Complex Classical Trajectories and Chaotic Tunneling

Shudo, Akira; Ikeda, Kensuke S.

doi:10.1103/physrevlett.74.682

Cited by 140 publications

(238 citation statements)

References 10 publications

Supporting

Mentioning

228

Contrasting

Order By: Relevance

“…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 n 0 is the inverse of the effective Planck constant in our problem (see the discussion in section 3.3.1 and eq. (147)), this shows that where S, corresponding to some effective imaginary action [188], is found to be given for our specific choice of parameters by S ≃ 0.06 ± 0.01 (as fitted from the plot). Such an exponential dependence is a hallmark of a tunneling process, thus confirming that the wave-packets are strongly localized in the island and communicate with the outside world via tunneling.…”

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%

See 2 more Smart Citations

Non-dispersive wave packets in periodically driven quantum systems

2002

View full text Add to dashboard Cite

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

show abstract

Section: Ionization Rates and Chaos Assisted Tunnelingmentioning

confidence: 99%

Section: Ionization Rates and Chaos Assisted Tunnelingmentioning

confidence: 99%

See 1 more Smart Citation

Non-dispersive wave packets in periodically driven quantum systems

2002

View full text Add to dashboard Cite

show abstract

“…dynamics is difficult [79][80][81][82][83][84][85][86][87][88] for the semiclassical methods, we avoid it by changing the form of the scalar potential. We checked that the model (3.1) is not chaotic, 11 i.e.…”

Section: Choosing the Potentialmentioning

confidence: 99%

Semiclassical description of soliton-antisoliton pair production in particle collisions

Demidov

Levkov

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

We develop a consistent semiclassical method to calculate the probability of topological soliton-antisoliton pair production in collisions of elementary particles. In our method one adds an auxiliary external field pulling the soliton and antisoliton in the opposite directions. This transforms the original scattering process into a Schwinger pair creation of the solitons induced by the particle collision. One describes the Schwinger process semiclassically and recovers the original scattering probability in the limit of vanishing external field. We illustrate the method in (1 + 1)-dimensional scalar field model where the suppression exponents of soliton-antisoliton production in the multiparticle and two-particle collisions are computed numerically.

show abstract

“…Creagh and Whelan [20,21,22,23] developed a semiclassical approach to tunneling (for a semiclassical treatment concentrating on other aspects of tunneling see e.g. [24,25]) which enabled them to give an improved statistical distribution of tunneling rates [26]. The distribution has been tested on a model system and shown to faithfully represent the tunneling splitting distribution provided the classical dynamics is sufficiently chaotic.…”

Section: Introductionmentioning

confidence: 99%

Experimentally attainable example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields

Delande

Zakrzewski

2003

Phys. Rev. A

View full text Add to dashboard Cite

Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel uniform static electric and magnetic fields, where tunneling is followed by ionization along the fields direction. Depending on the magnetic quantum number, one may observe either a standard Porter-Thomas distribution of tunneling rates or, for strong scarring by a periodic orbit parallel to the external fields, strong deviations from it. For the latter case, a simple model based on random matrix theory gives the correct distribution.

show abstract

Complex Classical Trajectories and Chaotic Tunneling

Cited by 140 publications

References 10 publications

Non-dispersive wave packets in periodically driven quantum systems

Non-dispersive wave packets in periodically driven quantum systems

Semiclassical description of soliton-antisoliton pair production in particle collisions

Experimentally attainable example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields

Contact Info

Product

Resources

About