2013/06/18 by Wojciech De Roeck, Jürg Fröhlich, Juerg Froehlich +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Coupling constant #Diffusion #Drift velocity #Einstein relation #Electric field #Ergodic theory #Fick's laws of diffusion #Lattice (music) #Massless particle #Mathematics #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Quantum particle #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1063/1.4881532
published in Journal of Mathematical Physics 55(7) (American Institute of Physics) · 31 pages, some proofs are contained in the joint arxiv submission 'Quantum Diffusion with Drift and the Einstein Relation II'
arxiv created 2013/06/18 · openalex publication_date 2014/06/25 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the dynamics of a quantum particle hopping on a simple cubic lattice and driven by a constant external force. It is coupled to an array of identical, independent thermal reservoirs consisting of free, massless Bose fields, one at each site of the lattice. When the particle visits a site x of the lattice it can emit or absorb field quanta of the reservoir at x. Under the assumption that the coupling between the particle and the reservoirs and the driving force are sufficiently small, we establish the following results: The ergodic average over time of the state of the particle approaches a non-equilibrium steady state describing a non-zero mean drift of the particle. Its motion around the mean drift is diffusive, and the diffusion constant and the drift velocity are related to one another by the Einstein relation.