Publications
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The Red Queen shook her head. "You may call it `nonsense' if you like,"
she said, "but I've heard nonsense, compared with which that would be
as sensible as a dictionary !"
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D. Krejcirik and P. Siegl:
"Elements of Spectral Theory
without the Spectral Theorem".
In "Non-Selfadjoint Operators in Quantum Physics:
Mathematical Aspects",
F. Bagarello, J.-P. Gazeau, F. H. Szafraniec, and M. Znojil, Eds.,
Wiley-Interscience, 2015.
Back to Contents
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D. Krejcirik, T. Nguyen Duc and N. Raymond:
"The Laplacian with complex magnetic fields";
Preprint on
arXiv:2410.01377 [math.ph]
and on
HAL.
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D. Krejcirik, P. D. Lamberti and M. Zaccaron:
"A note on the failure of the Faber-Krahn inequality
for the vector Laplacian";
Preprint on
arXiv:2409.07206 [math.OC].
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L. Boulton, D. Krejcirik and T. Nguyen Duc:
"Spectral analysis of Dirac operators for dislocated potentials
with a purely imaginary jump";
Preprint on
arXiv:2409.06480 [math.SP].
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L. Cossetti and D. Krejcirik:
"The virial theorem and the method of multipliers in spectral theory";
Preprint on
arXiv:2407.12379 [math.SP].
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D. Kramar and D. Krejcirik:
"Dirac operators on the half-line: stability of spectrum and non-relativistic limit";
Preprint on
arXiv:2405.10009 [math.SP].
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D. Krejcirik and J. Lipovsky:
"Spectral determinant for the wave equation on an interval with Dirac damping";
Preprint on
arXiv:2404.11992 [math.SP].
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F. Herau, D. Krejcirik and N. Raymond:
"Semiclassical asymptotics of the Bloch-Torrey operator in two dimensions";
Preprint on
arXiv:2402.08574 [math.SP]
and on
HAL.
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L. Baldelli and D. Krejcirik:
"Curved nonlinear waveguides";
Preprint on
arXiv:2312.10357 [math.AP].
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B. Gerhat, D. Krejcirik and F. Stampach:
"Criticality transition for positive powers of
the discrete Laplacian on the half line";
Preprint on
arXiv:2307.09919 [math.SP].
Back to Contents
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P. Antunes, F. Bento and D. Krejcirik:
"Numerical optimisation of Dirac eigenvalues";
J. Phys. A: Math. Theor., to appear.
Preprint on
arXiv:2403.18556 [math.OC].
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L. Cossetti, L. Fanelli and D. Krejcirik:
"Uniform resolvent estimates and absence of eigenvalues of
biharmonic operators with complex potentials";
J. Funct. Anal. 287 (2024) 110646.
Available on
[
Elsevier (published version)
].
Preprint on
arXiv:2309.06823 [math.AP].
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D. Krejcirik and V. Lotoreichik:
"Optimisation and monotonicity of the second Robin eigenvalue
on a planar exterior domain";
Calc. Var. Partial Differ. Equ. 63 (2024) art. no. 223.
Preprint on
arXiv:2307.14286 [math.OC].
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D. Krejcirik and V. Lotoreichik:
"Quasi-conical domains with embedded eigenvalues";
Bull. London Math. Soc. 56 (2024) 2969-2981.
Available on
[
LMS (published version)
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Preprint on
arXiv:2205.08172 [math.SP].
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C. Cazacu, D. Krejcirik, N. Lam and A. Laptev:
"Hardy inequalities for magnetic p-Laplacians";
Nonlinearity 37 (2024) 035004.
Available on
[
IOP (published version)
].
Preprint on
arXiv:2201.02482 [math.AP].
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D. Krejcirik and J. Kriz:
"Bound states in soft quantum layers";
Publ. RIMS, Kyoto University 60 (2024), 4.
Preprint on
arXiv:2205.04919 [math-ph].
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D. Krejcirik, V. Lotoreichik and T. Vu:
"Reverse isoperimetric inequality for the lowest Robin eigenvalue of a triangle";
Appl. Math. Optim. 88 (2023) 63.
Available on
[
Springer (published version)
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Preprint on
arXiv:2204.03235 [math.OC].
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B. Cassano, V. Franceschi, D. Krejcirik and D. Prandi:
"Horizontal magnetic fields
and improved Hardy inequalities in the Heisenberg group";
Comm. Partial Differential Equations 48 (2023) 711-752.
Available on
[
Taylor & Francis (published version)
].
Preprint on
arXiv:2110.13775 [math.SP].
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D. Krejcirik and J. Royer:
"Spectrum of the wave equation with Dirac damping on a non-compact star graph";
Proc. Amer. Math. Soc. 151 (2023) 4673-4691.
Available on
[
AMS (published version)
].
