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Pseudospectra in non-Hermitian quantum mechanics. (English) Zbl 1328.81116
Let $$H$$ be the harmonic oscillator Hamiltonian perturbed by imaginary shift. The authors derive a lower estimate for the resolvent of $$H$$ of the form $$\ln \| ( H - z )^{ -1 } \| \geq C \sqrt{ \operatorname{Re} z }$$, $$C > 0$$, in a parabolic region of the right half plane by semiclassical methods.

##### MSC:
 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 47E05 General theory of ordinary differential operators 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
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