Supersymmetric Quantum Mechanics with Lévy Disorder in One Dimension

Alain Comtet, Christophe Texier, YJM Tourigny

Research output: Contribution to journalArticle (Academic Journal)peer-review

12 Citations (Scopus)


We consider the Schrödinger equation with a random potential of the form V(x) = w^2(x)/4-w'(x)/2 where w is a Lévy noise. We focus on the problem of computing the so-called complex Lyapunov exponent Ω = γ - iπN where N is the integrated density of states of the system, and γ is the Lyapunov exponent. In the case where the Lévy process is non-decreasing, we show that the calculation of Ω reduces to a Stieltjes moment problem, we ascertain the low-energy behaviour of the density of states in some generality, and relate it to the distributional properties of the Lévy process. We review the known solvable cases—where Ω can be expressed in terms of special functions—and discover a new one.
Translated title of the contributionSupersymmetric Quantum Mechanics with Lévy Disorder in One Dimension
Original languageEnglish
Pages (from-to)1291 - 1323
Number of pages33
JournalJournal of Statistical Physics
Issue number5
Publication statusPublished - Dec 2011

Bibliographical note

Publisher: Springer


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