Preprint on
arXiv:2204.12747 [math.SP]
and on
HAL.
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B. Gerhat, D. Krejcirik and F. Stampach:
"An improved discrete Rellich inequality on the half-line";
Israel J. Math., to appear.
Preprint on
arXiv:2206.11007 [math.SP].
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M. C. Camara and D. Krejcirik:
"Complex-self-adjointness";
Anal. Math. Phys. 13 (2023), art. no. 6.
Available on
[
Springer (published version)
].
Preprint on
arXiv:2208.05739 [math.FA].
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D. Krejcirik, A. Laptev and F. Stampach:
"Spectral enclosures and stability
for non-self-adjoint discrete Schrodinger operators on the half-line";
Bull. London. Math. Soc. 54 (2022) 2379-2403.
Available on
[
LMS (published version)
].
Preprint on
arXiv:2111.08265 [math.SP].
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M. Hansmann and D. Krejcirik:
"The abstract Birman-Schwinger principle and spectral stability";
J. Anal. Math. 148 (2022) 361-398.
Available on
[
Springer (published version)
].
Preprint on
arXiv:2010.15102 [math.SP].
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D. Krejcirik and T. Nguyen Duc:
"Pseudomodes for non-self-adjoint Dirac operators";
J. Funct. Anal. 282 (2022) 109440.
Available on
[
Elsevier (published version)
].
Preprint on
arXiv:2011.09433 [math-ph].
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W. Borrelli, Ph. Briet, D. Krejcirik and T. Ourmieres-Bonafos:
"Spectral properties of relativistic quantum waveguides";
Ann. Henri Poincare 23 (2022) 4069-4114.
Available on
[
Springer (published version)
].
Preprint on
arXiv:2101.04009 [math.SP] and on
HAL.
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T. G. Pedersen, H. Cornean, D. Krejcirik, N. Raymond and E. Stockmeyer:
"Stark-localization as a probe of nanostructure geometry";
New. J. Phys 24 (2022) 093005.
Available on
[
IOP (published version)
].
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H. Cornean, D. Krejcirik, T. G. Pedersen, N. Raymond and E. Stockmeyer:
"On the two-dimensional quantum confined Stark effect in strong electric fields";
SIAM J. Math. Anal. 54 (2022) 2114-2127.
Available on
[
SIAM (published version)
].
Preprint on
arXiv:2012.09145 [math-ph].
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Ph. Briet and D. Krejcirik:
"Spectral optimisation of Dirac rectangles";
J. Math. Phys. 63 (2022) 013502.
Available on
[
AIP (published version)
].
Preprint on
arXiv:2103.08881 [math.SP].
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D. Krejcirik and F. Stampach:
"A sharp form of the discrete Hardy inequality and the Keller-Pinchover-Pogorzelski inequality";
Amer. Math. Monthly 129 (2022) 281-283.
Available on
[
Taylor & Francis (published version)
].
Preprint on
arXiv:2108.04379 [math.SP].
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P. D'Ancona, L. Fanelli, D. Krejcirik, N. M. Schiavone:
"Localization of eigenvalues for non-self-adjoint Dirac and Klein-Gordon operators";
Nonlinear Anal. 214 (2022) 112565.
Available on
[
Elsevier (published version)
].
Preprint on
arXiv:2104.13647 [math.SP].
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O. O. Ibrogimov, D. Krejcirik and A. Laptev:
"Sharp bounds for eigenvalues of biharmonic operators
with complex potentials in low dimensions";
Math. Nachr. 294 (2021) 1333-1349.
Available on
[
Wiley (published version)
].
Preprint on
arXiv:1903.01810 [math.SP].
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S. Kondej, D. Krejcirik and J. Kriz:
"Soft quantum waveguides with an explicit cut-locus";
J. Phys. A: Math. Theor. 54 (2021) 30LT01.
Available on
[
IOP (published version)
].
Preprint on
arXiv:2007.10946 [math-ph].
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D. Krejcirik, V. Lotoreichik, K. Pankrashkin and M. Tusek:
"Spectral analysis of the multi-dimensional diffusion operator
with random jumps from the boundary";
J. Evol. Equ. 21 (2021) 1651-1675.
Available on
[
Springer (published version)
].
Preprint on
arXiv:2006.14392 [math.SP].
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D. Krejcirik and P. Antunes:
"Bound states in semi-Dirac semi-metals";
Phys. Lett. A 386 (2021) 126991.
Available on
[
Elsevier (published version)
].
Preprint on
arXiv:2007.01643 [math-ph].
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D. Krejcirik and T. Kurimaiova:
"From Lieb-Thirring inequalities
to spectral enclosures for the damped wave equation";
Integral Equations Operator Theory 92 (2020) 47.
Available on
[
Springer (published version)
].
Preprint on
arXiv:2008.05176 [math-SP].
