dorsal/arxiv
View SchemaConvergence of continuous-time quantum walks on the line
| Authors | Alex D. Gottlieb |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409042 |
| URL | https://arxiv.org/abs/quant-ph/0409042 |
| DOI | 10.1103/PhysRevE.72.047102 |
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.
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"abstract": "The position density of a \"particle\" performing a continuous-time quantum\nwalk on the integer lattice, viewed on length scales inversely proportional to\nthe time t, converges (as t tends to infinity) to a probability distribution\nthat depends on the initial state of the particle. This convergence behavior\nhas recently been demonstrated for the simplest continuous-time random walk\n[see quant-ph/0408140]. In this brief report, we use a different technique to\nestablish the same convergence for a very large class of continuous-time\nquantum walks, and we identify the limit distribution in the general case.",
"arxiv_id": "quant-ph/0409042",
"authors": [
"Alex D. Gottlieb"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevE.72.047102",
"title": "Convergence of continuous-time quantum walks on the line",
"url": "https://arxiv.org/abs/quant-ph/0409042"
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