2007/12/03 by Steven Tomsovic, Denis Ullmo, Arnd Bäcker +1 · 2 citations
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Chaotic #Cold Atom Physics and Bose-Einstein Condensates #Coulomb #Eigenvalues and eigenvectors #Electron #Ground state #Mathematical analysis #Mathematics #Physics #Plane wave #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Residual #Semiclassical physics #Statistical physics #Theoretical and Computational Physics #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.100.164101
arxiv created 2007/12/03 · openalex publication_date 2008/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients. The quintessential example is given by the short-range approximation to the first order ground state contribution of the residual Coulomb interaction. The dominant features come from the region near the boundary where there is an interplay between Friedel oscillations and fluctuations in the eigenstates. Quite naturally, the fluctuation scale is significantly enhanced for Neumann boundary conditions as compared to Dirichlet. Elements missing from random plane wave modeling of chaotic eigenstates lead surprisingly to significant errors, which can be corrected within a purely semiclassical approach.