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L. Cossetti, L. Fanelli and D. Krejcirik:
"Absence of eigenvalues of Dirac and Pauli Hamiltonians via the method of multipliers";
Comm. Math. Phys. 379 (2020) 633-691.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1912.02443 [math.SP].
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L. Cossetti and D. Krejcirik:
"Absence of eigenvalues of non-self-adjoint Robin Laplacians on the half-space";
Proc. London. Math. Soc. 121 (2020) 584-616.
Available on
[
LMS (published version)
].
Preprint on
arXiv:1812.05348 [math.SP].
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L. Fanelli, D. Krejcirik, A. Laptev and L. Vega:
"On the improvement of the Hardy inequality
due to singular magnetic fields";
Comm. Partial Differential Equations 45 (2020) 1202-1212.
Available on
[
Taylor & Francis (published version)
].
Preprint on
arXiv:1807.04430 [math.SP].
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B. Cassano, O. O. Ibrogimov, D. Krejcirik and F. Stampach:
"Location of eigenvalues of non-self-adjoint discrete Dirac operators";
Ann. Henri Poincare 21 (2020) 2193-2217.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1910.10710 [math.SP].
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T. Kalvoda, D. Krejcirik and K. Zahradova:
"Effective quantum dynamics on the Moebius strip";
J. Phys. A: Math. Theor. 53 (2020) 375201.
Available on
[
IOP (published version)
].
Preprint on
arXiv:1912.05365 [math.ph].
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D. Krejcirik and K. Zahradova:
"Quantum strips in higher dimensions";
Oper. Matrices 14 (2020) 635-665.
Available on
[
Ele-Math (published version)
].
Preprint on
arXiv:1906.02431 [math.ph].
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D. Krejcirik and V. Lotoreichik:
"Optimisation of the lowest Robin eigenvalue
in the exterior of a compact set, II:
non-convex domains and higher dimensions";
Potential Anal. 52 (2020), 601-614.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1707.02269 [math.SP].
Citations: 2
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Ph. Briet, J. Dittrich and D. Krejcirik:
"Absolute continuity of the spectrum
in a twisted Dirichlet-Neumann waveguide";
J. Math. Phys. 61 (2020) 013503.
Available on
[
AIP (published version)
].
Preprint on
arXiv:1906.05617 [math.ph].
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D. Krejcirik:
"Complex magnetic fields:
An improved Hardy-Laptev-Weidl inequality and quasi-self-adjointness";
SIAM J. Math. Anal. 51 (2019) 790-807.
Available on
[
SIAM (published version)
].
Preprint on
arXiv:1802.05586 [math.ph].
Citations: 1
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Ph. Briet, H. Abdou-Soimadou and D. Krejcirik:
"Spectral analysis of sheared nanoribbons";
Z. Angew. Math. Phys. 70 (2019) 48.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1807.10006 [math.ph].
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L. Fanelli and D. Krejcirik:
"Location of eigenvalues of three-dimensional non-self-adjoint Dirac operators";
Lett. Math. Phys. 109 (2019) 1473-1485.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1809.07580 [math.SP].
Citations: 1
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D. Krejcirik, G. P. Leonardi and P. Vlachopulos:
"The Cheeger constant of curved tubes";
Arch. Math. 112 (2019), 429-436.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1811.12095 [math.OC].
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D. Krejcirik and P. Siegl:
"Pseudomodes for Schrodinger operators with complex potentials";
J. Funct. Anal. 276 (2019), 2856-2900.
Available on
[
Elsevier (published version)
].
Preprint on
arXiv:1705.01894 [math.SP].
Citations: 2
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D. Krejcirik and M. Tusek:
"Location of hot spots in thin curved strips";
J. Differential Equations 266 (2019), 2953-2977.
Available on
[
Elsevier (published version)
].
Preprint on
arXiv:1709.01279 [math.AP].
Citations: 1
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D. Krejcirik, V. Lotoreichik and Thomas Ourmieres-Bonafos:
"Spectral transitions for Aharonov-Bohm Laplacians on conical layers";
Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), 1663-1687.
Available on
[
Cambridge (published version)
].
Preprint on
arXiv:1607.02454 [math.SP].
Citations: 1
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D. Krejcirik, V. Lotoreichik and M. Znojil:
"The minimally anisotropic metric operator
in quasi-Hermitian quantum mechanics";
Proc. Royal Soc. A - Math. Phy. Eng. Sci., 474 (2018) 20180264.
Available on
[
The Royal Society (published version)
].
Preprint on
arXiv:1804.06766 [math.ph].
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B. Kawohl and D. Krejcirik:
"From Symmetry to Monotonicity";
Math. Intell. 40 (2018), 12-13.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1712.08415 [math.CA].
