Quantum tunneling and chaos in a driven anharmonic oscillator

Lin, Wen-Shin; Ballentine, L. E.

doi:10.1103/physrevlett.65.2927

Cited by 300 publications

(259 citation statements)

References 12 publications

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“…Expression (10) shows that the probability of tunneling (square of the absolute value of the tunneling amplitude) grows while chaotic region spreads (∆H increases). The result is obtained in the first order on coupling constant α and does not take into account possible structure of stochastic layer is valid if the layer is narrow and is in agreement with results of numerical [20] and real [6] experiments for similar problems. We have also correspondence in (10) with the nonperturbed case [15].…”

Section: The Calculation Of the Tunneling Amplitude And Ground Zone Wsupporting

confidence: 73%

Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Kuvshinov

Kuzmin²,

Shulyakovsky³

2003

Phys. Rev. E

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For the system with one-dimensional spatially periodic potential we demonstrate that small periodic in time perturbation results in appearance of chaotic instanton solutions. We estimate parameter of local instability, width of stochastic layer and correlator for perturbed instanton solutions. Application of the instanton technique enables to calculate the amplitude of the tunneling, the form of the spectrum and the lower bound for width of the ground quasi-energy zone.

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Section: The Calculation Of the Tunneling Amplitude And Ground Zone Wsupporting

confidence: 73%

Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Kuvshinov

Kuzmin²,

Shulyakovsky³

2003

Phys. Rev. E

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“…Simultaneously, the chaotic state repels the wave-packet state leading to a deviation of the energy from its smooth behavior, and thus to the observed fluctuations. This mechanism is similar to "chaos assisted tunneling", described in the literature [179][180][181][182][183][184][185][186][187][188][189] for both, driven one-dimensional and two-dimensional autonomous systems. There, the tunneling rate between two symmetric islands -which manifests itself through the splitting between the symmetric and antisymmetric states of a doublet -may be strongly enhanced by the chaotic transport between the islands.…”

Section: Ionization Rates and Chaos Assisted Tunnelingmentioning

confidence: 99%

Non-dispersive wave packets in periodically driven quantum systems

2002

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With the exception of the harmonic oscillator, quantum wave packets usually spread as time evolves. This is due to the non-linear character of the classical equations of motion which makes the various components of the wave packet evolve at various frequencies. We show here that, using the non-linear resonance between an internal frequency of a system and an external periodic driving, it is possible to overcome this spreading and build non-dispersive (or non-spreading) wave packets which are well localized and follow a classical periodic orbit without spreading. From the quantum mechanical point of view, the non-dispersive wave packets are time periodic eigenstates of the Floquet Hamiltonian, localized in the non-linear resonance island. We discuss the general mechanism which produces the non-dispersive wave packets, with emphasis on simple realization in the electronic motion of a Rydberg electron driven by a microwave field. We show the robustness of such wave packets for a model one-dimensional as well as for realistic three-dimensional atoms. We consider their essential properties such as the stability versus ionization, the characteristic energy spectrum and long lifetimes. The requirements for experiments aimed at observing such non-dispersive wave packets are also considered. The analysis is extended to situations in which the driving frequency is a multiple of the internal atomic frequency. Such a case allows us to discuss non-dispersive states composed of several, macroscopically separated wave packets communicating among themselves by tunneling. Similarly we briefly discuss other closely related phenomena in atomic and molecular physics as well as possible further extensions of the theory. (C) 2002 Elsevier Science B.V. All rights reserved

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“…They utilized the occurrence of tunnel doublets with exponentially small splittings as a filter to separate "regular" quantal eigenstates (i.e., those localized in classically regular phase-space regions) from "chaotic" ones (in an analogous sense). While their work was based on a time-independent, twodimensional nonlinear oscillator, the first inquiry into driven tunneling in a one-dimensional, bistable system was undertaken by Lin and Ballentine [11] and Grossmann et al [12][13][14], and subsequently by Plata and Gomez Llorente [15].…”

Section: Introductionmentioning

confidence: 99%

Tunneling and the onset of chaos in a driven bistable system

1994

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We study the interplay between coherent transport by tunneling and diffusive transport through classically chaotic phase-space regions, as it is reflected in the Floquet spectrum of the periodically driven quartic double well. The tunnel splittings in the semiclassical regime are determined with high numerical accuracy, and the association of the corresponding doublet states to either chaotic or regular regions of the classical phase space is quantified in terms of the overlap of the Husimi distribution with the chaotic layer along the separatrix. We find a strong correlation between both quantities. They show an increase by orders of magnitude as chaotic diffusion between the wells starts to dominate the classical dynamics. We discuss semiclassical explanations for this correlation. 05.45.+b, 03.65.Sq, 73.40.Gk

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Quantum tunneling and chaos in a driven anharmonic oscillator

Cited by 300 publications

References 12 publications

Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Chaos-assisted instanton tunneling in one-dimensional perturbed periodic potential

Non-dispersive wave packets in periodically driven quantum systems

Tunneling and the onset of chaos in a driven bistable system

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