Special energies and special frequencies |
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Authors: | M Endrullis H Englisch |
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Institution: | (1) Sektion Mathematik, Karl-Marx-Universität Leipzig, DDR-7010 Leipzig, German Democratic Republic |
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Abstract: | Special frequencies have been asserted to be zeros of the density of frequencies corresponding to a random chain of coupled oscillators. Our investigation includes both this model and the random one-dimensional Schrödinger operator describing an alloy or its discrete analogue. Using the phase method we exactly determine a bilateral Lif ic asymptotic of the integrated density of statesk(E) at special energiesE
s
, which is not only of the classical type exp(–c/|E–E
s
|1/2) but also exp(–c /|E–E
s
|) is a typical behaviour. In addition, other asymptotics occur, e.g. |E–E
s
|
c
, which show thatk(E) need not bek
. |
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Keywords: | |
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