1997/04/14 by B. L. Altshuler, B.L. Altshuler, L. S. Levitov +1 · 3 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum many-body systems #cond-mat
paper · pdf · doi:10.1016/s0370-1573(97)00038-0
published as Phys. Rep. 288, 487 (1997) · 28 pages, ReVTeX, 4 EPS figures, to appear in the I. M. Lifshitz memorial volume of Physics Reports
arxiv created 1997/04/14 · openalex publication_date 1997/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Transition from regular to chaotic dynamics in a crystal made of singular scatterers U(r)=λ|r|-σ can be reached by varying either sigma or lambda. We map the problem to a localization problem, and find that in all space dimensions the transition occurs at sigma=1, i.e., Coulomb potential has marginal singularity. We study the critical line sigma=1 by means of a renormalization group technique, and describe universality classes of this new transition. An RG equation is written in the basis of states localized in momentum space. The RG flow evolves the distribution of coupling parameters to a universal stationary distribution. Analytic properties of the RG equation are similar to that of Boltzmann kinetic equation: the RG dynamics has integrals of motion and obeys an H-theorem. The RG results for sigma=1 are used to derive scaling laws for transport and to calculate critical exponents.