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On the metric operator for the imaginary cubic oscillator
- P. Siegl, D. Krejčiřík
- Mathematics
- 9 August 2012
We show that the eigenvectors of the PT-symmetric imaginary cubic oscillator are complete, but do not form a Riesz basis. This results in the existence of a bounded metric operator having intrinsic…
The first Robin eigenvalue with negative boundary parameter
- P. Freitas, D. Krejčiřík
- Mathematics
- 26 March 2014
Bound States in Curved Quantum Layers
- P. Duclos, P. Exner, D. Krejčiřík
- Physics
- 27 February 2001
Abstract: We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in ℝ3. We suppose that the latter is endowed with…
Spectral stability of Schrödinger operators with subordinated complex potentials
- L. Fanelli, D. Krejčiřík, L. Vega
- MathematicsJournal of Spectral Theory
- 4 June 2015
We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness…
Pseudospectra in non-Hermitian quantum mechanics
- D. Krejčiřík, P. Siegl, M. Tater, J. Viola
- Physics
- 5 February 2014
We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity…
A Hardy Inequality in Twisted Waveguides
- T. Ekholm, H. Kovarík, D. Krejčiřík
- Mathematics
- 15 December 2005
We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we…
Twisting versus bending in quantum waveguides
- D. Krejčiřík
- Mathematics
- 20 December 2007
We make an overview of spectral-geometric effects of twisting and bending in quantum waveguides modelled by the Dirichlet Laplacian in an unbounded three-dimensional tube of uniform cross-section. We…
Closed formula for the metric in the Hilbert space of a -symmetric model
- D. Krejčiřík, H. Bíla, M. Znojil
- Mathematics, Physics
- 24 April 2006
We introduce a very simple, exactly solvable -symmetric non-Hermitian model with a real spectrum, and derive a closed formula for the metric operator which relates the problem to a Hermitian one.
Location of the nodal set for thin curved tubes
- P. Freitas, D. Krejčiřík
- Mathematics
- 21 February 2006
The Dirichlet Laplacian in curved tubes of arbitrary constant cross-section rotating together with the Tang frame along a bounded curve in Euclidean spaces of arbitrary dimension is investigated in…
Topologically nontrivial quantum layers
- G. Carron, P. Exner, D. Krejčiřík
- Mathematics
- 11 February 2003
Given a complete noncompact surface Σ embedded in R3, we consider the Dirichlet Laplacian in the layer Ω that is defined as a tubular neighborhood of constant width about Σ. Using an intrinsic…
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