Corpus ID: 118705216

The Heun differential equation and the Gauss differential equation related to quantum walks

@article{Konno2011TheHD,
  title={The Heun differential equation and the Gauss differential equation related to quantum walks},
  author={N. Konno and T. Machida and Tohru Wakasa},
  journal={arXiv: Quantum Physics},
  year={2011}
}
The limit theorems of discrete- and continuous-time quantum walks on the line have been intensively studied. We show a relation among limit distributions of quantum walks, Heun differential equations and Gauss differential equations. Indeed, we derive the second-order Fucksian differential equations which limit density functions of quantum walks satisfy. Moreover, using both differential equations, we discuss a relationship between discrete- and continuous-time quantum walks. Taking suitable… Expand

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