Version 1
: Received: 2 January 2024 / Approved: 3 January 2024 / Online: 3 January 2024 (23:55:26 CET)
How to cite:
Bier, M. Can We Still Get Bose-Einstein Condensates If the Noise Is Not Thermal?. Preprints2024, 2024010282. https://doi.org/10.20944/preprints202401.0282.v1
Bier, M. Can We Still Get Bose-Einstein Condensates If the Noise Is Not Thermal?. Preprints 2024, 2024010282. https://doi.org/10.20944/preprints202401.0282.v1
Bier, M. Can We Still Get Bose-Einstein Condensates If the Noise Is Not Thermal?. Preprints2024, 2024010282. https://doi.org/10.20944/preprints202401.0282.v1
APA Style
Bier, M. (2024). Can We Still Get Bose-Einstein Condensates If the Noise Is Not Thermal?. Preprints. https://doi.org/10.20944/preprints202401.0282.v1
Chicago/Turabian Style
Bier, M. 2024 "Can We Still Get Bose-Einstein Condensates If the Noise Is Not Thermal?" Preprints. https://doi.org/10.20944/preprints202401.0282.v1
Abstract
Bosons are particles that can occupy the same quantum state. Identical classical particles are considered distinguishable, but with bosons this is no longer the case. With bosons 1 and 2 in states α and β, the compound state function, ΨS=(1/2)Ψα(1)Ψβ(2)+Ψβ(1)Ψα(2), does not change when the particles are interchanged, i.e., there is one state where classically there would be two. This leads to boson statistics, which is different from Boltzmann statistics in that it favors putting more particles in the same state. For a sufficiently low temperature, it is possible that all bosons aggregate in the ground state where they effectively form a single megaparticle. We cover boson statistics and show how and why Bose-Einstein condensation can occur. We also show how growing networks like the WWW, the economy, or citation networks in scientific literature can follow boson statistics. Analyses of Bose-Einstein condensation have generally assumed a bath with a temperature, i.e., a thermal equilibrium where random collisions lead to a Gaussian-noise-term. However, many setups in physics involve conversion or transport of energy, i.e., nonequilibrium. Nonequilibrium noise is commonly characterized by the frequent occurrence of large kicks, i.e., outliers. We model this by implementing α-stable noise. No temperature exists in that case. We find that Bose-Einstein condensation is still theoretically possible, but probably much harder to engineer. Social and economic traffic is also often best modeled as nonequilibrium and our results may be significant in these contexts.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