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L. Fanelli, D. Krejcirik and L. Vega:
"Absence of eigenvalues of two-dimensional
magnetic Schrodinger operators";
J. Funct. Anal. 275 (2018), 2453-2472.
Available on
[
Elsevier (published version)
].
Preprint on
arXiv:1710.016176 [math.SP].
Citations: 3
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D. Krejcirik and R. Tiedra de Aldecoa:
"Ruled strips with asymptotically diverging twisting";
Ann. Henri Poincare 19 (2018), 2069-2086.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1802.00321 [math.SP].
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W. Kirsch, D. Krejcirik and G. Raikov:
"Lifshits tails for randomly twisted quantum waveguides";
J. Stat. Phys. 171 (2018), 383-399.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1705.04772 [math.SP].
Citations: 1
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D. Krejcirik, N. Raymond, J. Royer and P. Siegl:
"Reduction of dimension as a consequence of norm-resolvent
convergence and applications";
Mathematika 64 (2018), 406-429.
Available on
[
Cambridge Core (published version)
].
Preprint on
arXiv:1701.08819 [math-ph].
Citations: 1
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L. Fanelli, D. Krejcirik and L. Vega:
"Spectral stability of Schrodinger operators
with subordinated complex potentials";
J. Spectr. Theory 8 (2018), 575-604.
Available on
[
EMS (published version)
].
Preprint on
arXiv:1506.01617 [math.SP].
Citations: 3
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J. Behrndt and D. Krejcirik:
"An indefinite Laplacian on a rectangle";
J. Anal. Math. 134 (2018), 501-522.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1407.7802 [math.SP].
Citations: 3
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D. Krejcirik and V. Lotoreichik:
"Optimisation of the lowest Robin eigenvalue
in the exterior of a compact set";
J. Convex Anal. 25 (2018), 319-337.
Available on
[
Heldermann (published version)
].
Preprint on
arXiv:1608.04896 [math.SP].
Citations: 6
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D. Krejcirik, N. Raymond, J. Royer and P. Siegl:
"Non-accretive Schrodinger operators
and exponential decay of their eigenfunctions";
Israel J. Math. 221 (2017), 779-802.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1605.02437 [math.SP]
and on
HAL.
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S. Kondej and D. Krejcirik:
"Asymptotic spectral analysis in colliding leaky quantum layers";
J. Math. Anal. Appl. 446 (2017), 1328-1355.
Available on
[
Elsevier (published version)
].
Preprint on
arXiv:1606.07273 [math.ph].
Citations: 1
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P. Antunes, P. Freitas and D. Krejcirik:
"Bounds and extremal domains for Robin eigenvalues
with negative boundary parameter";
Adv. Calc. Var. 10 (2017), 357-380.
Available on
[
De Gruyter (published version)
].
Preprint on
arXiv:1605.08161 [math.SP]
Citations: 10
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R. Henry and D. Krejcirik:
"Pseudospectra of the Schrodinger operator
with a discontinuous complex potential";
J. Spectr. Theory 7 (2017), 659-697.
Available on
[
EMS (published version)
].
Preprint on
arXiv:1503.02478 [math.SP].
Citations: 4
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M. Kolb and D. Krejcirik:
"Spectral analysis of the diffusion operator
with random jumps from the boundary";
Math. Z. 284 (2016), 877-900.
Available on
[
Springer Link (published version)
].
Preprint on
arXiv:1507.08487 [math.SP].
Citations: 2
Corrigendum: Math. Z. 296 (2020), 883-885.
Available on
[
Springer Link (published version)
].
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B. Brandolini, F. Chiacchio, D. Krejcirik and C. Trombetti:
"The equality case in
a Poincare-Wirtinger type inequality";
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 27 (2016), 443-464.
Available on
[
EMS (published version)
].
Preprint on
arXiv:1410.0676 [math.AP].
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C. Cazacu and D. Krejcirik:
"The Hardy inequality and the heat equation
with magnetic field in any dimension";
Comm. Partial Differential Equations 41 (2016), 1056-1088.
Available on
[
Taylor & Francis (published version)
].
Preprint on
arXiv:1409.6433 [math.SP].
Citations: 3
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D. Krejcirik:
"The Hardy inequality and the heat flow in curved wedges";
Portugal. Math. 73 (2016), 91-113.
Available on
[
EMS (published version)
].
Preprint on
arXiv:1507.03627 [math.SP].
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D. Krejcirik, P. Siegl, M. Tater and J. Viola:
"Pseudospectra in non-Hermitian quantum mechanics";
J. Math. Phys. 56 (2015), 103513.
Available on
[
AIP (published version)
].
Preprint on
arXiv:1402.1082 [math-SP].
Citations: 29
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P. Freitas and D. Krejcirik:
"The first Robin eigenvalue with negative boundary parameter";
Adv. Math. 280 (2015), 322-339.
Available on
[
ScienceDirect (published version)
].
Preprint on
arXiv:1403.6666 [math-SP].
