Chaos-assisted tunneling

Tomsovic, Steven; Ullmo, Denis

doi:10.1103/physreve.50.145

Cited by 263 publications

(337 citation statements)

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“…In the perturbative regime (γ/∆, σ/∆ ≪ 1) it is possible to obtain analytical [65] predictions for the statistical distribution of the energy shifts P (s) (of the wave-packet's energy from its unperturbed value) and for the distribution of its widths P (Γ). P (s) turns out to be a Cauchy distribution (Lorentzian), similarly to the tunneling splitting distribution found in [187]. The distribution of the widths is a bit more complicated (it is the square root of Γ which is approximately Lorentzian distributed).…”

Section: Ionization Rates and Chaos Assisted Tunnelingmentioning

confidence: 93%

“…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%

“…Since these fluctuations stem from the coupling between the regular wavepacket state and a set of chaotic states, it is quite natural to model such a situation via a Random Matrix model [65], the approach being directly motivated by a similar treatment of the tunneling splitting in [187]. For details, we refer the reader to the original work [65].…”

Section: Ionization Rates and Chaos Assisted Tunnelingmentioning

confidence: 99%

“…The distribution of the widths is a bit more complicated (it is the square root of Γ which is approximately Lorentzian distributed). The perturbative approach fails for the asymptotic behavior of the tails of the distributions, where an exponential cut-off is expected and observed in numerical studies [65,187]. By fitting the predictions of the Random Matrix model to the numerical data of fig.…”

Section: Ionization Rates and Chaos Assisted Tunnelingmentioning

confidence: 99%

“…3.4.4, eqs. (185)(186)(187)(188), the equilibrium position x eq of the molecular Rydberg electron is easily estimated according to (assuming a small value of a, limited by the size of the molecular core)…”

Section: Non-dispersive Wave-packets In Rotating Moleculesmentioning

confidence: 99%

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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 Tunnelingmentioning

confidence: 93%