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We present an investigation of many-particle quantum walks in systems ofnon-interacting distinguishable particles. Along with a redistribution of themany-particle density profile we show that the collective evolution of themany-particle system resembles the single-particle quantum walk evolution whenthe number of steps is greater than the number of particles in the system. Fornon-uniform initial states we show that the quantum walks can be effectivelyused to separate the basis states of the particle in position space andgrouping like state together. We also discuss a two-particle quantum walk on atwo- dimensional lattice and demonstrate an evolution leading to thelocalization of both particles at the center of the lattice. Finally we discussthe outcome of a quantum walk of two indistinguishable particles interacting atsome point during the evolution.

Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle