Abstract
We prove the spectral instability of the complex cubic oscillator \({-\frac{{\rm d}^{2}}{{\rm d}x^{2}} + ix^{3} + i \alpha x}\) for non-negative values of the parameter α, by getting the exponential growth rate of \({\|\Pi_{n}(\alpha)\|}\), where \({\Pi_{n}(\alpha)}\) is the spectral projection associated with the nth eigenvalue of the operator. More precisely, we show that for all non-negative α
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Communicated by Jan Derezinski.
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Henry, R. Spectral Projections of the Complex Cubic Oscillator. Ann. Henri Poincaré 15, 2025–2043 (2014). https://doi.org/10.1007/s00023-013-0292-2
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DOI: https://doi.org/10.1007/s00023-013-0292-2