Quantum tunneling in ultra-near-integrable systems

Iijima, Riku; Koda, Ryonosuke; Hanada, Yasutaka; Shudo, Akira

doi:10.1103/physreve.106.064205

Cited by 5 publications

(5 citation statements)

References 49 publications

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“…Recently, the ultra-near integrable system has been studied in order to explore the difference of tunneling between integrable and nonintegrable systems [13,24]. Ultra-near integrable systems are defined as those systems in which the classical phase spaces do not exhibit any invariant structures inherent in nonintegrability in the size of the Planck cell.…”

Section: Of 17mentioning

confidence: 99%

“…Ultra-near integrable systems are defined as those systems in which the classical phase spaces do not exhibit any invariant structures inherent in nonintegrability in the size of the Planck cell. Even without islands of stability or chaotic seas, the tail of the wave function generates non-monotonic step structures [24], and the ergodicity of complex dynamics has been shown to play a key role in reproducing non-trivial tunneling behavior in nonintegrable maps [13]. Since there are no symptoms in the real phase space, the origin of the non-trivial tunneling tails comes down to the question of how chaos is born in the complex plane.…”

Section: Of 17mentioning

confidence: 99%

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On complex dynamics in a Suris's integrable map

Hanada,

Shudo

2024

Preprint

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Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. It is found that the behavior of tunneling splitting for the integrable map and the associated Hamiltonian system is qualitatively the same, with only a slight difference in magnitude. However, the tunneling tails of the wave functions, obtained by superposing the eigenfunctions that form the doublet, exhibit significant difference. To explore the origin of the difference, we observe the classical dynamics in the complex plane and find that the existence of branch points appearing in the potential function of the integrable map could play the role for yielding non-trivial behavior in the tunneling tail. The result highlights the subtlety of quantum tunneling, which cannot be captured in nature only by the dynamics in the real plane.

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Section: Of 17mentioning

confidence: 99%

Section: Of 17mentioning

confidence: 99%

On complex dynamics in a Suris's integrable map

Hanada,

Shudo

2024

Preprint

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“…Recently, the ultra-near integrable system has been studied in order to explore the difference in tunneling between integrable and nonintegrable systems [23,37]. Ultra-near integrable systems are defined as those systems in which the classical phase spaces do not exhibit any invariant structures inherent in nonintegrability in the size of the Planck cell.…”

Section: Introductionmentioning

confidence: 99%

“…Ultra-near integrable systems are defined as those systems in which the classical phase spaces do not exhibit any invariant structures inherent in nonintegrability in the size of the Planck cell. Even without islands of stability or chaotic seas, the tail of the wave function generates non-monotonic step structures [37], and the ergodicity of complex dynamics has been shown to play a key role in reproducing non-trivial tunneling behavior in nonintegrable maps [23]. Since there are no symptoms in the real phase space, the origin of the non-trivial tunneling tails comes down to the question of how chaos is born in the complex plane.…”

Section: Introductionmentioning

confidence: 99%

Quantum Tunneling and Complex Dynamics in the Suris’s Integrable Map

Hanada,

Shudo

2024

Entropy

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Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. It is found that the behavior of tunneling splitting for the integrable map and the associated Hamiltonian system is qualitatively the same, with only a slight difference in magnitude. However, the tunneling tails of the wave functions, obtained by superposing the eigenfunctions that form the doublet, exhibit significant differences. To explore the origin of the difference, we observe the classical dynamics in the complex plane and find that the existence of branch points appearing in the potential function of the integrable map could play the role of yielding non-trivial behavior in the tunneling tail. The result highlights the subtlety of quantum tunneling, which cannot be captured in nature only by the dynamics in the real plane.

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“…A comprehensive review of the different mechanisms and their interplay can be found in the articles in the two edited volumes [44,45]. On the other hand, Shudo and coworkers have recently suggested [46][47][48] that in the limit of "ultra" near-integrable systems, enhancements in tunneling probabilities may not correspond to any classical phase space structure and a careful look at the complex phase space dynamics is necessary. Nevertheless, in this review, the former viewpoint is taken for a couple of reasons.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Tunneling in More than Two Degrees of Freedom

Keshavamurthy

2024

Entropy

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Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose–Einstein condensates trapped in optical lattices.

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Quantum tunneling in ultra-near-integrable systems

Cited by 5 publications

References 49 publications

On complex dynamics in a Suris's integrable map

On complex dynamics in a Suris's integrable map

Quantum Tunneling and Complex Dynamics in the Suris’s Integrable Map

Dynamical Tunneling in More than Two Degrees of Freedom

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