Abstract
The subtle and complex nature of classical Hamiltonian mechanics is now well recognised: long-time predictability and the topologies of the orbits of a system are known to depend critically on the form of the Hamiltonian and the phase space may support regions of regular and chaotic motion interwoven on all scales.1 A natural question is: how does this classical complexity manifest itself in the corresponding quantum system? Sometimes this question is put in the form: what is Quantum Chaos?
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A.J. Lichtenberg and M.A. Liberman, ‘regular and Stochastic Motion”, Springer: New York (1983)
M. V.Berry, Regular and Irregular Motion in “Topics in Nonlinear Mechanics”, S.Jorna, Ed.,Am.Inst.Phys.Conf. Proc. 46:16–120 (1978)
H.G.Schuster, “Deterministic Chaos”, Physik-Verlag GMBH: Weinheim (1984)
J.E. Bayfield, L.D. Gardner and P.M. Koch, Phys.Rev.Lett. 39: 76–79 (1977)
G. Casati, B.V. Chirikov, and D.L. Shepelyansky, Phys.-Rev.Lett. 53 2525–2528 (1984)
G. Casati, B.V. Chirikov, D.L. Shepelyansky and I. Guarneri Phys.Rev.Lett. 57 823–826 (1986)
G. Casati, B.V.Chirikov, J.Ford and F.M.Izraelev in “Stochastic Behaviour in Classical and Quantum Hamilto- nian Systems,” G.Casati, J.Ford, ed., Springer Lecture Notes in Physics 93: 334–352 (1979)
M.V. Berry, N.L. Balazs, M. Tabor and A. Voros, Ann.Phys.-(N.Y) 122:26–63 (1979)
H. J.Korsch and M.V.Berry 3D: 627–636 (1981)
M.V.Berry, Physica l0D: 369–378 (1984)
B.V. Chirikov, F.M. Izraelev and D.L.Shepelyansky, Sov.Sci.-Revs. 2C: 209–267 (1981)
D.L.Shepelyansky, Physica 8D: 208–222 (1983)
Shmuel Fishman, D.R.Grempel and R.E.Prange,Phys.Rev.Lett. 49: 509–512 (1982)
B.V. Chirikov, F.M. Izraelev and D.L. Shepelyansky, Sov.Sci. Revs. 2C 209–267 (1981)
Shmuel Fishman, D.R.Grempel and R.E.Prange Phys.Rev.Lett. 49 509–512 (1982)
D.R.Grempel, Shmuel Fishman and R.E.Prange Phys.Rev.A 29 1639–1647 (1984)
M.V. Berry “Quantum Chaology” Proc.Royal Soc. 1987, in press.
V.I. Arnold, “Mathematical Methods of Classical Mechanics,” Springer, New York (1978)
V.P. Maslov and M.V. Fedoriuk, “Semiclassiccal Approximation in Quantum Mechanics,” D.Reidel: Dordrecht, (1981)M.V.Berry, Semiclassical Mechanics of Regular and Irregular Motion in “Chaotic Behavior of Deterministic Systems,” Les Houches Lectures XXXVI, G.Iooss, R.H.G.Helleman and R.Stora, eds., North-Holland, Amsterdam, pp 171–271 (1983)
I. C.Percival, Adv.Chem.Phys. 36:1–61 (1977)
H.P.Baltes and E.R.Hilf, Spectra of finite systems (B.I.Wissenschaftsverlag: Mannheim)
C.E.Porter,Statistical Theories of Spectra: Fluctuations (Academic-Press: New York).
F.J. Dyson, and M.L. Mehta, J.Math.Phys. 4 701–712 (1963)
M.V. Berry and M. Tabor Proc.Roy.Soc.Lond. A356 375–394 M.V.Berry Proc.Roy.Soc.Lond. A400 229–251 (1985)
E. Wigner “Group Theory and its Application to the Theory of Atomic Spectra” Academic: New York (1959)
M. Robnik J.Phys.A: Math.Gen. 17 1049–74 (1984)
M.V. Berry and M. Robnik J.Phys.A 19 649–668 (1986a)
M. Robnik and M.V. Berry J.Phys.A. 19 669–682 (1986)
M.V.Berry and R.J.Mondragon Proc.Roy.Soc. in press. (1987)
G. Casati, B.V. Chirikov and I. Guarneri Phys.Rev.Lett. 54 1350–1353 (1985) Berry, M.V. and M.Robnik J.Phys.A. 17 2413–2421 (1984)
M.C. Gutzwiller J Math.Phys. 12 343–358 (1971) M.C.Gutzwiller in “Path Integrals and their Applications in Quantum Statistical and Solid-State Physics”, eds. G.J.Papadopoulos and J.T.Devreese) Plenum,N.H.163–200 (1978)
R.Balian and C.Bloch Ann.Phys.(N.Y) 69 76–160 (1972)
J.P. Keating and M.V. Berry. In preparation (1987)
J.H. Hannay and A.M. Ozorio de Almeida A.M. J.Phys.A. 17 3429–3440 ( )
M.V. Berry in “Quantum Chaos and Statistical Nuclear Physics” (eds.T.H. Seligman and H. Nishioka) Springer lecture notes in physics No. 263, pp 1–17 (1986b)
H.M. Edwards, Riemann’s Zeta Function Academic Press: New York and London (1974)
J. Van de Lune, H.J.J. te Riele and D.T. Winter Math.of Comp. 46 No.174 667–681 (1986)
A.M. Odlyzko, Math.of Comp. Vol. 48 No.177, 273–308 (1987)
M.V.Berry and A.M.Odlyzko, Classical Formula for the Variance of the Riemann Zeros, in preparation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Plenum Press, New York
About this chapter
Cite this chapter
Keating, J., Mondragon, R. (1988). Quantum Chaology of Energy Levels Notes Based on Lectures by Michael Berry. In: Gallavotti, G., Zweifel, P.F. (eds) Nonlinear Evolution and Chaotic Phenomena. NATO ASI Series, vol 176. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1017-4_15
Download citation
DOI: https://doi.org/10.1007/978-1-4613-1017-4_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8294-5
Online ISBN: 978-1-4613-1017-4
eBook Packages: Springer Book Archive