2002/09/04 by Satya N. Majumdar, Alain Comtet · 3 citations
Mathematics · Physics and Astronomy · #Brownian motion #Energy spectrum #Geology #Hamiltonian (control theory) #Limit (mathematics) #Mathematical analysis #Mathematical optimization #Mathematics #Persistence (discontinuity) #Physics #Quantum many-body systems #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.66.061105
published as Phys. Rev. E 66, 061105 (2002) · 17 pages, two eps figures (included)
arxiv created 2002/09/04 · openalex publication_date 2002/12/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a method that maps the problem of computing the persistence to the problem of finding the energy spectrum of a single-particle quantum Hamiltonian, which can be subsequently found. Our method allows us analytical access to arbitrary values of the drift (bias), thus going beyond the previous methods that provide results only in the limit of vanishing drift. We show that on varying the drift the persistence displays a variety of rich asymptotic behaviors including, in particular, interesting qualitative changes at some special values of the drift.