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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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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