Convergence of continuous-time quantum walks on the line

Abstract

The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that depends on the initial state of the particle. This convergence behavior has recently been demonstrated for the simplest continuous-time random walk [see quant-ph/0408140]. In this brief report, we use a different technique to establish the same convergence for a very large class of continuous-time quantum walks, and we identify the limit distribution in the general case.

Version to appear in Phys. Rev. E

References in corpus (4)

• Weak limits for quantum random walks
• Limit Theorem for Continuous-Time Quantum Walk on the Line
• Quantum random walks in one dimension
• A New Type of Limit Theorems for the One-Dimensional Quantum Random Walk

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• Mixing and Decoherence in Continuous-time quantum walks on long-range interacting cycles
• The Heun differential equation and the Gauss differential equation related to quantum walks
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• Continuous-time quantum walk on integer lattices and homogeneous trees
• Limit distribution of a continuous-time quantum walk with a spatially 2-periodic Hamiltonian
• Distributions of continuous-time quantum walks
• Phase transition of a continuous-time quantum walk on the half line