Analytic “Newton’s cradles” with perfect transfer and fractional revival

Hugo Schérer, ∗ Luc Vinet, 2, 3, † and Alexei Zhedanov 4, ‡ Centre de recherches mathématiques, Université de Montréal P.O. Box 6128, Centre-ville Station, Montréal (Québec), H3C 3J7, Canada Département de Physique, Université de Montréal, Montréal (Québec), H3C 3J7, Canada Institut de valorisation des données (IVADO), Montréal (Québec), H2S 3H1, Canada School of Mathematics, Renmin University of China, Beijing, 100872, China (Dated: August 24, 2021)

[1]  Dispersionless pulse transport in mass-spring chains: All possible perfect Newton's cradles. , 2020, Physical review. E.

[2]  Alastair Kay,et al.  Basics of perfect communication through quantum networks , 2011, 1102.2338.

[3]  L. Vinet,et al.  Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer , 2011, 1110.6475.

[4]  Alastair Kay,et al.  Perfect, Efficent, State Transfer and its Application as a Constructive Tool , 2009, 0903.4274.

[5]  Luc Vinet,et al.  How to construct spin chains with perfect state transfer , 2011, 1110.6474.

[6]  L. Vinet,et al.  The para-Racah polynomials , 2015, 1511.05215.

[7]  L. Vinet,et al.  An analytic spin chain model with fractional revival , 2015, 1509.08965.

[8]  G. M. L. Gladwell,et al.  Inverse Problems in Vibration , 1986 .

[9]  L. Vinet,et al.  Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials , 2016, 1605.00708.

[10]  Matthias Christandl,et al.  Mirror inversion of quantum states in linear registers. , 2004, Physical review letters.

[11]  Perfect state transfer in a spin chain without mirror symmetry , 2019, Journal of Physics A: Mathematical and Theoretical.

[12]  Antonio Cantoni,et al.  Properties of the Eigenvectors of Persymmetric Matrices with Applications to Communication Theory , 1976, IEEE Trans. Commun..

[13]  R. Vaia,et al.  Persymmetric Jacobi matrices with square-integer eigenvalues and dispersionless mass-spring chains , 2019, Linear Algebra and its Applications.

[14]  L. Vinet,et al.  Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results , 2017, 1705.04841.

[15]  Luc Vinet,et al.  Quantum spin chains with fractional revival , 2015, 1507.05919.

[16]  F. Uhlig,et al.  Inverse eigenvalue problems associated with spring-mass systems , 1997 .

[17]  L. Vinet,et al.  Exact Fractional Revival in Spin Chains , 2015, 1506.08434.

[18]  Matthias Christandl,et al.  Analytic next-to-nearest-neighbor X X models with perfect state transfer and fractional revival , 2016, 1607.02639.