Abdul-Rahman, H., Darras, M., Fischbacher, C., Stolz, G.: Slow propagation velocities in Schrödinger operators with large periodic potential. Ann. Henri Poincaré 26, 3635–3663 (2025). arXiv:2401.11508

Article  ADS  MathSciNet  Google Scholar 

Abdul-Rahman, H., Fillman, J., Fischbacher, C., Liu, W.: Sharp polynomial velocity decay bounds for multidimensional periodic Schrödinger operators. arXiv:2509.04381

Abdul-Rahman, H., Stolz, G.: Exponentially decaying velocity bounds of quantum walks in periodic fields. Commun. Math. Phys. 403(3), 1297–1327 (2023). arXiv:2302.01869

Article  ADS  MathSciNet  Google Scholar 

Ahlbrecht, A.: Asymptotic behavior of decoherent and interacting quantum walks. Doctoral Thesis, Gottfried Wilhelm Leibniz Universität Hannover, Hannover (2013)

Ahlbrecht, A., Scholz, V.B., Werner, R.F.: Disordered quantum walks in one lattice dimension. J. Math. Phys. 52(10), 102201 (2011). arXiv:1101.2298

Article  ADS  MathSciNet  Google Scholar 

Ahlbrecht, A., Vogts, H., Werner, A.H., Werner, R.F.: Asymptotic evolution of quantum walks with random coin. J. Math. Phys. 52(4), 042201 (2011). arXiv:1009.2019

Article  ADS  MathSciNet  Google Scholar 

Ambainis, A., Bach, E., Nayak, A., Vishwanath, A., Watrous, J.: One-dimensional quantum walks. In: Proceedings of the thirty-third annual ACM symposium on Theory of computing - STOC ’01, Hersonissos, Greece, pp. 37–49 (2001). ACM Press

Asbóth, J.K.: Symmetries, topological phases, and bound states in the one-dimensional quantum walk. Phys. Rev. B 86(19), 195414 (2012). arXiv:1208.2143

Article  ADS  Google Scholar 

Asbóth, J.K., Obuse, H.: Bulk-boundary correspondence for chiral symmetric quantum walks. Phys. Rev. B 88(12), 121406 (2013). arXiv:1303.1199

Article  ADS  Google Scholar 

Asch, J., Knauf, A.: Motion in periodic potentials. Nonlinearity 11(1), 175–200 (1998). arXiv:cond-mat/9710169

Article  ADS  MathSciNet  Google Scholar 

Aspuru-Guzik, A., Walther, P.: Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012)

Article  Google Scholar 

Bourgain, J., Grünbaum, F.A., Velázquez, L., Wilkening, J.: Quantum recurrence of a subspace and operator-valued Schur functions. Commun. Math. Phys. 329(3), 1031–1067 (2014). arXiv:1302.7286

Article  ADS  MathSciNet  Google Scholar 

Bourget, O., Howland, J.S., Joye, A.: Spectral analysis of unitary band matrices. Commun. Math. Phys. 234(2), 191–227 (2003). arXiv:math-ph/0204016

Article  ADS  MathSciNet  Google Scholar 

Buerschaper, O., Burnett, K.: Stroboscopic quantum walks (2004). (quant-ph/0406039)

Cantero, M.J., Grünbaum, F.A., Moral, L., Velázquez, L.: The CGMV method for quantum walks. Quantum Inf. Process. 11(5), 1149–1192 (2012)

Article  MathSciNet  Google Scholar 

Cantero, M.J., Moral, L., Grünbaum, F.A., Velázquez, L.: Matrix-valued Szegő polynomials and quantum random walks. Commun. Pure Appl. Math. 63(4), 464–507 (2010). arXiv:0901.2244

Article  Google Scholar 

Cantero, M.J., Moral, L., Velázquez, L.: Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle. Linear Algebra Appl. 362, 29–56 (2003). arXiv:math/0204300

Article  MathSciNet  Google Scholar 

Cedzich, C.: Quantum walks: electromagnetism and topological classification. PhD thesis, Leibniz Universität Hannover (2019)

Cedzich, C., Fillman, J., Geib, T., Werner, A.H.: Singular continuous Cantor spectrum for magnetic quantum walks. Lett. Math. Phys. 110(6), 1141–1158 (2020). arXiv:1908.09924

Article  ADS  MathSciNet  Google Scholar 

Cedzich, C., Fillman, J., Li, L., Ong, D., Zhou, Q.: Exact mobility edges for almost-periodic CMV matrices via gauge symmetries. Int. Math. Res. Not. 2024, 6906–6941 (2023). arXiv:2307.10909

