Quantum centipedes: collective dynamics of interacting quantum walkers

* Corresponding author
Abstract : We consider the quantum centipede made of $N$ fermionic quantum walkers on the one-dimensional lattice interacting by means of the simplest of all hard-bound constraints: the distance between two consecutive fermions is either one or two lattice spacings. This composite quantum walker spreads ballistically, just as the simple quantum walk. However, because of the interactions between the internal degrees of freedom, the distribution of its center-of-mass velocity displays numerous ballistic fronts in the long-time limit, corresponding to singularities in the empirical velocity distribution. The spectrum of the centipede and the corresponding group velocities are analyzed by direct means for the first few values of $N$. Some analytical results are obtained for arbitrary $N$ by exploiting an exact mapping of the problem onto a free-fermion system. We thus derive the maximal velocity describing the ballistic spreading of the two extremal fronts of the centipede wavefunction, including its non-trivial value in the large-$N$ limit.
Document type :
Journal articles
Complete list of metadata

Cited literature [50 references]

https://hal-cea.archives-ouvertes.fr/cea-01307044
Contributor : Emmanuelle de Laborderie Connect in order to contact the contributor
Submitted on : Friday, October 23, 2020 - 2:08:10 PM
Last modification on : Wednesday, April 14, 2021 - 12:12:08 PM
Long-term archiving on: : Sunday, January 24, 2021 - 6:42:13 PM

File

krap1.pdf
Files produced by the author(s)

Citation

P. L. Krapivsky, J. M. Luck, Kirone Mallick. Quantum centipedes: collective dynamics of interacting quantum walkers. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2016, 49, pp.335303. ⟨10.1088/1751-8113/49/33/335303⟩. ⟨cea-01307044⟩

Record views