تقرير
Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator
| العنوان: | Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator |
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| المؤلفون: | Gallagher, I., Gallay, Th., Nier, F. |
| سنة النشر: | 2008 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, 35P15, 35P20, 35P99 |
| الوصف: | Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator $H_\epsilon = -\partial_x^2 + x^2 + i\epsilon^{-1}f(x)$ on $L^2(R)$, where $f$ is a real-valued function and $\epsilon > 0$ a small parameter. We define $\Sigma(\epsilon)$ as the infimum of the real part of the spectrum of $H_\epsilon$, and $\Psi(\epsilon)^{-1}$ as the supremum of the norm of the resolvent of $H_\epsilon$ along the imaginary axis. Under appropriate conditions on $f$, we show that both quantities $\Sigma(\epsilon)$, $\Psi(\epsilon)$ go to infinity as $\epsilon \to 0$, and we give precise estimates of the growth rate of $\Psi(\epsilon)$. We also provide an example where $\Sigma(\epsilon)$ is much larger than $\Psi(\epsilon)$ if $\epsilon$ is small. Our main results are established using variational "hypocoercive" methods, localization techniques and semiclassical subelliptic estimates. Comment: 38 pages, 4 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/0809.0574 |
| رقم الأكسشن: | edsarx.0809.0574 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |