We consider two interacting particles evolving in a one-dimensional periodic structure embedded in a magnetic field. We show that the strong localization induced by the magnetic field for particular values of the flux per unit cell is destroyed as soon as the particles interact. We study the spectral and dynamical aspects of this transition.

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We report transport measurements on superconducting wire networks which provide the first experimental evidence of a new localization phenomenon induced by magnetic field on a 2D periodic structure. In the case of a superconducting wave function this phenomenon manifests itself as a depression of the network critical current and of the superconducting transition temperature at a half magnetic flux quantum per tile. In addition, the strong broadening of the resistive transition observed at this field is consistent with enhanced phase fluctuations due to this localization mechanism.PACS numbers: 72.15, 73.23, 74.25 In a recent paper [1] a novel case of extreme localization induced by a transverse magnetic field was predicted for non interacting electrons in a two-dimensional (2D) periodic structure. This new phenomenon, due to a subtle interplay between lattice geometry and the magnetic field, differs from Anderson localization on two essential points: it occurs in a pure system, without disorder, and the system eigenstates are not localized but nondispersive states. In a tight-binding (TB) approach, it can be simply understood in terms of Aharonov-Bohm effect which, at half a flux quantum per unit tile (halfflux), leads to fully destructive quantum interferences. For this flux, the set of sites visited by an initially localized wave-packet will be bounded in Aharonov-Bohm cages [1]. This effect is absent on other regular periodic lattices at half-flux, such as the square and the triangular lattices.Superconducting wire networks are suitable to address phase interference phenomena driven by a magnetic field [2]. These systems are extremely sensitive to phase coherence of the superconducting order parameter over the network sites which is exclusively determined by the competition between the external field and the network geometry [3]. Besides, the quantum regime is accessible even in low T c diffusive superconductors: since all Cooper pairs condense in a quantum state, the relevant wavelength is associated with the macroscopic superfluid velocity and can be much larger than the lattice elementary cell [4]. Also, the magnetic field corresponding to one superconducting flux quantum Φ o = hc/2e, is easily accessible: it is about 1 mT for a network cell of 1 µm 2 , in contrast to the unattainable 10 3 T for an atomic lattice. In addition, some features of the TB spectrum, namely the Hofstadter butterfly [5], are experimentally accessible in the model system of a superconducting wire network [3,6]. As shown by de Gennes and Alexander [7,8], the linearized Ginzburg-Landau (GL) equations for a superconducting wire network can be mapped onto the eigenvalues equation of a TB hamiltonian for the same geometry. This mapping is of particular relevance since one of the remarkable findings of Ref.[1] is the total absence of dispersion in the TB spectrum at half-flux. In the context of a superconducting network, the localization effect is expressed by the inability of the superconducting wave function to carry phase informati...