Abstract
We consider a coupled system of Schrödinger equations with time-periodic coefficients \begin{eqnarray*} i\, u_t = -\Delta u + V(x,t)u + g(x,t)v \\ i\, v_t = -\Delta v + W(x,t)v + g(x,t)u \end{eqnarray*} on the Hilbert space $ \mathcal H = L^2({\mathbb R}^n) \times L^2({\mathbb R}^n)$, where $g$, $V$ and $W$ are periodic time-dependent potentials, with period $T$. We denote by $(U(t,s))_{(t,s) \in {\mathbb R}\times {\mathbb R}}$ its associated propagator. By using a multiplier method, we rule out the existence of regular eigenvectors of the Floquet operator $U(T,0)$.
Citation
M Angelica Astaburuaga. R. Coimbra Charão. Claudio Fernández. G. Perla Menzala. "Spectral properties of a coupled system of Schrödinger equations with time-periodic coefficients." Differential Integral Equations 25 (1/2) 21 - 30, January/February 2012. https://doi.org/10.57262/die/1356012823
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