Manifestations of classical phase space structures in quantum mechanics

Bohigas, O.; Tomsovic, Steven; Ullmo, Denis

doi:10.1016/0370-1573(93)90109-q

Cited by 517 publications

(604 citation statements)

References 100 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%

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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 Tunnelingsupporting

confidence: 56%

“…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%

Non-dispersive wave packets in periodically driven quantum systems

2002

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“…Except for the factor of i,Ĝ tun looks formally identical to its splitting counterpart defined in Eq. (21). As in that case, the real time evolutions coming fromĜ and G † will cancel -following saddle point integration,Ĝ tun is approximated with a single orbit γ = β • α obtained by concatenating an orbit α of positive real time evolution with an orbit β of negative real time evolution.…”

Section: The Case Of Resonancesmentioning

confidence: 98%

“…In fact, we need the densities corresponding to a given value of the y parity, π y = ±1. The problem of symmetry decomposition of the smooth density of states has been discussed in various papers both for potential systems [21] and billiards [22]. Our case is rather simple since it is a simple parity group and the result is,…”

Section: A1 Thomas-fermi Calculationmentioning

confidence: 99%

A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities

Creagh

Whelan

1999

Annals of Physics

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It is shown that tunnelling splittings in ergodic double wells and resonant widths in ergodic metastable wells can be approximated as easily-calculated matrix elements involving the wavefunction in the neighbourhood of a certain real orbit. This orbit is a continuation of the complex orbit which crosses the barrier with minimum imaginary action. The matrix element is computed by integrating across the orbit in a surface of section representation, and uses only the wavefunction in the allowed region and the stability properties of the orbit. When the real orbit is periodic, the matrix element is a natural measure of the degree of scarring of the wavefunction. This scarring measure is canonically invariant and independent of the choice of surface of section, within semiclassical error. The result can alternatively be interpretated as the autocorrelation function of the state with respect to a transfer operator which quantises a certain complex surface of section mapping. The formula provides an efficient numerical method to compute tunnelling rates while avoiding the need for the exceedingly precise diagonalisation endemic to numerical tunnelling calculations.

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“…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.

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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.

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Manifestations of classical phase space structures in quantum mechanics

Cited by 517 publications

References 100 publications

Non-dispersive wave packets in periodically driven quantum systems

Non-dispersive wave packets in periodically driven quantum systems

A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities

Semiclassical description of soliton-antisoliton pair production in particle collisions

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