| Name |
Albert H. Werner |
| Country |
Germany |
| Email |
albert.werner@fu-berlin.de |
| Co-Author(s) |
A. Ahlbrecht, A. Alberti, C. Cedzich, M. Genske, D. Meschede, T. Rybar, V.B. Scholz, R.F. Werner |
| Submit Time |
2014-04-01 08:14:21 |
Session |
Special Session 26: Dynamical systems and spectral theory
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| Contents |
| We consider the effects of interactions and simulated homogeneous electric fields on the propagation properties of one dimensional quantum walks. For interacting two particles quantum walks we show the existence of stable bound states, in the spectral gap of the free Evolution Operator and exponentially decay of the corresponding eigenfunction with respect to the relative position of the two particles. Furthermore, for a certain class of interactions, we develop an effective theory and find that the dynamics of the molecule is described by a quantum walk in its own right.
Homogeneous electric fields are introduced by an additional local phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $\Phi$, e.g., on whether $\Phi/(2\pi)$ is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions about the behavior on finite time scales. |
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