Dynamical localization in the unitary process of quantum walks

Název anglicky / Title English: Dynamical localization in the unitary process of quantum walks
Osnova / Outline:

The process of discrete time quantum walks are described as succesively applied unitaries. We aim to study the effect of randomization of these unitaries, leading to a phenomena analogous to Anderson localization. The properties of Anderson localization, which appears in systems governed by a Hamiltonian, are well known in the solid state physics community, however, for unitary dynamical localization only the one dimensional case is well-understood. For the higher dimensional case there are only few results so far, which indicate several differences from Anderson localization. In particular, we can expect to find a metal-insulator transition already at 2D: a system that is even within reach for an experimental realization.

The topic is one of the promising research directions being considered in the our research group lead by Prof. Igor Jex. There will be possibility for the joining student to subsequently continue with a master project.

Literatura / reference:
  1. A. Schreiber, et al.: Decoherence and disorder in quantum walks: "From ballistic spread to localization," Phys. Rev. Lett. 106, 180403 (2011)
  2. A. Joye and M. Merkli: "Dynamical Localization of Quantum Walks in Random Environments," Journal of Statistical Physics, 140, (2010), 1025-1053.
  3. A. Joye: "Dynamical localization for d-dimensional random quantum walks," Quantum Inf. Process 11, 1251 (2012)
Jméno vedoucího / Supervisor name: Aurél Gábris, PhD
Pracoviště vedoucího / Supervisor office: KF FJFI, BR 13b
Email vedoucího / Supervisor email: gabris.aurel@fjfi.cvut.cz
Datum zadání / Date of creation: 20/03/2017
Jazyk / Language:
  • Anglicky / English
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