2016/04/07 by A. F. Kemper, Alexander F. Kemper, J. K. Freericks +1 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Differential equation #Electron #Equations of motion #Excited state #Formalism (music) #Phonon #Physics #Population #Quantum many-body systems #Quantum mechanics #Statistical physics #cond-mat.mes-hall #cond-mat.stat-mech #cond-mat.str-el #quant-ph
paper · pdf · doi:10.3390/e18050180
Submitted to Entropy
arxiv created 2016/04/07 · openalex publication_date 2016/05/13 · arxiv updated 2016/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches must give the same answer, it is common to make a number of simplifying assumptions, within the differential equation for the populations, that allows one to interpret the decay in terms of hot electrons interacting with a phonon bath. Here, we show how care must be taken to ensure an accurate treatment of the equation of motion for the populations due to the fact that there are identities that require cancellations of terms that naively look like they contribute to the decay rates. In particular, the average time dependence of the Green’s functions and self-energies plays a pivotal role in determining these decay rates.