borisov, D. I.; Zezyulin, D. A. On the bifurcation of thresholds of the essential spectrum with a spectral singularity. (English. Russian original) Zbl 1527.81055 Differ. Equ. 59, No. 2, 278-282 (2023); translation from Differ. Uravn. 59, No. 2, 270-274 (2023). MSC: 81Q10 34L40 34L05 34L15 34M35 34F10 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{D. A. Zezyulin}, Differ. Equ. 59, No. 2, 278--282 (2023; Zbl 1527.81055); translation from Differ. Uravn. 59, No. 2, 270--274 (2023) Full Text: DOI
Borisov, D. I.; Zezyulin, D. A. Bifurcations of essential spectra generated by a small non-Hermitian hole. II: Eigenvalues and resonances. (English) Zbl 1498.35214 Russ. J. Math. Phys. 29, No. 3, 321-341 (2022). MSC: 35J25 35P05 35B32 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{D. A. Zezyulin}, Russ. J. Math. Phys. 29, No. 3, 321--341 (2022; Zbl 1498.35214) Full Text: DOI
Znojil, Miloslav; Borisov, Denis I. Arnold’s potentials and quantum catastrophes. II. (English) Zbl 1497.81055 Ann. Phys. 442, Article ID 168896, 15 p. (2022). MSC: 81Q05 26C05 81Q15 58K35 31C35 35B20 PDFBibTeX XMLCite \textit{M. Znojil} and \textit{D. I. Borisov}, Ann. Phys. 442, Article ID 168896, 15 p. (2022; Zbl 1497.81055) Full Text: DOI arXiv
Borisov, D. I.; Zezyulin, D. A. Bifurcations of essential spectra generated by a small non-Hermitian hole. I: Meromorphic continuations. (English) Zbl 1479.35582 Russ. J. Math. Phys. 28, No. 4, 416-433 (2021). MSC: 35P05 35J25 35B20 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{D. A. Zezyulin}, Russ. J. Math. Phys. 28, No. 4, 416--433 (2021; Zbl 1479.35582) Full Text: DOI
Znojil, Miloslav; Borisov, Denis I. Anomalous mechanisms of the loss of observability in non-Hermitian quantum models. (English) Zbl 1473.81151 Nucl. Phys., B 957, Article ID 115064, 19 p. (2020). MSC: 81T32 82B26 82B27 14H55 PDFBibTeX XMLCite \textit{M. Znojil} and \textit{D. I. Borisov}, Nucl. Phys., B 957, Article ID 115064, 19 p. (2020; Zbl 1473.81151) Full Text: DOI arXiv
Borisov, Denis; Cardone, Giuseppe Spectra of operator pencils with small \(\mathcal{PT}\)-symmetric periodic perturbation. (English) Zbl 1444.47023 ESAIM, Control Optim. Calc. Var. 26, Paper No. 21, 32 p. (2020). Reviewer: Yaudat Sultanaev (Ufa) MSC: 47A56 34L20 PDFBibTeX XMLCite \textit{D. Borisov} and \textit{G. Cardone}, ESAIM, Control Optim. Calc. Var. 26, Paper No. 21, 32 p. (2020; Zbl 1444.47023) Full Text: DOI
Znojil, Miloslav; Borisov, Denis I. Two patterns of \(\mathcal{PT}\)-symmetry breakdown in a non-numerical six-state simulation. (English) Zbl 1390.81172 Ann. Phys. 394, 40-49 (2018). MSC: 81Q12 PDFBibTeX XMLCite \textit{M. Znojil} and \textit{D. I. Borisov}, Ann. Phys. 394, 40--49 (2018; Zbl 1390.81172) Full Text: DOI arXiv
Borisov, Denis I.; Znojil, Miloslav Mathematical and physical meaning of the crossings of energy levels in \(\mathcal {PT}\)-symmetric systems. (English) Zbl 1402.81149 Bagarello, Fabio (ed.) et al., Non-Hermitian Hamiltonians in quantum physics. Selected contributions from the 15th international conference on non-Hermitian Hamiltonians in quantum physics, Palermo, Italy, May 18–23, 2015. Cham: Springer (ISBN 978-3-319-31354-2/hbk; 978-3-319-31356-6/ebook). Springer Proceedings in Physics 184, 201-217 (2016). MSC: 81Q10 81Q12 46C05 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{M. Znojil}, Springer Proc. Phys. 184, 201--217 (2016; Zbl 1402.81149) Full Text: DOI arXiv
Borisov, D. I. The emergence of eigenvalues of a \(\mathcal{PT}\)-symmetric operator in a thin strip. (English. Russian original) Zbl 1364.35077 Math. Notes 98, No. 6, 872-883 (2015); translation from Mat. Zametki 98, No. 6, 809-823 (2015). Reviewer: Lorenzo Zanelli (Padova) MSC: 35J10 PDFBibTeX XMLCite \textit{D. I. Borisov}, Math. Notes 98, No. 6, 872--883 (2015; Zbl 1364.35077); translation from Mat. Zametki 98, No. 6, 809--823 (2015) Full Text: DOI
Borisov, Denis I.; Ružička, František; Znojil, Miloslav Multiply degenerate exceptional points and quantum phase transitions. (English) Zbl 1329.81037 Int. J. Theor. Phys. 54, No. 12, 4293-4305 (2015). MSC: 81P05 81Q10 82B26 PDFBibTeX XMLCite \textit{D. I. Borisov} et al., Int. J. Theor. Phys. 54, No. 12, 4293--4305 (2015; Zbl 1329.81037) Full Text: DOI arXiv
Borisov, D. I. On a \(\mathcal{PT}\)-symmetric waveguide with a pair of small holes. (English. Russian original) Zbl 1321.47166 Proc. Steklov Inst. Math. 281, Suppl. 1, S5-S21 (2013); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 18, No. 2, 22-37 (2012). Reviewer: Vladimir N. Karpushkin (Moskva) MSC: 47N50 81Q37 PDFBibTeX XMLCite \textit{D. I. Borisov}, Proc. Steklov Inst. Math. 281, S5--S21 (2013; Zbl 1321.47166); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 18, No. 2, 22--37 (2012) Full Text: DOI