Volume 27, 2021
Special issue in the honor of Enrique Zuazua's 60th birthday
|Number of page(s)||25|
|Published online||27 July 2021|
A reaction network approach to the convergence to equilibrium of quantum Boltzmann equations for Bose gases
Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison,
2 Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA.
* Corresponding author: firstname.lastname@example.org
Accepted: 7 July 2021
When the temperature of a trapped Bose gas is below the Bose-Einstein transition temperature and above absolute zero, the gas is composed of two distinct components: the Bose-Einstein condensate and the cloud of thermal excitations. The dynamics of the excitations can be described by quantum Boltzmann models. We establish a connection between quantum Boltzmann models and chemical reaction networks. We prove that the discrete differential equations for these quantum Boltzmann models converge to an equilibrium point. Moreover, this point is unique for all initial conditions that satisfy the same conservation laws. In the proof, we then employ a toric dynamical system approach, similar to the one used to prove the global attractor conjecture, to study the convergence to equilibrium of quantum kinetic equations.
Mathematics Subject Classification: 35Q20 / 45A05 / 47G10 / 82B40 / 82B40 / 37N25 / 92C42 / 37C10 / 80A30 / 92D25
Key words: Quantum Boltzmann equation / dynamical systems / bosons / Bose-Einstein condensate / rate of convergence to equilibrium / global attractor conjecture / mass-action kinetics / power law systems / biochemical networks / Petri net
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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