Interacting quantum walkers: Two-body bosonic and fermionic bound states

Abstract

We investigate the dynamics of bound states of two interacting particles, either bosons or fermions, performing a continuous-time quantum walk on a one-dimensional lattice. We consider the situation where the distance between both particles has a hard bound, and the richer situation where the particles are bound by a smooth confining potential. The main emphasis is on the velocity characterizing the ballistic spreading of these bound states, and on the structure of the asymptotic distribution profile of their center-of-mass coordinate. The latter profile generically exhibits many internal fronts.

31 pages, 14 figures

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Cited by in corpus (12)

• A review of Quantum Cellular Automata
• Multi-particle quantum walks and Fisher information in one-dimensional lattices
• Revivals in Quantum Walks with quasi-periodically time-dependent coin
• Quantum return probability of a system of $N$ non-interacting lattice fermions
• Analysis of Coined Quantum Walks with Renormalization
• Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps
• Singular continuous Cantor spectrum for magnetic quantum walks
• Light-cone and local front dynamics of a single-particle extended quantum walk
• Typical equilibrium state of an embedded quantum system
• Revivals in One-dimensional Quantum Walks with a Time and Spin-dependent Phase Shift
• Quantum walks assisted by particle number fluctuations
• An investigation of $\mathcal{P}\mathcal{T}$-symmetry breaking in tight-binding chains