Classical-quantum correspondence for barrier crossing in a driven bistable potential

Plata, J.; Llorente, J. M. Gomez

doi:10.1088/0305-4470/25/7/004

Cited by 48 publications

(33 citation statements)

References 18 publications

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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 Tunnelingsupporting

confidence: 56%

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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Section: Ionization Rates and Chaos Assisted Tunnelingsupporting

confidence: 56%

Non-dispersive wave packets in periodically driven quantum systems

2002

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“…Among them, questions concerning tunneling effects receive now an increasing degree of attention. Indeed, although they are often considered as purely quantum, since they correspond to classically forbidden events, it appears amply clear now that tunneling processes are strongly affected by the nature of the underlying classical dynamics [4,5,6,7,8,9]. This is made most explicit when considering time-dependent systems as well as systems in more than one dimension, for which, in contradistinction to the one-d conservative problems usually considered in basic quantum mechanics textbooks, energy conservation does not constrain the motion to be integrable.…”

Section: Introductionmentioning

confidence: 99%

The level splitting distribution in chaos-assisted tunnelling

Leyvraz

Ullmo²

1996

J. Phys. A: Math. Gen.

109

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A compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar features of tunneling in certain two-dimensional systems. This mechanism is known as chaos-assisted tunneling. We study its consequences for the distribution of the level splittings and obtain a general analytical form for this distribution under the assumption that chaos assisted tunneling is the only operative mechanism. We have checked that the analytical form we obtain agrees with splitting distributions calculated numerically for a model system in which chaos-assisted tunneling is known to be the dominant mechanism. The distribution depends on two parameters: The first gives the scale of the splittings and is related to the magnitude of the classically forbidden processes, the second gives a measure of the efficiency of possible barriers to classical transport which may exist in the chaotic region. If these are weak, this latter parameter is irrelevant; otherwise it sets an energy scale at which the splitting distribution crosses over from one type of behavior to another. The detailed form of the crossover is also obtained and found to be in good agreement with numerical results for models for chaos-assisted tunneling.

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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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Classical-quantum correspondence for barrier crossing in a driven bistable potential

Cited by 48 publications

References 18 publications

Non-dispersive wave packets in periodically driven quantum systems

Non-dispersive wave packets in periodically driven quantum systems

The level splitting distribution in chaos-assisted tunnelling

Tunneling and the onset of chaos in a driven bistable system

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