Fractal Weyl laws for quantum resonances

Maciej Zworski[1]

  • [1] Mathematics Department, University of California Evans Hall, Berkeley, CA 94720

Séminaire Équations aux dérivées partielles (2004-2005)

  • Volume: 2004-2005, page 1-27

How to cite

top

Zworski, Maciej. "Fractal Weyl laws for quantum resonances." Séminaire Équations aux dérivées partielles 2004-2005 (2004-2005): 1-27. <http://eudml.org/doc/11116>.

@article{Zworski2004-2005,
affiliation = {Mathematics Department, University of California Evans Hall, Berkeley, CA 94720},
author = {Zworski, Maciej},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-27},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Fractal Weyl laws for quantum resonances},
url = {http://eudml.org/doc/11116},
volume = {2004-2005},
year = {2004-2005},
}

TY - JOUR
AU - Zworski, Maciej
TI - Fractal Weyl laws for quantum resonances
JO - Séminaire Équations aux dérivées partielles
PY - 2004-2005
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2004-2005
SP - 1
EP - 27
LA - eng
UR - http://eudml.org/doc/11116
ER -

References

top
  1. E. Bogomolny, Spectral statistics, in Proc. Int. Congress of Mathematicians (Doc. Math. Extra vol. 3) 99–108, Springer Verlag, Berlin, 1998. Zbl0963.81022MR1648144
  2. J.-M. Bony and J.-Y. Chemin, Espaces fonctionnels associés au calcul de Weyl-Hörmander, Bull. Soc. math. France, 122(1994), 77-118. Zbl0798.35172MR1259109
  3. H. Christianson, Growth and zeros of the zeta function for hyperbolic rational maps, to appear in Can. J. Math. Zbl1116.37032MR2310619
  4. M. Dimassi and J. Sjöstrand, Spectral Asymptotics in the semiclassical limit, Cambridge University Press, 1999. Zbl0926.35002MR1735654
  5. C. Gérard and J. Sjöstrand, Semiclassical resonances generated by a closed trajectory of hyperbolic type, Comm. Math. Phys. 108(1987), 391-421. Zbl0637.35027MR874901
  6. L. Guillopé, K. Lin, and M. Zworski, The Selberg zeta function for convex co-compact Schottky groups, Comm. Math. Phys, 245(2004), 149 - 176. Zbl1075.11059MR2036371
  7. V. Ivrii, Microlocal Analysis and Precise Spectral Asymptotics, Springer Verlag, 1998. Zbl0906.35003MR1631419
  8. K. Lin, Numerical study of quantum resonances in chaotic scattering, J. Comp. Phys. 176(2002), 295-329. Zbl1021.81021MR1894769
  9. K. Lin and M. Zworski, Quantum resonances in chaotic scattering, Chem. Phys. Lett. 355(2002), 201-205. 
  10. W. Lu, S. Sridhar, and M. Zworski, Fractal Weyl laws for chaotic open systems, Phys. Rev. Lett. 91(2003), 154101. 
  11. R.B. Melrose, Polynomial bounds on the number of scattering poles, J. Funct. Anal. 53(1983), 287-303. Zbl0535.35067MR724031
  12. R.B. Melrose, Polynomial bounds on the distribution of poles in scattering by an obstacle, Journeés “Equations aux dériveés Partielles”, Saint-Jean-des-Monts, 1984. Zbl0621.35073
  13. T. Morita, Periodic orbits of a dynamical system in a compound central field and a perturbed billiards system. Ergodic Theory Dynam. Systems 14(1994), 599–619. Zbl0810.58014MR1293411
  14. S. Nonnenmacher and M. Zworski, Distribution of resonances for open quantum maps, preprint 2005, math-ph/0505034. Zbl1114.81043MR2274550
  15. H. Schomerus and J. Tworzydło, Quantum-to-classical crossover of quasi-bound states in open quantum systems, Phys. Rev. Lett. 93(2004), 154102. 
  16. J. Sjöstrand, Geometric bounds on the density of resonances for semiclassical problems, Duke Math. J., 60(1990), 1–57. Zbl0702.35188MR1047116
  17. J. Sjöstrand and M. Zworski, Quantum monodromy and semiclassical trace formulae, J. Math. Pure Appl. 81(2002), 1–33. Zbl1038.58033MR1994881
  18. J. Sjöstrand and M. Zworski, Fractal upper bounds for the density of semiclassical resonances, preprint 2005, www.math.berkeley.edu/ zworski. Zbl1201.35189MR2309150
  19. P. Stefanov, Approximating resonances with the complex absorbing potential method, preprint 2004, math-ph/0409020, to appear in Comm. P.D.E. Zbl1095.35017MR2182314
  20. J. Strain and M. Zworski, Growth of the zeta function for a quadratic map and the dimension of the Julia set, Nonlinearity, 17(2004), 1607-1622. Zbl1066.37031MR2086141
  21. M. Zworski, Distribution of poles for scattering on the real line, J. Funct. Anal. 73(1987), 277-296. Zbl0662.34033MR899652
  22. M. Zworski, Sharp polynomial bounds on the distribution of scattering poles, Duke Math. J. 59(1989), 311-323. Zbl0705.35099MR1016891
  23. M. Zworski, Dimension of the limit set and the density of resonances for convex co-compact Riemann surfaces, Inv. Math. 136(1999), 353-409. Zbl1016.58014MR1688441

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.