no. 6

Strong scarring of logarithmic quasimodes  [ Quasimode logarithmique et grosse balafre ]
Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2307-2347.

Nous considérons un opérateur pseudodifférentiel semiclassique sur une surface compacte, tel que le flot Hamiltonien engendré par son symbole principal possède, à une certaine énergie, une orbite périodique hyperbolique. Pour un paramètre ε>0 arbitrairement petit, nous construisons une famille de quasimodes de cet opérateur, dont la largeur en énergie est d’ordre εℏ/|logℏ|, mais qui possèdent un poids positif (une «  grosse balafre ») autour de cette orbite périodique. Notre construction procède par un contrôle de l’évolution de paquets d’onde gaussiens jusqu’au temps d’Ehrenfest.

We consider a semiclassical pseudodifferential operator on a compact surface, such that the Hamiltonian flow generated by its principal symbol admits a hyperbolic periodic orbit at some energy. For an arbitrary small ε>0, we construct semiclassical families of quasimodes of this operator, with energy widths of order εℏ/|logℏ|, and which feature a strong scar along that hyperbolic orbit. Our construction proceeds by controlling the evolution of Gaussian wavepackets up to the Ehrenfest time.

Reçu le :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/aif.3137
Classification : 35-xx,  58Jxx,  37-xx
Mots clés : analyse semiclassique, quasimode, unique ergodicité quantique, balafre d’orbite périodique 
@article{AIF_2017__67_6_2307_0,
     author = {Eswarathasan, Suresh and Nonnenmacher, St\'ephane},
     title = {Strong scarring of logarithmic quasimodes},
     journal = {Annales de l'Institut Fourier},
     pages = {2307--2347},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {67},
     number = {6},
     year = {2017},
     doi = {10.5802/aif.3137},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2017__67_6_2307_0/}
}
Eswarathasan, Suresh; Nonnenmacher, Stéphane. Strong scarring of logarithmic quasimodes. Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2307-2347. doi : 10.5802/aif.3137. https://aif.centre-mersenne.org/item/AIF_2017__67_6_2307_0/

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