Citations: 18
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D. Krejcirik:
"Waveguides with asymptotically diverging twisting";
Appl. Math. Lett. 46 (2015), 7-10.
Available on
[
ScienceDirect (published version)
].
Preprint on
arXiv:1407.4028 [math.SP].
Citations: 1
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P. Freitas and D. Krejcirik:
"Alexandrov's isodiametric conjecture and the cut locus of a surface";
Tohoku Math. J. 67 (2015), 405-417.
Available on
[
ProjectEuclid (published version)
].
Preprint on
arXiv:1406.0811 [math.DG].
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Ph. Briet, H. Hammedi and D. Krejcirik:
"Hardy inequalities in globally twisted waveguides";
Lett. Math. Phys. 105 (2015), 939-958.
Available on
[
SpringerLink (published version)
].
Preprint on
arXiv:1406.2841 [math-SP].
Citations: 2
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A. Hussein, D. Krejcirik and P. Siegl:
"Non-self-adjoint graphs";
Trans. Amer. Math. Soc. 367 (2015), 2921-2957.
Available on
[
AMS (published version)
].
Preprint on
arXiv:1308.4264 [math-SP].
Citations: 7
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D. Krejcirik and M. Tusek:
"Nodal sets of thin curved layers";
J. Differential Equations 258 (2015), 281-301.
Available on
[
ScienceDirect (published version)
].
Preprint on
arXiv:1406.4103 [math.AP].
Citations: 1
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D. Krejcirik, N. Raymond and M. Tusek:
"The magnetic Laplacian in shrinking tubular
neighbourhoods of hypersurfaces";
J. Geom. Anal. 25 (2015), 2546-2564.
Available on
[
SpringerLink (published version)
].
Preprint on
arXiv:1303.4753 [math-ph]
and on
HAL.
Citations: 4
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V. Jakubsky and D. Krejcirik:
"Qualitative analysis of trapped Dirac fermions in graphene";
Ann. Phys. 349 (2014), 268-287.
Available on
[
ScienceDirect (published version)
].
Preprint on
arXiv:1405.2535 [cond-mat.mes-hall].
Citations: 11
Corrigendum: Ann. Phys. 353 (2015), 340-341.
Available on
[
ScienceDirect (published version)
].
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D. Krejcirik and N. Raymond:
"Magnetic effects in curved quantum waveguides";
Ann. Henri Poincare 15 (2014), 1993-2024.
Available on
[
SpringerLink (published version)
].
Preprint on
arXiv:1303.6844 [math-ph]
and on
HAL.
Citations: 6
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D. Krejcirik and Z. Lu:
"Location of the essential spectrum
in curved quantum layers";
J. Math. Phys. 55 (2014), 083520.
Available on
[
AIP (published version)
].
Preprint on
arXiv:1211.2541 [math-DG].
Citations: 4
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D. Krejcirik:
"Spectrum of the Laplacian in narrow tubular neighbourhoods
of hypersurfaces with combined Dirichlet
and Neumann boundary conditions";
Math. Bohem. 139 (2014), 185-193.
Available on
[
IM (published version)
].
Preprint on
arXiv:1311.2386 [math-SP].
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M. Kolb and D. Krejcirik:
"The Brownian traveller on manifolds";
J. Spectr. Theory 4 (2014), 235-281.
Available on
[
EMS (published version)
].
Preprint on
arXiv:1108.3191 [math.AP].
Citations: 2
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D. Krejcirik, P. Siegl and J. Zelezny:
"On the similarity of Sturm-Liouville operators
with non-Hermitian boundary conditions to
self-adjoint and normal operators";
Complex Anal. Oper. Theory 8 (2014), 255-281.
Available on
[
Springer (published version)
].
Preprint on
arXiv:1108.4946 [math.SP].
Citations: 12
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S. Kondej and D. Krejcirik:
"Spectral analysis of a quantum system
with a double line singular interaction";
Publ. RIMS, Kyoto University 49 (2013), 831-859.
Available on
[
EMS (published version)
].
Preprint on
arXiv:1307.1233 [math-SP].
Citations: 2
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D. Krejcirik:
"The improved decay rate for the heat semigroup
with local magnetic field in the plane";
Calc. Var. Partial Differ. Equ. 47 (2013), 207-226.
Available on
[
SpringerLink (published version)
].
Preprint on
arXiv:1101.1806 [math.AP].
Citations: 4
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P. Siegl and D. Krejcirik:
"On the metric operator for
the imaginary cubic oscillator";
Phys. Rev. D 86 (2012), 121702(R).
Available on
[
APS (published version)
].
Preprint on
arXiv:1208.1866 [quant-ph].
Citations: 49
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D. Krejcirik and H. Sedivakova:
"The effective Hamiltonian in curved quantum waveguides
under mild regularity assumptions";
Rev. Math. Phys. 24 (2012), 1250018.
