Fractal Weyl laws for quantum resonances
- [1] Mathematics Department, University of California Evans Hall, Berkeley, CA 94720
Séminaire Équations aux dérivées partielles (2004-2005)
- Volume: 2004-2005, page 1-27
Access Full Article
topHow to cite
topZworski, 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- E. Bogomolny, Spectral statistics, in Proc. Int. Congress of Mathematicians (Doc. Math. Extra vol. 3) 99–108, Springer Verlag, Berlin, 1998. Zbl0963.81022MR1648144
- 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
- H. Christianson, Growth and zeros of the zeta function for hyperbolic rational maps, to appear in Can. J. Math. Zbl1116.37032MR2310619
- M. Dimassi and J. Sjöstrand, Spectral Asymptotics in the semiclassical limit, Cambridge University Press, 1999. Zbl0926.35002MR1735654
- C. Gérard and J. Sjöstrand, Semiclassical resonances generated by a closed trajectory of hyperbolic type, Comm. Math. Phys. 108(1987), 391-421. Zbl0637.35027MR874901
- 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
- V. Ivrii, Microlocal Analysis and Precise Spectral Asymptotics, Springer Verlag, 1998. Zbl0906.35003MR1631419
- K. Lin, Numerical study of quantum resonances in chaotic scattering, J. Comp. Phys. 176(2002), 295-329. Zbl1021.81021MR1894769
- K. Lin and M. Zworski, Quantum resonances in chaotic scattering, Chem. Phys. Lett. 355(2002), 201-205.
- W. Lu, S. Sridhar, and M. Zworski, Fractal Weyl laws for chaotic open systems, Phys. Rev. Lett. 91(2003), 154101.
- R.B. Melrose, Polynomial bounds on the number of scattering poles, J. Funct. Anal. 53(1983), 287-303. Zbl0535.35067MR724031
- 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
- 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
- S. Nonnenmacher and M. Zworski, Distribution of resonances for open quantum maps, preprint 2005, math-ph/0505034. Zbl1114.81043MR2274550
- H. Schomerus and J. Tworzydło, Quantum-to-classical crossover of quasi-bound states in open quantum systems, Phys. Rev. Lett. 93(2004), 154102.
- J. Sjöstrand, Geometric bounds on the density of resonances for semiclassical problems, Duke Math. J., 60(1990), 1–57. Zbl0702.35188MR1047116
- J. Sjöstrand and M. Zworski, Quantum monodromy and semiclassical trace formulae, J. Math. Pure Appl. 81(2002), 1–33. Zbl1038.58033MR1994881
- J. Sjöstrand and M. Zworski, Fractal upper bounds for the density of semiclassical resonances, preprint 2005, www.math.berkeley.edu/zworski. Zbl1201.35189MR2309150
- P. Stefanov, Approximating resonances with the complex absorbing potential method, preprint 2004, math-ph/0409020, to appear in Comm. P.D.E. Zbl1095.35017MR2182314
- 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
- M. Zworski, Distribution of poles for scattering on the real line, J. Funct. Anal. 73(1987), 277-296. Zbl0662.34033MR899652
- M. Zworski, Sharp polynomial bounds on the distribution of scattering poles, Duke Math. J. 59(1989), 311-323. Zbl0705.35099MR1016891
- 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 ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.