Article  Google Scholar 

Cedzich, C., Fillman, J., Ong, D.C.: Almost everything about the unitary almost-Mathieu operator. Commun. Math. Phys. 403, 745–794 (2023). arXiv:2112.03216

Article  ADS  MathSciNet  Google Scholar 

Cedzich, C., Geib, T., Grünbaum, F., Velázquez, L., Werner, A., Werner, R.: Quantum walks: Schur functions meet symmetry protected topological phases. Commun. Math. Phys. 389, 31–74 (2022). arXiv:1903.07494

Article  ADS  MathSciNet  Google Scholar 

Cedzich, C., Geib, T., Grünbaum, F.A., Stahl, C., Velázquez, L., Werner, A.H., Werner, R.F.: The topological classification of one-dimensional symmetric quantum walks. Ann. Henri Poincaré 19(2), 325–383 (2018). arXiv:1611.04439

Article  ADS  MathSciNet  Google Scholar 

Cedzich, C., Geib, T., Werner, A.H., Werner, R.F.: Quantum walks in external gauge fields. J. Math. Phys. 60(1), 012107 (2019). arXiv:1808.10850

Article  ADS  MathSciNet  Google Scholar 

Cedzich, C., Geib, T., Werner, A.H., Werner, R.F.: Chiral Floquet systems and quantum walks at half period. Ann. Henri Poincaré 22(2), 375–413 (2021). arXiv:2006.04634

Article  ADS  MathSciNet  Google Scholar 

Cedzich, C., Geib, T., Werner, R.F.: An algorithm to factorize quantum walks into shift and coin operations. Lett. Math. Phys. 112(85), 2022 (2022). arXiv:2102.12951

Article  MathSciNet  Google Scholar 

Cedzich, C., Grünbaum, F.A., Velázquez, L., Werner, A.H., Werner, R.F.: A quantum dynamical approach to matrix Khrushchev’s formulas. Commun. Pure Appl. Math. 69(5), 909–957 (2016). arXiv:1405.0985

Article  MathSciNet  Google Scholar 

Cedzich, C., Joye, A., Werner, A.H., Werner, R.F.: Exponential tail estimates for quantum lattice dynamics. In: Annales Henri Poincaré (2025). arXiv:2408.02108

Cedzich, C., Rybár, T., Werner, A.H., Alberti, A., Genske, M., Werner, R.F.: Propagation of quantum walks in electric fields. Phys. Rev. Lett. 111, 160601 (2013). arXiv:1302.2081

Article  ADS  Google Scholar 

Cedzich, C., Werner, A.H.: Anderson localization for electric quantum walks and skew-shift CMV matrices. Commun. Math. Phys. 387, 1257–1279 (2021). arXiv:1906.11931

Article  ADS  MathSciNet  Google Scholar 

Childs, A.M.: Universal computation by quantum walk. Phys. Rev. Lett. 102(18), 180501 (2009). arXiv:0806.1972

Article  ADS  MathSciNet  Google Scholar 

Damanik, D., Fillman, J., Ong, D.C.: Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices. J. Math. Pures Appl. 105(3), 293–341 (2016). arXiv:1505.07292

Article  MathSciNet  Google Scholar 

Damanik, D., Malinovitch, T., Young, G.: What is ballistic transport? (2024). arXiv:2403.19618

Fillman, J.: Measure of the spectra of periodic graph operators in the large-coupling limit (2025). arXiv:2511.00757

Fillman, J., Ong, D.C., Vandenboom, T.: Spectral approximation for ergodic CMV operators with an application to quantum walks. J. Math. Anal. Appl. 467(1), 132–147 (2017). arXiv:1712.04620

Article  MathSciNet  Google Scholar 

Grimmett, G., Janson, S., Scudo, P.F.: Weak limits for quantum random walks. Phys. Rev. E 69(2), 026119 (2004). arXiv:quant-ph/0309135

Article  ADS  Google Scholar 

Gross, D., Nesme, V., Vogts, H., Werner, R.F.: Index theory of one dimensional quantum walks and cellular automata. Commun. Math. Phys. 310(2), 419–454 (2012). arXiv:0910.3675

Article  ADS  MathSciNet  Google Scholar 

Grünbaum, F., Velázquez, L., Werner, A., Werner, R.: Recurrence for discrete time unitary evolutions. Commun. Math. Phys. 320, 543–569 (2013). arXiv:1202.3903

Article  ADS  MathSciNet