Available on
[
World Scientific (published version)
].
Preprint on
arXiv:1203.1189 [math.SP].
Citations: 14
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D. Kochan, D. Krejcirik, R. Novak and P. Siegl:
"The Pauli equation with complex boundary conditions";
J. Phys. A: Math. Theor. 45 (2012), 444019.
Available on
[
IoP (published version)
].
Preprint on
arXiv:1203.5011 [quant.ph].
See a related
animation.
Citations: 5
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D. Borisov and D. Krejcirik:
"The effective Hamiltonian for thin layers
with non-Hermitian Robin-type boundary conditions";
Asympt. Anal. 76 (2012), 49-59.
Available on
[
IOS Press (published version)
].
Preprint on
arXiv:1102.5051 [math.SP].
Citations: 7
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D. Krejcirik:
"PT-symmetric waveguides and the lack of
variational techniques";
Integral Equations Operator Theory 73 (2012), 1-2.
Available on
[
SpringerLink (published version)
].
Preprint available on the homepage of
ESF Exploratory Workshop, Prague 2010 (Open problems link).
-
D. Krejcirik and A. Pratelli:
"The Cheeger constant of curved strips";
Pacific J. Math. 254 (2011), 309-333.
Available on
[
journal homepage (published version)
].
Preprint on
arXiv:1011.3490 [math.OC]
and on
CVGMT.
Citations: 12
-
H. Hernandez-Coronado, D. Krejcirik and P. Siegl:
"Perfect transmission scattering
as a PT-symmetric spectral problem";
Phys. Lett. A 375 (2011), 2149-2152.
Available on
[
ScienceDirect (published version)
].
Preprint on
arXiv:1011.4281 [math.ph].
See a related
animation.
Citations: 22
-
D. Krejcirik and E. Zuazua:
"The asymptotic behaviour of the heat equation
in a twisted Dirichlet-Neumann waveguide";
J. Differential Equations 250 (2011), 2334-2346.
Available on
[
ScienceDirect (published version)
].
Preprint on
arXiv:1006.2619 [math.AP].
Citations: 6
-
D. Krejcirik and P. Siegl:
"PT-symmetric models in curved manifolds";
J. Phys. A: Math. Theor. 43 (2010) 485204.
Available on
[
IoP (published version)
].
Preprint on
arXiv:1001.2988 [math.ph].
See a related
animation.
Citations: 12
-
M. Fraas, D. Krejcirik and Y. Pinchover:
"On some strong ratio limit theorems for heat kernels";
Discrete Contin. Dynam. Systems A 28 (2010), 495-509.
A special issue
dedicated to Louis Nirenberg on the occasion of his 85th birthday.
Available on
[
AIMS (published version)
].
Preprint on
arXiv:0912.4337 [math.AP].
Citations: 1
-
D. Krejcirik and E. Zuazua:
"The Hardy inequality
and the heat equation in twisted tubes";
J. Math. Pures Appl. 94 (2010), 277-303.
Available on
[
ScienceDirect (published version)
].
Preprint on
arXiv:0906.3359 [math.AP].
Citations: 9
-
D. Krejcirik:
"Spectrum of the Laplacian in a narrow curved strip
with combined Dirichlet and Neumann boundary conditions";
ESAIM: Control, Optimisation and Calculus of Variations
15 (2009), 555-568.
Available on
[
COCV (published version)
].
Preprint available on
arXiv:0803.0937 [math.SP].
Citations: 13
-
D. Borisov and D. Krejcirik:
"PT-symmetric waveguides";
Integral Equations Operator Theory 62
(2008), no. 4, 489-515.
Available on
[
Springer (published version)
].
Preprint on
arXiv:0707.3039 [math-ph].
Citations: 17
-
D. Krejcirik and M. Tater:
"Non-Hermitian spectral effects in a PT-symmetric waveguide";
J. Phys. A: Math. Theor. 41 (2008) 244013.
Available on
[
IoP (published version)
].
Preprint available on
arXiv:0802.0921 [math-ph].
See a related
animation.
Citations: 12
-
D. Krejcirik:
"Calculation of the metric in the Hilbert space
of a PT-symmetric model via the spectral theorem".
J. Phys. A: Math. Theor. 41 (2008) 244012.
Available on
[
IoP (published version)
].
Preprint available on
arXiv:0707.1781 [math-ph].
Citations: 28
-
P. Freitas and D. Krejcirik:
"A sharp upper bound for the first Dirichlet eigenvalue
and the growth of the isoperimetric constant of convex domains";
Proc. Amer. Math. Soc. 136 (2008), 2997-3006.
Available on
[
AMS (published version)
].
Preprint available on
arXiv:0710.5475 [math.SP].
