Dynamical Tunneling in Many-Dimensional Chaotic Systems

Ishikawa, Akiyuki; Tanaka, Atushi; Shudo, Akira

doi:10.1103/physrevlett.104.224102

Cited by 6 publications

(8 citation statements)

References 33 publications

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“…For systems with a mixed phase space one thus expects that (almost all) eigenstates either concentrate in the chaotic region or within the regular regions on the invariant tori. Away from the semi-classical limit this can be violated due to dynamical tunneling [31][32][33][34] and partial transport barriers [35]. The semi-classical eigenfunction hypothesis has been confirmed in several studies for 2d billiard systems and maps, see e.g.…”

Section: Introductionmentioning

confidence: 71%

Visualization and comparison of classical structures and quantum states of four-dimensional maps

et al. 2014

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For generic 4d symplectic maps we propose the use of 3d phase-space slices which allow for the global visualization of the geometrical organization and coexistence of regular and chaotic motion. As an example we consider two coupled standard maps. The advantages of the 3d phase-space slices are presented in comparison to standard methods like 3d projections of orbits, the frequency analysis, and a chaos indicator. Quantum mechanically, the 3d phase-space slices allow for the first comparison of Husimi functions of eigenstates of 4d maps with classical phase space structures. This confirms the semi-classical eigenfunction hypothesis for 4d maps.

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Section: Introductionmentioning

confidence: 71%

Visualization and comparison of classical structures and quantum states of four-dimensional maps

et al. 2014

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“…For the parameters used there it is irrelevant as M ≪ N ch , while for M ≈ N ch we find that it is necessary to use Eq. (23).…”

Section: A Universal Scaling Of the Asymptotic Flooding Weightmentioning

confidence: 99%

“…An important consequence are huge localization lengths in nano wires with surface disorder [21,22]. Also eigenstates in higher-dimensional systems are influenced by flooding [23]. Flooding also occurs in the time evolution of wave packets.…”

Section: Introductionmentioning

confidence: 99%

Temporal flooding of regular islands by chaotic wave packets

2014

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We investigate the time evolution of wave packets in systems with a mixed phase space where regular islands and chaotic motion coexist. For wave packets started in the chaotic sea on average the weight on a quantized torus of the regular island increases due to dynamical tunneling. This flooding weight initially increases linearly and saturates to a value which varies from torus to torus. We demonstrate for the asymptotic flooding weight universal scaling with an effective tunneling coupling for quantum maps and the mushroom billiard. This universality is reproduced by a suitable random matrix model.

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“…For systems with a large density of states, it is observed [15,[32][33][34][35][36]] that a regular WKB state strongly couples to many chaotic states. As a consequence, the corresponding regular eigenstate disappears and chaotic eigenstates penetrate into the regular island, ignoring the semiclassical eigenfunction hypothesis.…”

Section: Introductionmentioning

confidence: 99%

Consequences of flooding on spectral statistics

et al. 2012

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We study spectral statistics in systems with a mixed phase space, in which regions of regular and chaotic motion coexist. Increasing their density of states, we observe a transition of the level-spacing distribution P(s) from Berry-Robnik to Wigner statistics, although the underlying classical phase-space structure and the effective Planck constant h(eff) remain unchanged. This transition is induced by flooding, i.e., the disappearance of regular states due to increasing regular-to-chaotic couplings. We account for this effect by a flooding-improved Berry-Robnik distribution, in which an effectively reduced size of the regular island enters. To additionally describe power-law level repulsion at small spacings, we extend this prediction by explicitly considering the tunneling couplings between regular and chaotic states. This results in a flooding- and tunneling-improved Berry-Robnik distribution which is in excellent agreement with numerical data.

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Dynamical Tunneling in Many-Dimensional Chaotic Systems

Cited by 6 publications

References 33 publications

Visualization and comparison of classical structures and quantum states of four-dimensional maps

Visualization and comparison of classical structures and quantum states of four-dimensional maps

Temporal flooding of regular islands by chaotic wave packets

Consequences of flooding on spectral statistics

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