Quantum decay rates in chaotic scattering
Nonnenmacher, Stéphane1 ; Zworski, Maciej2
1 Service de Physique Théorique, CEA/DSM/PhT, Unité de recherche associé CNRS, CEA/Saclay, 91191 Gif-sur-Yvette, France
2 Mathematics Department, University of California Evans Hall, Berkeley, CA 94720, USA
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 22, 6 p.
Nonnenmacher, Stéphane 1 ; Zworski, Maciej 2

1 Service de Physique Théorique, CEA/DSM/PhT, Unité de recherche associé CNRS, CEA/Saclay, 91191 Gif-sur-Yvette, France
2 Mathematics Department, University of California Evans Hall, Berkeley, CA 94720, USA 
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Nonnenmacher, Stéphane; Zworski, Maciej. Quantum decay rates in chaotic scattering. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 22, 6 p. http://archive.numdam.org/item/SEDP_2005-2006____A22_0/

[1] N. Anantharaman, Entropy and the localization of eigenfunctions, preprint (2004-2006), to appear in Ann. of Math.

[2] N. Anantharaman and S. Nonnenmacher, Half-delocalization of eigenfunctions of the Laplacian, in preparation (2006).

[3] R. Bowen and D. Ruelle, The ergodic theory of Axiom A flows, Invent. math. 29 (1975), 181–202 | EuDML | MR | Zbl

[4] N. Burq, Contrôle de l’équation des plaques en présence d’obstacle stictement convexes. Mémoires de la Société Mathématique de France, Sér. 2, 55 (1993), 3-126. | EuDML | Numdam | Zbl

[5] P. Gaspard and S.A. Rice, Semiclassical quantization of the scattering from a classically chaotic repellor, J. Chem. Phys. 90(1989), 2242-2254. | MR

[6] M. Ikawa, Decay of solutions of the wave equation in the exterior of several convex bodies, Ann. Inst. Fourier, 38(1988), 113-146. | EuDML | Numdam | MR | Zbl

[7] A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, 1997. | 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] 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

[12] F. Naud, Classical and Quantum lifetimes on some non-compact Riemann surfaces, Journal of Physics A, 38(2005), 10721-10729. | MR | Zbl

[13] S. Nonnenmacher and M. Zworski, Distribution of resonances for open quantum maps, preprint 2005, math-ph/0505034, Fractal Weyl laws in discrete models of chaotic scattering, Journal of Physics A, 38(2005), 10683-10702. | MR | Zbl

[14] S. Nonnenmacher and M. Zworski, Lower bounds for quantum decay rates in chaotic scattering, in preparation.

[15] Ya. B. Pesin and V. Sadovskaya, Multifractal Analysis of Conformal Axiom A Flows, Comm. Math. Phys. 216(2001), 277-312. | MR | Zbl

[16] H. Schomerus and J. Tworzydło and, Quantum-to-classical crossover of quasi-bound states in open quantum systems, Phys. Rev. Lett. Phys. Rev. Lett. 93(2004), 154102.

[17] J. Sjöstrand, Geometric bounds on the density of resonances for semiclassical problems, Duke Math. J., 60(1990), 1–57 | MR | Zbl

[18] J. Sjöstrand and M. Zworski, Fractal upper bounds on the density of semiclassical resonances, http://math.berkeley.edu/~zworski/sz10.ps.gz, to appear in Duke Math. J. | MR | Zbl

[19] 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

[20] A. Wirzba, Quantum Mechanics and Semiclassics of Hyperbolic n-Disk Scattering Systems, Physics Reports 309 (1999) 1-116 | MR