Abstract
The problem of characterizing stability and instability for general nonstationary quantum systems is investigated. Some characterizations are reported and some elementary properties of a topological characterization are established. Then, it is proven, by considering a simple example, that there are nonperiodic driven systems whose orbits are neither precompact nor leave on average any compact set. Autocorrelation measures are computed and the possible roles of the generalizes quasienergy operator and energy growth are briefly discussed.
Similar content being viewed by others
References
V. Enns and K. Veselic,Ann. Inst. Henri Poincaré A 39:159 (1983).
G. Casati and L. Molinari,Prog. Theor. Phys. Suppl. 98:287 (1989).
G. Casati and I. Guarneri,Phys. Rev. Lett. 50:640 (1983).
G. Casati, I. Guarneri, and D. L. Shepelyansky,Phys. Rev. Lett. 62:345 (1989).
M. Combescure,J. Stat. Phys. 62:779 (1991).
M. Combescure,Ann. Inst. Henri Poincaré 57:67 (1992).
T. Geisel,Phys. Rev. A 41:2889 (1990).
J. Bellissard, inStochastic Processes in Classical and Quantum Systems, S. Albeverio, G. Casati, and D. Merlini, eds. (Springer-Verlag, Berlin, 1986).
H. R. Jauslin and J. L. Lebowitz,Chaos 1:114 (1991).
L. Bunimovich, H. R. Jauslin, J. L. Lebowitz, A. Pellegrinotti, and P. Niebala,J. Stat. Phys. 62:793 (1991).
N. F. de Godoy and R. Graham,Europhys. Lett. 16:519 (1991).
D. L. Shepelyansky,Physica 8D:208 (1983).
J. M. Luck, H. Orland, and U. Smilansky,J. Stat. Phys. 53:551 (1988).
Y. Pomeau, B. Dorizzi, and B. Grammaticos,Phys. Rev. A 35:1714 (1987).
M. Samuelides, R. Fleckinger, L. Touzillier, and J. Bellissard,Europhys. Lett. 1: 203 (1986).
C.-A. Pillet,Commun. Math. Phys. 102:237 (1985);105:259 (1986).
I. Guarneri,Lett. Nuovo Cimento 40:171 (1984).
S. E. Cheremshantsev,Math. USSR Sbornik 65:531 (1990).
J.-P. Bellissard, inTrends and Developments in the Eighties, S. Albeverio and Ph. Blanchard, eds. (World Scientific, Singapore, 1985).
T. Hogg and H. Huberman,Phys. Rev. A 28:22 (1983).
K. Yajima,Commun. Math. Phys. 87:331 (1982).
C. R. de Oliveira,J. Math. Phys. 34:3878 (1993).
J. S. Howland,J. Funct. Anal. 74:52 (1987).
G. A. Hagedorn, M. Loss, and J. Slawny,J. Phys. A 19:521 (1986).
M. Queffélec,Substitution Dynamical Systems—Spectral Analysis (Springer-Verlag, Berlin 1987).
C. R. de Oliveira, On kicked systems modulated along the Thue-Morse Sequence,J. Phys. A., to appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
de Oliveira, C.R. Some remarks concerning stability for nonstationary quantum systems. J Stat Phys 78, 1055–1066 (1995). https://doi.org/10.1007/BF02183701
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02183701