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**Example text**

Before introducing the kicked Harper model formally, let us recall some facts about the Harper model. It was ﬁrst derived to describe electrons moving in a two-dimensional periodic potential, so-called Bloch electrons, in a magnetic ﬁeld directed perpendicularly to the potential plane [16,17]. Its Hamiltonian is discrete and reads H= n V cos (2πσn + ν) a†n an + a†n+1 an + a†n−1 an , (1) where V is the potential strength, σ a measure of the magnetic ﬂux, ν a phase, and a†n , an are the creation and annihilation operators at site n.

24) Note that Kondo conductance (24) in the strongly asymmetric set-up is signiﬁcantly smaller than the conductance quantum e2 /h even at T = 0. The maximal value of GK is substantially increased, if the asymmetry between the junctions is reduced, and the condition GL e2 /h is lifted. To show this, we further generalize the above results to include the experimentally important case |rR | |rL | 1. Like in the case of a single strong junction considered above, the backscattering in the junctions becomes increasingly eﬀective at low electron energies.

H. Blick et al. , (1998), Phys. Rev. Lett. G. , (1998), J. Appl. Phys. , cond-mat/9904382. , (1997), Phys. Rev. , (1996), Appl. Phys. Lett. , (1961), Phys. Rev. , (1989), Phys. Rev. Lett. , (1990), Phys. Rev. Lett. , (1996), Phys. Rev. Lett. , (1990), Phys. Rev. , (1995), Phys. Rev. Lett. , (1993), Phys. Rev. Lett. , (1998) Appl. Phys. Lett. , (1999), Superlattices and Microstructures 25, 785 Quantum Chaos and Spectral Transitions in the Kicked Harper Model Karsten Kruse, Roland Ketzmerick, and Theo Geisel Max-Planck-Institut f¨ ur Str¨ omungsforschung und Fakult¨ at Physik der Universit¨ at G¨ ottingen, Bunsenstraße 10, D-37073 G¨ ottingen, Germany Abstract.