## Differential and Integral Equations

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

### 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

#### 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