Dispersive estimates for quantum walks on 1D lattice

Maeda Masaya; Sasaki Hironobu; Segawa EtsuoSuzuki AkitoSuzuki Kanako

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Dispersive estimates for quantum walks on 1D lattice

机译：Dispersive estimates for quantum walks on 1D lattice

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摘要

We consider quantum walks with position dependent coin on 1D lattice Z. The dispersive estimate parallel to U(t)P(c)u(0)parallel to(l)infinity less than or similar to (1 + vertical bar t vertical bar)(-1/3)parallel to u(0)parallel to(l)1 is shown under l(1,1) perturbation for the generic case and l(1,2) perturbation for the exceptional case, where U is the evolution operator of a quantum walk and P-c is the projection to the continuous spectrum. This is an analogous result for Schrodinger operators and discrete Schrodinger operators. The proof is based on the estimate of oscillatory integrals expressed by Jost solutions.

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来源
《Journal of the Mathematical Society of Japan》 |2022年第1期|217-246|共30页
作者
Maeda Masaya; Sasaki Hironobu; Segawa EtsuoSuzuki AkitoSuzuki Kanako;
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作者单位

Chiba Univ;

Tohoku Univ;

Shinshu UnivIbaraki Univ;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种英语
中图分类数学;
关键词
quantum walks; dispersive estimates; DISCRETE NONLINEAR SCHRODINGER; ASYMPTOTIC STABILITY; ORTHOGONAL POLYNOMIALS; INVERSE SCATTERING; CMV OPERATORS; BEHAVIOR; EQUATION;

Dispersive estimates for quantum walks on 1D lattice

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