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Open Quantum Systems Decoherence Quantum Simulation Quantum State Preparation Representation Entanglement Theory Quantum Correlations

Perturbations around the zeros of classical orthogonal polynomials

arXiv
Authors: Ryu Sasaki

Year

2014

Paper ID

46496

Status

Preprint

Abstract Read

~2 min

Abstract Words

87

Citations

N/A

Abstract

Starting from degree N solutions of a time dependent Schroedinger-like equation for classical orthogonal polynomials, a linear matrix equation describing perturbations around the N zeros of the polynomial is derived. The matrix has remarkable Diophantine properties. Its eigenvalues are independent of the zeros. The corresponding eigenvectors provide the representations of the lower degree (0,1,...,N-1) polynomials in terms of the zeros of the degree N polynomial. The results are valid universally for all the classical orthogonal polynomials, including the Askey scheme of hypergeometric orthogonal polynomials and its q-analogues.

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  • Starting from degree N solutions of a time dependent Schroedinger-like equation for classical orthogonal polynomials, a linear matrix equation describing perturbations around...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1411.3045 [2] arXiv https://arxiv.org/abs/1411.3045 [3] Publisher https://arxiv.org/abs/1411.3045

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