Quantum centipedes: collective dynamics of interacting quantum walkers

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.

20 pages, 11 figures

References in corpus (14)

• The electronic properties of graphene
• Universal computation by quantum walk
• Quantum walks of correlated particles
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Realization of quantum walks with negligible decoherence in waveguide lattices
• Connecting the discrete and continuous-time quantum walks
• Quantum Correlations in Two-Particle Anderson Localization
• Quantum Walk on a Line with Two Entangled Particles
• Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions
• Limit distributions of three-state quantum walks: the role of coin eigenstates
• Continuous-time quantum walks on one-dimension regular networks
• Coherent exciton transport and trapping on long-range interacting cycles
• Universal Behavior of Quantum Walks with Long-Range Steps
• Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle

Cited by in corpus (3)

• Quantum return probability of a system of $N$ non-interacting lattice fermions
• Quantum walks assisted by particle number fluctuations
• Quantum centipedes with strong global constraint