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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2512.05627 |
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| _version_ | 1866917127869431808 |
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| author | Yan, Hua |
| author_facet | Yan, Hua |
| contents | We investigate mixed eigenstates in systems with sharply-divided phase space, using different piecewise-linear maps whose regular-chaotic boundaries are formed by marginally unstable periodic orbits (MUPOs) or by quasi-periodic orbits. With the overlap index and the entropy localization length, we classify mixed eigenstates and show that the contribution from dynamical tunneling scales as $\sim \hbar\, \exp(-b/\hbar)$, with $b>0$ associated with the relative size of the regular region. The dominant fraction of states that remain sticky to the boundaries, referred to as sticky eigenstates, scales as $\hbar^{1/2}$ in the MUPO case and oscillates around this algebraic behavior in the quasi-periodic case. This behavior generalizes established predictions for hierarchical states in KAM systems, which scale as $\hbar^{1 - 1/γ}$, with $γ$ set by the corresponding classical stickiness reflected in the algebraic decay of cumulative RTDs $t^{-γ}$. For the piecewise-linear maps studied here, $γ= 2$. These results reveal a clear quantum signature of classical stickiness in non-KAM systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05627 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sticky eigenstates in systems with sharply-divided phase space Yan, Hua Statistical Mechanics Quantum Physics We investigate mixed eigenstates in systems with sharply-divided phase space, using different piecewise-linear maps whose regular-chaotic boundaries are formed by marginally unstable periodic orbits (MUPOs) or by quasi-periodic orbits. With the overlap index and the entropy localization length, we classify mixed eigenstates and show that the contribution from dynamical tunneling scales as $\sim \hbar\, \exp(-b/\hbar)$, with $b>0$ associated with the relative size of the regular region. The dominant fraction of states that remain sticky to the boundaries, referred to as sticky eigenstates, scales as $\hbar^{1/2}$ in the MUPO case and oscillates around this algebraic behavior in the quasi-periodic case. This behavior generalizes established predictions for hierarchical states in KAM systems, which scale as $\hbar^{1 - 1/γ}$, with $γ$ set by the corresponding classical stickiness reflected in the algebraic decay of cumulative RTDs $t^{-γ}$. For the piecewise-linear maps studied here, $γ= 2$. These results reveal a clear quantum signature of classical stickiness in non-KAM systems. |
| title | Sticky eigenstates in systems with sharply-divided phase space |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2512.05627 |