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<p>In this paper, we consider the localization properties of coupled harmonic oscillators in random media. Each of these oscillators is restricted to the lattice <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {Z}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation>. We show that for most localized initial states and an arbitrarily chosen realization of the random media, most of the solutions of the coupled system remain localized over a sub-exponential time scale, in the Sobolev space.</p>

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Localization for random coupled harmonic oscillators on \(\mathbb {Z}^d\)

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Hongzi Cong,
  • Yunfeng Shi,
  • Zhihan Zhang

摘要

In this paper, we consider the localization properties of coupled harmonic oscillators in random media. Each of these oscillators is restricted to the lattice \(\mathbb {Z}^d\) Z d . We show that for most localized initial states and an arbitrarily chosen realization of the random media, most of the solutions of the coupled system remain localized over a sub-exponential time scale, in the Sobolev space.