Propagation and spectral properties of quantum walks in electric fields

@inproceedings{Cedzich2013PropagationAS,
  title={Propagation and spectral properties of quantum walks in electric fields},
  author={Christopher Cedzich and T. Ryb'ar and Albert H. Werner and Andrea Alberti and Maximilian Genske and Reinhard F. Werner},
  year={2013}
}
We study one-dimensional quantum walks in a homogenous electric field. The field is given by a 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 Φ, e.g., on whether Φ/(2π) is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given… 

Figures and Tables from this paper

Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices
We consider the spectral and dynamical properties of one-dimensional quantum walks placed into homogenous electric fields according to a discrete version of the minimal coupling principle. We show
Singular continuous Cantor spectrum for magnetic quantum walks
In this note, we consider a physical system given by a two-dimensional quantum walk in an external magnetic field. In this setup, we show that both the topological structure and its type depend
Quantum walk with quadratic position-dependent phase defects
TLDR
A comprehensive study of the property of one-dimensional quantum walks, via position distribution of the walker, is adopted herein by considering position-dependent quadratic phase defect and shed light on the analysis of discrete quantum processes and the potential relevant for physical implementations of quantum computing with various mesoscopic systems.
Guiding and confining of light in a two-dimensional synthetic space using electric fields
Synthetic dimensions provide a promising platform for photonic quantum simulations. Manipulating the flow of photons in these dimensions requires an electric field. However, photons do not have
From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks
TLDR
It is shown that the spacetime-dependent QW simulates the Dirac equation in (2 + 1)–dimensional curved spacetime, and opens the possibility to simulate field theories on curved manifolds via the quantum walk on different kinds of lattices.
Mimicking the Hadamard discrete-time quantum walk with a time-independent Hamiltonian
TLDR
It is found that the dynamics of the walker probability distribution and the corresponding standard deviation, the coin-walker entanglement, and the quantum-to-classical transition of the discrete-time quantum walk model can be approximately generated by the optimized time-independent Hamiltonian.
An overview of quantum cellular automata
TLDR
An overview of quantum cellular automata theory is given, with particular focus on structure results; computability and universality results; and quantum simulation results.
Absorption probabilities of quantum walks
TLDR
In the one-dimensional cases, these results are extended to general two-state quantum walks and three-state Grover walks, while providing a partial calculation for absorption in d-dimensional Grover walk by a d-1-dimensional wall.
...
...

References

SHOWING 1-10 OF 13 REFERENCES
Electric quantum walks with individual atoms.
TLDR
The regime of strong fields is explored, demonstrating contrasting quantum behaviors: quantum resonances versus dynamical localization depending on whether the accumulated Bloch phase is a rational or irrational fraction of 2π.
Ann
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed
Phys
  • Today 62, 30
  • 2009
Phys
  • 90, 1201
  • 1998
arXiv/quant-ph
  • 0406039
  • 2004
Phys
  • Rev. E 69, 026119
  • 2004
Phys
  • Rev. B 14, 2239
  • 1976
Phys
  • Rev. A 73, 062304
  • 2006
Phys
  • Rev. 109, 1492
  • 1958
Quant
  • Inf. Processing 11, 1219
  • 2012
...
...