Resonance-assisted tunneling in four-dimensional normal-form Hamiltonians

Firmbach, Markus; Fritzsch, Felix; Ketzmerick, Roland; Bäcker, Arnd

doi:10.1103/physreve.99.042213

Cited by 7 publications

(8 citation statements)

References 80 publications

(150 reference statements)

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“…However, with more degrees of freedom resonances of higher rank may arise which give rise to a much more complex way of resonance-assisted coupling between optical modes. This was recently demonstrated for a normal-form Hamiltonian [48]. On an even more fundamental level the interplay of tunneling and classical transport mechanisms, e.g., the famous Arnold diffusion, could become important in three-dimensional cavities.…”

Section: Discussionmentioning

confidence: 93%

Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space

2019

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The life times of optical modes in whispering-gallery cavities crucially depend on the underlying classical ray dynamics and may be spoiled by the presence of classical nonlinear resonances due to resonance-assisted tunneling. Here we present an intuitive semiclassical picture which allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space and find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths.

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Section: Discussionmentioning

confidence: 93%

Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space

2019

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“…We expect [42,44] that the dynamical stabilisation will survive quantisation. However, the extent to which quantum effects like dynamical tunnelling [65,66] can lead to enhanced localisation or de-trapping from the junctions [44,67] requires a systematic study of the classical and quantum dynamics near the junctions, particularly those with multiplicities greater than two. Such studies, given the modest effective dimensionality of the vibrational state space even for large molecules [68], may prove important towards the possibility of control by nudging the system to the regions of stable chaos using weak external fields [69][70][71].…”

Section: Discussionmentioning

confidence: 99%

Stable chaos and delayed onset of statisticality in unimolecular dissociation reactions

2020

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Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific assumptions about the extent of intramolecular vibrational energy flow in the system. However, the nature of the transition to the statistical regime as a function of the molecular parameters is far from being completely understood. Here, we use tools from nonlinear dynamics to study the transition to statisticality in a model unimolecular reaction by explicitly visulaizing the high dimensional classical phase space. We identify generic features in the phase space involving the intersection of two or more independent anharmonic resonances and show that the presence of correlated, but chaotic, intramolecular dynamics near such junctions leads to nonstatisticality. Interestingly, akin to the stability of asteroids in the Solar System, molecules can stay protected from dissociation at the junctions for several picoseconds due to the phenomenon of stable chaos.

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“…Since the Arnold web is a network of nonlinear resonances, one expects on rather general grounds that the phenomenon of resonance-assisted [32] and chaos-assisted [33] tunneling (RAT and CAT) will also be sensitive to the features on the web. In particular, due to the substantial degeneracy of the quantum states near the junctions one can have enhanced quantum transport due to the availability of multiple pathways [34][35][36]. Therefore, combined with the fact that chaotic dynamics occurs in the vicinity of the junctions, there is an intriguing possibility of subtle competition between the classical and quantum transport.…”

Section: Introductionmentioning

confidence: 99%

Arnold web and dynamical tunneling in a four-site Bose-Hubbard model

Karmakar,

Keshavamurthy

2021

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We present the quantum and classical study of a four-well trapped Bose-Einstein condensate (BEC) modeled by the Bose-Hubbard Hamiltonian. The model used is fashioned as a minimal bipartite system consisting of a trimer coupled weakly to a monomer. Semiclassical insights into the fragmentation dynamics of the condensate is obtained by mapping out the Arnold web of the high dimensional classical phase space. A remarkable one-to-one correspondence between the quantum state space in occupation number representation and the classical Arnold web in action space is observed. The relevance of dynamical tunneling for the dynamics of Fock states near resonance junctions on the Arnold web is highlighted. We also predict the possibility of manipulating the transport within the trimer subsystem due to the weak coupling to the monomer.

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Resonance-assisted tunneling in four-dimensional normal-form Hamiltonians

Cited by 7 publications

References 80 publications

Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space

Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space

Stable chaos and delayed onset of statisticality in unimolecular dissociation reactions

Arnold web and dynamical tunneling in a four-site Bose-Hubbard model

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