Citations: 14
-
P. Freitas and D. Krejcirik:
"Location of the nodal set for thin curved tubes";
Indiana Univ. Math. J. 57 (2008), no. 1, 343-376.
Available on
[
IUMJ (published version)
].
Preprint available on
[
math.SP/0602470
].
Citations: 17
-
H. Kovarik and D. Krejcirik:
"A Hardy inequality in a twisted
Dirichlet-Neumann waveguide";
Math. Nachr. 281 (2008), no. 8, 1159-1168.
Available on
[
InterScience (published version)
].
Preprint available on
[
math-ph/0603076
].
Citations: 5
-
T. Ekholm, H. Kovarik and D. Krejcirik:
"A Hardy inequality in twisted waveguides";
Arch. Ration. Mech. Anal. 188 (2008), no. 2, pp. 245-264.
Available on
[
Springer (published version)
].
Preprint available on
[
math-ph/0512050
].
Citations: 25
-
P. Freitas and D. Krejcirik:
"Unbounded planar domains whose second nodal line
does not touch the boundary";
Math. Res. Lett. 14 (2007), no.1, pp. 107-111.
Available on
[
MRL (published version)
].
Preprint available on
[
math.SP/0511516
].
Citations: 4
-
P. Freitas and D. Krejcirik:
"Waveguides with combined
Dirichlet and Robin boundary conditions";
Math. Phys. Anal. Geom. 9 (2006), no. 4, pp. 335-352.
Available on
[
math.ph/0701075;
Springer (published version)
].
Citations: 12
-
D. Krejcirik, H. Bila and M. Znojil:
"Closed formula for the metric
in the Hilbert space of a PT-symmetric model";
J. Phys. A 39 (2006), pp. 10143-10153.
Available on
[
IoP (published version)
].
Preprint available on
[
math-ph/0604055
].
Citations: 36
-
D. Krejcirik:
"Hardy inequalities in strips on ruled surfaces";
J. Inequal. Appl. 2006 (2006), Article ID 46409, 10 pages.
Available on
[
Hindawi (published version)
].
Preprint available on
[
math.SP/0511257
].
Citations: 2
-
B. Chenaud, P. Duclos, P. Freitas and D. Krejcirik:
"Geometrically induced discrete spectrum in curved tubes";
Differential Geom. Appl.
23 (2005), no. 2, pp. 95-105.
Available on
[
ScienceDirect (published version)
].
Preprint available on
[
math.SP/0412132 ;
mp_arc 04-403 ;
SPECT Preprints
].
Citations: 35
-
D. Krejcirik and J. Kriz:
"On the spectrum of curved quantum waveguides";
Publ. RIMS, Kyoto University, 41 (2005), no. 3.,
pp. 757-791.
Available on
[
Project Euclid (published version)
].
Preprint available on
[
mp_arc 03-264 ;
math-ph/0306008
].
Citations: 34
-
P. Freitas and D. Krejcirik:
"Instability results for the damped wave equation in unbounded domains";
J. Differential Equations 211 (2005),
no. 1, pp. 168-186.
Available on
[
ScienceDirect (published version)
].
Preprint available on
[
math.AP/0406041 ;
SPECT Preprints
].
Citations: 6
-
P. Exner, P. Freitas and D. Krejcirik:
"A lower bound to the spectral threshold in curved tubes";
R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 460 (2004),
no. 2052, pp. 3457-3467.
Available on
[
The Royal Society (published version)
].
Preprint available on
[
mp_arc 04-152 ;
math-ph/0405039 ;
SPECT Preprints
].
Citations: 5
-
D. Krejcirik and R. Tiedra de Aldecoa:
"The nature of the essential spectrum in curved quantum waveguides";
J. Phys. A 37 (2004), no. 20, pp. 5449-5466.
Available on
[
IoP (published version)
].
Preprint available on
[
mp_arc 03-321 ;
math-ph/0307019
].
Citations: 18
-
G. Carron, P. Exner and D. Krejcirik:
"Topologically nontrivial quantum layers";
J. Math. Phys. 45 (2004), pp. 774-784.
Available on
[
mp_arc 03-51 ;
math-ph/0302025 ;
AIP (published version)
].
Citations: 19
-
D. Krejcirik:
"Quantum strips on surfaces";
J. Geom. Phys. 45 (2003), no. 1-2, pp. 203-217.
Available on
[
mp_arc 02-200 ;
math-ph/0204049 ;
ScienceDirect (published version)
].
Citations: 7
-
P. Exner and D. Krejcirik:
"Bound states in mildly curved layers";
J. Phys. A 34 (2001), pp. 5969-5985.
Available on
[
mp_arc 01-110 ;
math-ph/0103032 ;
IoP (published version)
].
Citations: 6
-
P. Duclos, P. Exner and D. Krejcirik:
"Bound states in curved quantum layers";
Commun. Math. Phys. 223 (2001), pp. 13-28.
