2011/07/25 by Wojciech De Roeck, W. De Roeck, A. Kupiainen +2
Mathematics · Physics and Astronomy · #Boson #Dispersion relation #FOS: Physical sciences #Hamiltonian (control theory) #Mathematical Physics (math-ph) #Mathematics #Phonon #Photon #Physics #Quantum #Quantum mechanics #Quantum particle #Random Matrices and Applications #Randomness #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1107.4832
65 pages, to appear in CMP, typos and errors in volume-dependent normalization factors corrected, Section 11.2 slightly restructured
openalex publication_date 2011/07/25 · arxiv created 2013/04/19 · arxiv updated 2013/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove diffusion for a quantum particle coupled to a field of bosons (phonons or photons). The importance of this result lies in the fact that our model is fully Hamiltonian and randomness enters only via the initial (thermal) state of the bosons. This model is closely related to the one considered in [De Roeck, Fröhlich 2011], but various restrictive assumptions of the latter have been eliminated. In particular, depending on the dispersion relation of the bosons, the present result holds in dimension d ≥ 3.