发表机构
School of Mathematics and Statistics, Qinghai Minzu University; Qinghai Institute of Applied Mathematics（青海民族大学数学与统计学院; 青海省应用数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究有界谱宽和次数下多项式哈密顿量的完美态转移最短时间，给出最优时间为π/W整数倍的条件、仿射最小化器的次数界、超立方体上的精确结果及互补顶点上的指数增长与次指数构造。
AI 中文摘要
我们研究了在具有有界次数和谱宽的多项式哈密顿量下完美态转移的最短时间。对于强余弦谱对和宽度界$W$，当最优值有限时，它是$\pi/W$的整数倍，由具有规定奇偶性的整数插值决定。对于具有交替符号的等距支撑特征值，我们给出了次数界，在此界下每个最小化器都是仿射的，并给出了每个固定精确次数的尖锐渐近性。接近最小化的相位多项式满足定量切比雪夫稳定性估计。我们确定了奇素数维超立方体上每个次数界的最优转移时间。对于$J(2m,m)$的互补顶点，在固定谱宽下，最优时间在可行次数区间内随$m$指数增长。我们还构造了多项式哈密顿量，表明每个可行次数$m-t$（其中$t=o(m)$）都允许次指数转移时间。
英文摘要
We study the minimum time for perfect state transfer under polynomial Hamiltonians with bounded degree and spectral width. For a strongly cospectral pair and width bound $W$, the optimum, when finite, is an integer multiple of $π/W$, determined by integer interpolation with prescribed parities. For equally spaced supported eigenvalues with alternating signs, we give degree bounds under which every minimizer is affine, and sharp asymptotics for each fixed exact degree. Near-minimizing phase polynomials satisfy a quantitative Chebyshev stability estimate. We determine the optimal transfer time for every degree bound on hypercubes of odd prime dimension. For complementary vertices of $J(2m,m)$, the optimal time at fixed spectral width grows exponentially in $m$ throughout an interval of feasible degrees. We also construct polynomial Hamiltonians showing that every feasible degree $m-t$ with $t=o(m)$ admits subexponential transfer time.
Comments20 pages, 0 figures
