期刊
JOURNAL OF STATISTICAL PHYSICS
卷 98, 期 1-2, 页码 31-55出版社
KLUWER ACADEMIC/PLENUM PUBL
DOI: 10.1023/A:1018666620368
关键词
non-Hermitian quantum mechanics; density of states; invariant distribution; localisation
We calculate. using numerical methods, the Lyapunov exponent gamma(E) and the density of states rho(E) at energy E of a one-dimensional non-Hermitian Schrodinger equation with off-diagonal disorder. For the particular case we consider, both gamma(E) and rho(E) depend only on the modulus of E. We find a pronounced maximum of rho( \E\ ) at energy E= 2/root 3, which seems to be linked to the fixed point structure of an associated random map. We show how the density of states rho(E) can be expanded in powers of E. Wt find rho( \E\ ) = ( 1/pi(2)) + (4/3 pi(3)) \E\(2) +. This expansion, which seems to be asymptotic. can be carried out to an arbitrarily high order.
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