Differential and Integral Equations

Spectral properties of a coupled system of Schrödinger equations with time-periodic coefficients

M Angelica Astaburuaga, R. Coimbra Charão, Claudio Fernández, and G. Perla Menzala

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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 $U(T,0)$.

Article information

Source
Differential Integral Equations, Volume 25, Number 1/2 (2012), 21-30.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012823

Mathematical Reviews number (MathSciNet)
MR2906544

Zentralblatt MATH identifier
1249.35274

Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics 47A10: Spectrum, resolvent 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.) 47N50: Applications in the physical sciences 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 35P05: General topics in linear spectral theory 81D25

Citation

Coimbra Charão, R.; Perla Menzala, G.; Angelica Astaburuaga, M; Fernández, Claudio. Spectral properties of a coupled system of Schrödinger equations with time-periodic coefficients. Differential Integral Equations 25 (2012), no. 1/2, 21--30. https://projecteuclid.org/euclid.die/1356012823


Export citation