No abstract

The typical avoided crossings for Hermitian quantum systems depending on parameters, the diabolic crossing scenario, are generalized to the non-Hermitian case, e.g. for resonances. Two types of crossings appear: for type I, the real parts show an avoided and the imaginary parts a true crossing of the eigenenergies, and for type II the opposite is found. A simple symmetric non-Hermitian twostate matrix Hamiltonian is analysed in detail. The diabolic point bifurcates into two exceptional ones on exceptional lines where the matrices are defective. The adiabatic transport of eigenvectors and eigenstates in parameter space is discussed in this generalized diabolic crossing scenario, in particular the geometric Berry phases for a cyclic variation of system parameters, depending on the topology of the closed curves with respect to the exceptional lines.

We present an approach for the analysis of Bose-Einstein condensates in a few mode approximation. This method has already been used to successfully analyze the vibrational modes in various molecular systems and offers a perspective on the dynamics in many particle bosonic systems. We discuss a system consisting of a Bose-Einstein condensate in a triple well potential. Such systems correspond to classical Hamiltonian systems with three degrees of freedom. The semiclassical approach allows a simple visualization of the eigenstates of the quantum system referring to the underlying classical dynamics. From this classification we can read off the dynamical properties of the eigenstates such as particle exchange between the wells and entanglement without further calculations. In addition, this approach offers insights into the validity of the mean-field description of the many particle system by the Gross-Pitaevskii equation, since we make use of exactly this correspondence in our semiclassical analysis. We choose a three mode system in order to visualize it easily and, moreover, to have a sufficiently interesting structure, although the method can also be extended to higher dimensional systems.⌽ ͑r ជ͒ = ͚ n,m n,m ͑r ជ͒â n,m , ͑2͒where we assume that the basis functions ͕ n,m ͖ of the oneparticle Hilbert space are exponentially localized in space and real, as is the case for the Wannier functions ͓22͔. The index n describes basis functions in different wells and we *Electronic address: mossmann@fis.unam.mx PHYSICAL REVIEW A 74, 033601 ͑2006͒

Abstract.The stationary nonlinear Schrödinger equation, or Gross-Pitaevskii equation, is studied for the cases of a single delta potential and a delta-shell potential. These model systems allow analytical solutions, and thus provide useful insight into the features of stationary bound, scattering and resonance states of the nonlinear Schrödinger equation. For the single delta potential, the influence of the potential strength and the nonlinearity is studied as well as the transition from bound to scattering states. Furthermore, the properties of resonance states for a repulsive delta-shell potential are discussed.

We investigate the dynamics of Bose-Einstein condensates in a tilted one-dimensional periodic lattice within the mean-field (Gross-Pitaevskii) description. Unlike in the linear case the Bloch oscillations decay because of nonlinear dephasing. Pronounced revival phenomena are observed. These are analyzed in detail in terms of a simple integrable model constructed by an expansion in Wannier-Stark resonance states. We also briefly discuss the pulsed output of such systems for stronger static fields.