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In the absence of nonlinearity all eigenstates of a chain with disorder are spatially localized. This phenomenon is known as Anderson localization and has been observed in different systems such as Bose-Einstein condensates, the propagation of light waves in disordered waveguides and many others.
If we replace the disorder by an analogue of an electric field, again all eigenstates of the chain will be localized with an equidistant eigenvalue spectrum (Stark ladder), resulting in well-known Bloch oscillations of various expectation values.
We study the impact of nonlinear terms on localization in the framework of the nonlinear Schroedinger equation. For the case of spatial disorder, three different types of evolution outcomes are observed: i) localization as a transient, with subsequent subdiffusion; ii) the absence of the transient and immediate subdiffusion; iii) selftrapping of a part of the packet, and subdiffusion of the remainder [1]. Spreading is due to
corresponding weak chaos inside the packet, which slowly heats the cold exterior. In a similar way, we study the fate of Bloch oscillations in the presence of nonlinearities.
[1] S. Flach, D.O. Krimer and H. Skokos, Phys. Rev. Lett. 102, 024101 (2009) |
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