Scar Formation at the Edge of the Chaotic Region

Arranz, F. J.; Borondo, F.; Benito, R. M.

doi:10.1103/physrevlett.80.944

Cited by 54 publications

(52 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The vibrational dynamics associated with the isomerization LiNC LiCN process can be adequately followed by monitoring the motion along the angular θ coordinate [41]. For the sake of comparison in this work we will use, in addition to the SALI indicator, the more established procedure of PSOS specifically to select initial conditions in the phase space [35][36][37].…”

Section: B Classical Trajectories and Poincaré Surfaces Of Sectionsmentioning

confidence: 99%

“…In this paper we consider the system LiNC-LiCN that has been an attractive subject for computational work, since it constitutes an example of a simple isomerization reaction. It has been extensively studied by our group [35][36][37], and considered for reactivity control in the picosecond range [38,39] and also in coherent chemistry with THz pulses [40]. From a mechanical point of view, it can be seen as a vibrational Hamiltonian system, consisting of a collection of highly anharmonic, coupled oscillators with a highly nonlinear behavior.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Using the small alignment index chaos indicator to characterize the vibrational dynamics of a molecular system: LiNC-LiCN

et al. 2015

Self Cite

View full text Add to dashboard Cite

A study of the dynamical characteristics of the phase space corresponding to the vibrations of the LiNC-LiCN molecule using an analysis based on the small alignment index (SALI) is presented. SALI is a good indicator of chaos that can easily determine whether a given trajectory is regular or chaotic regardless of the dimensionality of the system, and can also provide a wealth of dynamical information when conveniently implemented. In two-dimensional (2D) systems SALI maps are computed as 2D phase space representations, where the SALI asymptotic values are represented in color scale. We show here how these maps provide full information on the dynamical phase space structure of the LiNC-LiCN system, even quantifying numerically the volume of the different zones of chaos and regularity as a function of the molecule excitation energy.

show abstract

Section: B Classical Trajectories and Poincaré Surfaces Of Sectionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Using the small alignment index chaos indicator to characterize the vibrational dynamics of a molecular system: LiNC-LiCN

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…The regular or chaotic behavior of quantum states has been characterized through the distributions of the Husimi zeros in the spin-boson interaction model [5,6], in quantum billiards [7,8], in one-dimensional autonomous (then integrable) systems [9,10], in spin SternGerlach apparatus [11] (where it is possible to experimentally measure the zeros), in acoustic waveguides [12], and also in molecular systems [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Onset of quantum chaos in molecular systems and the zeros of the Husimi function

et al. 2013

Self Cite

View full text Add to dashboard Cite

The distribution of zeros of the Husimi function has proven a useful tool in the characterization of regular and chaotic quantum states of dynamical systems. In a previous paper [Phys. Rev. E 82, 026201 (2010)], we showed how the quantum transition from order to chaos in three different molecular systems (LiCN, HCN, and HO 2 ) can be understood by means of the correlation diagram of eigenenergies versus the Planck's constant. An order-chaos frontier of scars (eigenstates localized over unstable and stable complementary, in the sense of the Poincaré-Birkhoff theorem, periodic orbits) was observed. In this paper, we show how the distribution of zeros of the Husimi function can be related to the onset of chaos in these molecular systems, showing a very interesting feature at the frontier of scars; namely, some zeros of the Husimi function localize over the stable and unstable fixed points corresponding to the two complementary periodic orbits, this representing the quantum equivalent to the Poincaré-Birkhoff theorem.

show abstract

“…One way is trying to disentangle the complexity involved in the distribution of individual levels in the spectra of classically chaotic systems [6][7][8]. For example, in Ref.…”

mentioning

confidence: 99%

Beyond the First Recurrence in Scar Phenomena

Borondo¹,

Benito²

2003

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

The scarring effect of short unstable periodic orbits up to times of the order of the first recurrence is well understood. Much less is known, however, about what happens past this short-time limit. By considering the evolution of a dynamically averaged wave packet, we show that the dynamics for longer times is controlled by only a few related short periodic orbits and their interplay.PACS numbers: 05.45.+b, 03.65.Ge, 03.65.Sq The study of the quantum manifestations of classical chaos is at present a topic of very active research interest [1]. Great advance came from random matrix theory (RMT) which provides an understanding of universal statistical properties of quantum spectra [2]. The most striking departure from RMT described so far in the literature is the phenomenon known as "scar" [3]. This term describes an anomalous localization of quantum probability density along unstable periodic orbits (PO) in classically chaotic systems. Heller showed [4] the importance of the first recurrences of POs in the scarring effect. In a subsequent work Tomsovic and Heller [5] demonstrated that the semiclassical propagation can be carried out with remarkable precission long after classical fine structure had developed on a scale much smaller thanh, by computing the corresponding correlation function, C scl (t), as a sum of contributions of the homoclinic excursions of the PO. This procedure is however cumbersome, since in general many orbits are needed to obtain converged results, and this number increases rapidly with time (see Ref.[5] for details). This picture is greatly simplified if alternatively considering the corresponding averaged dynamics for finite periods of time. In this case, as will be shown in this Letter, a structure of a few short POs emerges that govern the quantum dynamics for times past the first recurrence of the original PO.Understanding scarring can be tackled from two sides. One way is trying to disentangle the complexity involved in the distribution of individual levels in the spectra of classically chaotic systems [6][7][8]. For example, in Ref.[8] structures localized on short POs of the stadium were obtained, by considering state correlation diagrams and iteratively removing the parametric interactions (avoided crossings) between the involved eigenstates. The other way consists of approaching the problem in a much more straighforward fashion, by studying how the dynamics of POs induce scars in the eigenfunctions of the system.Heller's work provided a time-dependent view that shows how recurrences in the short time dynamics of a wave packet along the neighborhood of an isolated PO produces the accumulation of quantum probability density characteristic of scars. Very recently Kaplan and Heller [9] have shown how the use of coherent wave packet sums, decaying as the log-time, leads to enhanced scarring. Later, it was described by some of us [10] how (nonstationary) wave functions highly localized over POs can be constructed from finite time Fourier transform of wave packets. This method all...

show abstract

Scar Formation at the Edge of the Chaotic Region

Cited by 54 publications

References 20 publications

Using the small alignment index chaos indicator to characterize the vibrational dynamics of a molecular system: LiNC-LiCN

Using the small alignment index chaos indicator to characterize the vibrational dynamics of a molecular system: LiNC-LiCN

Onset of quantum chaos in molecular systems and the zeros of the Husimi function

Beyond the First Recurrence in Scar Phenomena

Contact Info

Product

Resources

About