Weak limit theorem for a nonlinear quantum walk

1. Di Molfetta, G., Debbasch, F., Brachet, M.: Nonlinear optical Galton board: thermalization and continuous limit. Phys. Rev. E 92, 042923 (2015)

   Article  ADS  Google Scholar 

2. Endo, S., Endo, T., Konno, N., Segawa, E., Takei, M.: Weak limit theorem of a two-phase quantum walk with one defect, Interdiscip. Inform. Sci. J-STAGE Advance, Graduate School of Information Sciences, Tohoku University (2016)

3. Endo, T., Konno, N., Obuse, H., Segawa, E.: Sensitivity of quantum walks to a boundary of two-dimensional lattices: approaches based on the CGMV method and topological phases. J. Phys. A Math. Theor. 50(45), 455302 (2017)

   Article  ADS  MathSciNet  MATH  Google Scholar 

4. Fuda, T., Funakawa, D., Suzuki, A.: Weak limit theorem for a one-dimensional split-step quantum walk, arXiv:1804.05125 (2018)

5. Gerasimenko, Y., Tarasinski, B., Beenakker, C.W.J.: Attractor-repeller pair of topological zero modes in a nonlinear quantum walk. Phys. Rev. A 93, 022329 (2016)

   Article  ADS  Google Scholar 

6. Grimmett, G., Janson, S., Scudo, P.F.: Weak limits for quantum random walks. Phys. Rev. E 69, 026119 (2004)

   Article  ADS  Google Scholar 

7. Higuchi, Yu., Konno, N., Sato, I., Segawa, E.: Spectral and asymptotic properties of Grover walks on crystal lattices. J. Funct. Anal. 267, 4197–4235 (2014)

   Article  MathSciNet  MATH  Google Scholar 

8. Higuchi, Yu., Segawa, E.: The spreading behavior of quantum walks induced by drifted random walks on some magnifier graph. Quantum Inf. Comput. 17, 0399–0414 (2017)

   MathSciNet  Google Scholar 

9. Konno, N.: Quantum random walks in one dimension. Quantum Inf. Process. 1(5), 345–354 (2002)

   Article  MathSciNet  MATH  Google Scholar 

10. Konno, N.: A new type of limit theorems for the one-dimensional quantum random walk. J. Math. Soc. Jpn. 57(4), 1179–1195 (2005)

    Article  MathSciNet  MATH  Google Scholar 

11. Konno, N., Łuczak, T., Segawa, E.: Limit measures of inhomogeneous discrete-time quantum walks in one dimension. Quantum Inf. Process. 12(1), 33–53 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

12. Lee, C.-W., Kurzyński, P., Nha, H.: Quantum walk as a simulator of nonlinear dynamics: nonlinear Dirac equation and solitons. Phys. Rev. A 92, 052336 (2015)

    Article  ADS  Google Scholar 

13. Machida, T., Segawa, E.: Trapping and spreading properties of quantum walk in homological structure. Quantum Inf. Process. 14, 1539–1558 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

14. Maeda, M., Sasaki, H., Segawa, E., Suzuki, A., Suzuki, K.: Scattering and inverse scattering for nonlinear quantum walks. Discrete Contin. Dyn. Syst. 38, 3687–3703 (2018)

    Article  MathSciNet  MATH  Google Scholar 

15. Maeda, M., Sasaki, H., Segawa, E., Suzuki, A., Suzuki, K.: Dynamics of solitons to a nonlinear quantum walk (in preparation)

16. Navarrete-Benlloch, C., Pérez, A., Roldán, E.: Nonlinear optical Galton board. Phys. Rev. A 75, 062333 (2007)

    Article  ADS  Google Scholar 

17. Richard, S., Suzuki, A., Tiedra de Aldecoa, R.: Quantum walks with an anisotropic coin I: spectral theory. Lett. Math. Phys. 108, 331–357 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

18. Richard, S., Suzuki, A., Tiedra de Aldecoa, R.: Quantum walks with an anisotropic coin II: scattering theory. Lett. Math. Phys. (2018). https://doi.org/10.1007/s11005-018-1100-1

19. Shikano, Y., Wada, T., Horikawa, J.: Discrete-time quantum walk with feed-forward quantum coin. Sci. Rep. 4, 4427 (2014)

    Article  ADS  Google Scholar 

20. Suzuki, A.: Asymptotic velocity of a position-dependent quantum walk. Quantum Inf. Process. 15(1), 103–119 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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