Fetching the paper…

Reading the bibliography…

2008

Topological Transition in a Non-Hermitian Quantum Walk

Rudner, M. S., Levitov, L. S.

Original
PDF
Post on X

Understand

We analyze a quantum walk on a bipartite one-dimensional lattice, in which the particle can decay whenever it visits one of the two sublattices.

The corresponding non-Hermitian tight-binding problem with a complex potential for the decaying sites exhibits two different phases, distinguished by a winding number defined in terms of the Bloch eigenstates in the Brillouin zone.
We find that the mean displacement of a particle initially localized on one of the non-decaying sites can be expressed in terms of the winding number, and is therefore quantized as an integer, changing from zero to one at the critical point.
This problem can serve as a simplified model for nuclear spin pumping in the spin-blockaded electron transport regime of quantum dots in the presence of competing hyperfine and spin-orbital interactions.

Topological Transition in a Non-Hermitian Quantum Walk · Around

Built on

D. J. Thouless, M. Kohmoto, M. P. Nightingale, M. den Nijs, Phys. Rev. Lett. 49
1982
Earlier work this paper cites.
D. J. Thouless, Phys. Rev. B 27
1984
Earlier work this paper cites.
Eduardo Fradkin, Field Theories of Condensed Matter Systems
1991
Earlier work this paper cites.
T. V. Shahbazyan and M. E. Raikh, Phys. Rev. B 49
1994
Earlier work this paper cites.
C. W. J. Beenakker, J. C. J. Paasschens, and P. W. Brouwer, Phys. Rev. Lett. 76, 1368 (1996)
1996
Earlier work this paper cites.
N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77
1997
Earlier work this paper cites.

Similar

K. B. Efetov, Phys. Rev. Lett. 79
1997
Cited alongside, same era.
J. Feinberg and A. Zee, Nucl. Phys. B 504, 579 (1997)
1997
Cited alongside, same era.
D. R. Nelson and N. M. Shnerb, Phys. Rev. E 58
1998
Cited alongside, same era.
A. V. Khaetskii, D. Loss, and L. Glazman, Phys. Rev. Lett. 88
2002
Cited alongside, same era.
J. M. Taylor, A. Imamoglu, and M. D. Lukin, Phys. Rev. Lett. 91, 246802 (2003)
2003
Cited alongside, same era.
M. S. Rudner and L. S. Levitov, in preparation
Cited in the paper.

Then

K. Ono and S. Tarucha, Phys. Rev. Lett. 92
2004
Later among the works it cites.
F. H. L. Koppens, J. A. Folk, J. M. Elzerman, R. Hanson, L. H. Willems van Beveren, I. T. Vink, H. P. Tranitz, W. Wegscheider, L. P. Kouwenhoven, L. M. K. Vandersypen, Science 309
2005
Later among the works it cites.
T. Brandes, Phys. Rep. 408
2005
Later among the works it cites.
A. Pfund, I. Shorubalko, K. Ensslin, R. Leturcq, Phys. Rev. Lett. 99
2007
Later among the works it cites.
M. S. Rudner and L. S. Levitov, Phys. Rev. Lett. 99
2007
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…