dorsal/arxiv
View SchemaDiffusive-ballistic crossover in 1D quantum walks
| Authors | Daniel K. Wojcik, J. R. Dorfman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209036 |
| URL | https://arxiv.org/abs/quant-ph/0209036 |
| DOI | 10.1103/PhysRevLett.90.230602 |
| Journal | Phys. Rev. Lett. 90 (2003) 230602 |
Abstract
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random matrix theory provides explicit analytical predictions for the mean square displacement of a particle in the system. These results exhibit a crossover from diffusive to ballistic motion, with crossover time from diffusive to ballistic motion on the order of the inverse of Planck's constant. We can argue, that for a large class of 1D quantum random walks, similar to the quantum multi-baker, a sufficient condition for diffusion in the semi-classical limit is classically chaotic dynamics in each cell. Using an initial equilibrium density matrix, we find that diffusive behavior is recovered in the semi-classical limit for such systems, without further interactions with the environment.
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"abstract": "We show that particle transport in a uniform, quantum multi-baker map, is\ngenerically ballistic in the long time limit, for any fixed value of Planck\u0027s\nconstant. However, for fixed times, the semi-classical limit leads to\ndiffusion. Random matrix theory provides explicit analytical predictions for\nthe mean square displacement of a particle in the system. These results exhibit\na crossover from diffusive to ballistic motion, with crossover time from\ndiffusive to ballistic motion on the order of the inverse of Planck\u0027s constant.\nWe can argue, that for a large class of 1D quantum random walks, similar to the\nquantum multi-baker, a sufficient condition for diffusion in the semi-classical\nlimit is classically chaotic dynamics in each cell. Using an initial\nequilibrium density matrix, we find that diffusive behavior is recovered in the\nsemi-classical limit for such systems, without further interactions with the\nenvironment.",
"arxiv_id": "quant-ph/0209036",
"authors": [
"Daniel K. Wojcik",
"J. R. Dorfman"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"nlin.CD"
],
"doi": "10.1103/PhysRevLett.90.230602",
"journal_ref": "Phys. Rev. Lett. 90 (2003) 230602",
"title": "Diffusive-ballistic crossover in 1D quantum walks",
"url": "https://arxiv.org/abs/quant-ph/0209036"
},
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