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In a quantum Markov chain, the temporal succession of states is modeled by the repeated action of a ``bistochastic quantum operation" on the density matrix of a quantum system. Based on this conceptua...
Limit Theorems for the Discrete-Time Quantum Walk on a Graph with Joined Half Lines
Theorems Discrete-Time Quantum Walk Graph Half Lines
2010/10/18
We consider a discrete-time quantum walk Wt, at time t on a graph with joined half lines J, which is composed of half lines with the same origin. Our analysis is based on a reduction of the walk o...
Some Limit Theorems for a Particle System of Single Point Catalytic Branching Random Walks
Renewal equation branching particle system scaling limit
2007/12/10
We study the scaling limit for a catalytic branching particle system whose particles perform random walks on ${\Bbb Z}$ and can branch at 0 only. Varying the initial (finite) number of particles, we g...