Quantum centipedes: collective dynamics of interacting quantum walkers - Archive ouverte HAL Access content directly
Journal Articles Journal of Physics A: Mathematical and Theoretical Year : 2016

## Quantum centipedes: collective dynamics of interacting quantum walkers

(1) , (2) , (2)
1
2
P. L. Krapivsky
• Function : Author
J. M. Luck
Kirone Mallick
• Function : Correspondent author
• PersonId : 830775

Connectez-vous pour contacter l'auteur

#### 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.

#### Domains

Physics [physics] Quantum Physics [quant-ph]

### Dates and versions

cea-01307044 , version 1 (23-10-2020)

### Identifiers

• HAL Id : cea-01307044 , version 1
• ARXIV :
• DOI :

### Cite

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

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

61 View