Statistics of energy spectra

When there is a stochastic disruption of the integrals of motion of a system, the corresponding quantum numbers disappear. The energy spectrum of the system becomes quasirandom. In the present paper, the quantization rules and the distribution of distances between pairs of adjacent levels are studied for this case. The probability for the appearance of very closely spaced levels is governed by a critical index which is expressed in terms of the Kolmogorov entropy for the given system (i.e., in terms of the growth rate for the instability of the classical trajectories in the corresponding phase space). Various physical situations are discussed in which a random spectral structure can arise. The capabilities of a quasiclassical analysis in the case of a stochastic disruption of the integrals of motion are discussed.

PACS: 05.30.−d
DOI: 10.1070/PU1979v022n10ABEH005614
URL: https://ufn.ru/en/articles/1979/10/b/
Citation: Zaslavskii G M "Statistics of energy spectra" Sov. Phys. Usp. 22 788–803 (1979)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Заславский Г М «Статистика энергетического спектра» УФН 129 211–238 (1979); DOI: 10.3367/UFNr.0129.197910b.0211

Cited by (27) Similar articles (20) ↓

G.M. Zaslavskii, B.V. Chirikov “Stochastic instability of non-linear oscillations” 14 549–568 (1972)
M.I. Rabinovich “Stochastic self-oscillations and turbulence” 21 443–469 (1978)
V.I. Tatarskii “The Wigner representation of quantum mechanics” 26 311–327 (1983)
G.M. Zaslavskii “Nonlinear waves and their interaction” 16 761–776 (1974)
S.S. Abdullaev, G.M. Zaslavskii “Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media” 34 (8) 645–664 (1991)
A.A. Migdal “Stochastic quantization of field theory” 29 389–411 (1986)
N.B. Delone, V.P. Krainov, D.L. Shepelyanskii “Highly-excited atoms in the electromagnetic field” 26 551–572 (1983)
E.L. Feinberg “Multiple generation of hadrons and statistical theory” 14 455–483 (1972)
M.F. Sarry “Theoretical calculation of equations of state: analytical results” 42 991–1015 (1999)
G.M. Zaslavskii, R.Z. Sagdeev et al “Minimal chaos, stochastic webs, and structures of quasicrystal symmetry” 31 887–915 (1988)
A.L. Efros “Electron localization in disordered systems (the Anderson transition)” 21 746–760 (1978)
N.V. Karlov, A.M. Prokhorov “Laser isotope separation” 19 285–300 (1976)
V.N. Pavlenko “Echo phenomena in plasmas” 26 931–951 (1983)
I.M. Beterov, P.B. Lerner “Spontaneous and induced emission of a Rydberg atom in a cavity” 32 1084–1110 (1989)
G.P. Berman, A.R. Kolovskii “Quantum chaos in interactions of multilevel quantum systems with a coherent radiation field” 35 (4) 303–326 (1992)
B.M. Smirnov “Scaling method in atomic and molecular physics” 44 1229–1253 (2001)
M.B. Menskii “Dissipation and decoherence in quantum systems” 46 1163–1182 (2003)
M.B. Menskii “Concept of consciousness in the context of quantum mechanics” 48 389–409 (2005)
M.F. Sarry “Analytical methods of calculating correlation functions in quantum statistical physics” 34 (11) 958–979 (1991)
A.V. Borisov, A.S. Vshivtsev et al “Photons and leptons in external fields at finite temperature and density” 40 229–255 (1997)

The list is formed automatically.