2016/04/28 by Juan Pablo Ramírez Valdes, Thomas Wellens · 6 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Diagrammatic reasoning #Energy (signal processing) #Lyapunov exponent #Mathematical analysis #Mathematics #Network packet #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Random lasers and scattering media #Statistical physics #Wave packet #cond-mat.dis-nn #quant-ph
paper · pdf · doi:10.1103/physreva.93.063634
published in Physical Review A 93(6) (American Physical Society) · 16 pages and 7 figures
arxiv created 2016/04/28 · openalex publication_date 2016/06/28 · arxiv updated 2016/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the expansion of an initially strongly confined wave packet in a one-dimensional weak random potential with short correlation length. At long times, the expansion of the wave packet comes to a halt due to destructive interferences leading to Anderson localization. We develop an analytical description for the disorder-averaged localized density profile. For this purpose, we employ the diagrammatic method of Berezinskii which we extend to the case of wave packets, present an analytical expression of the Lyapunov exponent which is valid for small as well as for high energies, and, finally, develop a self-consistent Born approximation in order to analytically calculate the energy distribution of our wave packet. By comparison with numerical simulations, we show that our theory describes well the complete localized density profile, not only in the tails but also in the center.