1,721,351 research outputs found
Numerical study of Bose–Einstein condensation in the Kaniadakis–Quarati model for bosons
Full text linkKaniadakis and Quarati (1994) proposed a Fokker–Planck equation with quadratic drift as a PDE model for the dynamics of bosons in the spatially homogeneous setting. It is an open question whether this equation has solutions exhibiting condensates in finite time. The main analytical challenge lies in the continuation of exploding solutions beyond their first blow-up time while having a linear diffusion term. We present a thoroughly validated timeimplicit numerical scheme capable of simulating solutions for arbitrarily long time, and thus enabling a numerical study of the condensation process in the Kaniadakis–Quarati model. We show strong numerical evidence that above the critical mass rotationally symmetric solutions of the Kaniadakis–Quarati model in 3D form a condensate in finite time and converge in entropy to the unique minimiser of the natural entropy functional. Our simulations further indicate that the spatial blow-up profile near the origin follows a universal power law and that transient condensates can occur for sufficiently concentrated initial data
Comments on Piero Quarati et al. Negentropy in Many-Body Quantum Systems. Entropy 2016, 18, 63
No full textThe purpose of this note is to express my concerns about the published paper by Quarati et al. (Entropy 2016, 18, 63). It is hoped that these comments will stimulate a constructive discussion of the issues involved
- …
