The phase formalism for one-dimensional random Schrödinger operations

Englisch, H.

doi:10.1016/0034-4877(86)90004-2

Cited by 3 publications

(2 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…periodic, boundary conditions and N E (H£) is the number of eigenvalues of H™ below E (counting multiplicity). Concerning the almost sure existence of the limit (3) and its independence of ω, see [3][4][5]. When we define the phase φ by [uniqueness by φ(x) continuous] with y satisfying H ω y = Ey as a differential equation, the following formula represents the "phase method" for the calculation offc(E)(cf.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Special energies and special frequencies

Endrullis

Englisch

1987

Commun.Math. Phys.

Self Cite

View full text Add to dashboard Cite

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 Schrόdinger operator describing an alloy or its discrete analogue. Using the phase method we exactly determine a bilateral Lifsic asymptotic of the integrated density of states k(E) at special energies E 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 that k(E) need not be C 00 .

show abstract

Section: Introductionmentioning

confidence: 99%

“…When we define the phase φ by [uniqueness by φ(x) continuous] with y satisfying H ω y = Ey as a differential equation, the following formula represents the "phase method" for the calculation offc(E)(cf. [5,6]):…”

Section: Introductionmentioning

confidence: 99%