Fractal Weyl laws for quantum resonances
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Exposé no. 4, 27 p.
Zworski, Maciej 1

1 Mathematics Department, University of California Evans Hall, Berkeley, CA 94720
@article{SEDP_2004-2005____A4_0,
     author = {Zworski, Maciej},
     title = {Fractal {Weyl} laws for quantum resonances},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:4},
     pages = {1--27},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2004-2005},
     mrnumber = {2182049},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2004-2005____A4_0/}
}
TY  - JOUR
AU  - Zworski, Maciej
TI  - Fractal Weyl laws for quantum resonances
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:4
PY  - 2004-2005
SP  - 1
EP  - 27
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://www.numdam.org/item/SEDP_2004-2005____A4_0/
LA  - en
ID  - SEDP_2004-2005____A4_0
ER  - 
%0 Journal Article
%A Zworski, Maciej
%T Fractal Weyl laws for quantum resonances
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:4
%D 2004-2005
%P 1-27
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://www.numdam.org/item/SEDP_2004-2005____A4_0/
%G en
%F SEDP_2004-2005____A4_0
Zworski, Maciej. Fractal Weyl laws for quantum resonances. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Exposé no. 4, 27 p. http://www.numdam.org/item/SEDP_2004-2005____A4_0/

[1] E. Bogomolny, Spectral statistics, in Proc. Int. Congress of Mathematicians (Doc. Math. Extra vol. 3) 99–108, Springer Verlag, Berlin, 1998. | MR | Zbl

[2] J.-M. Bony and J.-Y. Chemin, Espaces fonctionnels associés au calcul de Weyl-Hörmander, Bull. Soc. math. France, 122(1994), 77-118. | Numdam | MR | Zbl

[3] H. Christianson, Growth and zeros of the zeta function for hyperbolic rational maps, to appear in Can. J. Math. | MR | Zbl

[4] M. Dimassi and J. Sjöstrand, Spectral Asymptotics in the semiclassical limit, Cambridge University Press, 1999. | MR | Zbl

[5] C. Gérard and J. Sjöstrand, Semiclassical resonances generated by a closed trajectory of hyperbolic type, Comm. Math. Phys. 108(1987), 391-421. | MR | Zbl

[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. | MR | Zbl

[7] V. Ivrii, Microlocal Analysis and Precise Spectral Asymptotics, Springer Verlag, 1998. | MR | Zbl

[8] K. Lin, Numerical study of quantum resonances in chaotic scattering, J. Comp. Phys. 176(2002), 295-329. | MR | Zbl

[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. | MR | Zbl

[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. | Numdam | Zbl

[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. | MR | Zbl

[14] S. Nonnenmacher and M. Zworski, Distribution of resonances for open quantum maps, preprint 2005, math-ph/0505034. | MR | Zbl

[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. | MR | Zbl

[17] J. Sjöstrand and M. Zworski, Quantum monodromy and semiclassical trace formulae, J. Math. Pure Appl. 81(2002), 1–33. | MR | Zbl

[18] J. Sjöstrand and M. Zworski, Fractal upper bounds for the density of semiclassical resonances, preprint 2005, www.math.berkeley.edu/zworski. | MR | Zbl

[19] P. Stefanov, Approximating resonances with the complex absorbing potential method, preprint 2004, math-ph/0409020, to appear in Comm. P.D.E. | MR | Zbl

[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. | MR | Zbl

[21] M. Zworski, Distribution of poles for scattering on the real line, J. Funct. Anal. 73(1987), 277-296. | MR | Zbl

[22] M. Zworski, Sharp polynomial bounds on the distribution of scattering poles, Duke Math. J. 59(1989), 311-323. | MR | Zbl

[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. | MR | Zbl