Available on
[
mp_arc 01-79 ;
math-ph/0102033 ;
LINK (published version)
].
Citations: 35
-
D. Borisov, P. Exner, R. Gadyl'shin and D. Krejcirik:
"Bound states in weakly deformed strips and layers";
Ann. H. Poincare 2 (2001), pp. 553-572.
Available on
[
mp_arc 00-473 ;
math-ph/0011052 ;
LINK (published version)
].
Citations: 27
-
P. Exner and D. Krejcirik:
"Waveguides coupled through a semitransparent barrier:
a Birman-Schwinger analysis";
Rev. Math. Phys. 13 (2001), no. 3, pp. 307-334.
Available on
[
mp_arc 00-248 ;
math-ph/0005030 ;
WorldSciNet (published version)
].
Citations: 5
-
P. Duclos, P. Exner and D. Krejcirik:
"Locally curved quantum layers";
Ukrainian J. Phys. 45 (2000),
no. 4-5, pp. 595-601.
Available on
[
mp_arc 99-376 ;
quant-ph/9910035 ].
Citations: 5
-
P. Exner and D. Krejcirik:
"Quantum waveguides with a lateral semitransparent barrier:
spectral and scattering properties";
J. Phys. A 32 (1999), pp. 4475-4494.
Available on
[
mp_arc 99-124 ;
cond-mat/9904379 ;
IoP (published version)
].
Citations: 9
Back to Contents
-
P. Freitas and D. Krejcirik:
"A lower bound to the spectral threshold in curved quantum layers";
In "Functional Analysis
and Operator Theory for Quantum Physics",
J. Dittrich, H. Kovarik, and A. Laptev, Eds.,
EMS Series of Congress Reports.
Dedicated to Pavel Exner on the occasion of his 70th birthday.
Preprint on
arXiv:1602.04990 [math-ph].
-
D. Krejcirik:
"The Hardy inequality and the heat equation
with magnetic field";
Eigenvalue Problems in Surface Superconductivity
(Oberwolfach 2014),
Oberwolfach Reports 11 (2014), 3049-3051.
Preliminary version available on the
workshop page.
This article is an extended abstract of
my papers 37 and 57 above.
-
D. Krejcirik and H. Sedivakova:
"The effective Hamiltonian in curved quantum waveguides
and when it does not work";
Microlocal Methods in Mathematical Physics and Global Analysis
(Tubingen 2011),
Microlocal Methods in Mathematical Physics and Global Analysis,
Trends in Mathematics, pp. 29-32,
Springer, Basel, 2013.
Available on
[
Springer (published version)
].
This article is an extended abstract of my paper 35 above.
-
Jose M. Arrieta and D. Krejcirik:
"Geometric versus spectral convergence for the Neumann Laplacian
under exterior perturbations of the domain";
Integral Methods in Science and Engineering (Santander 2008),
Integral Methods in Science and Engineering, vol. 1, pp. 9-19,
Birkhauser, Boston, 2009.
Available on
[
Springer (published version)
].
Preprint on
arXiv:0901.4726 [math.SP].
Citations: 5
-
D. Krejcirik:
"Twisting versus bending in quantum waveguides";
Analysis on Graphs and Applications (Cambridge 2007),
Proc. Sympos. Pure Math.,
vol. 77, pp. 617-636,
Amer. Math. Soc., Providence, RI, 2008.
Available on
[
AMS (bookstore)
].
Corrected version on
arXiv:0712.3371v2 [math-ph].
Citations: 18
-
D. Krejcirik:
"Birman-Schwinger analysis for bound states in a pair
of parallel quantum waveguides with a semitransparent boundary";
Mathematical results in quantum mechanics (Prague 1998),
Oper. Theory Adv. Appl., vol. 108, pp. 281-289,
Birkhauser, Basel, 1999.
Available
[
PDF ].
Back to Contents
-
D. Krejcirik:
"Mathematical aspects of quantum mechanics
with non-self-adjoint operators";
Habilitation Thesis (September 2017),
Universitas Carolina Pragensis.
Available
[
PDF ].
-
D. Krejcirik:
"Geometrically induced spectral properties of physical systems";
DSc Thesis (November 2012),
Academy of Sciences of the Czech Republic.
Available
[
PDF ].
See a popular
[
html,
pdf
]
summary (in Czech) for
the Academic bulletin.
-
D. Krejcirik:
"Guides d'ondes quantiques bidimensionnels";
PhD Thesis (September 2001),
Universitas Carolina Pragensis & Universite de Toulon et du Var.
Available
[
PDF ].
-
D. Krejcirik:
"Spectral properties of straight quantum waveguides with a parallel
semitransparent barrier";
Diploma Thesis (April 1998),
Universitas Carolina Pragensis.
Available
[
PDF].
Back to Contents
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