 00163 Minami N.
 Level statistics for quantum HamiltoniansSome preliminary ideas toward
mathematical justification of the theory of Berry and Tabor
(16K, LATeX 2e)
Apr 5, 00

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. According to Berry and Tabor, the spectrum of a classically integrable
quantum Hamiltonian (the regular spectrum)
should generically have the same statistical property
of the Poisson point process. In particular, the spacings between energy
levels obey the exponential distribution, which is the phenomena called
"level clustering". Strict justification of this assertion
seems to be a very difficult mathematical problem. In this note, the author
shall introduce a weakened notion of level clustering and give a sufficient
condition for this in terms of factorial moments of the number of levels
in intervals of fixed length. A preliminary result is also stated, which is
closely related to the justification of this sufficient condition in the case
of regular spectra. All proofs are omitted, and will be published elsewhere.
 Files:
00163.tex