Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2003.07795 · Europhysics Letters (EPL)

Time-dependent entropy of a cooling Bose gas

Georg Wolschin

Published Mar 27, 2020• 6 citations
arXivHTMLPDF

Abstract

Exact analytic solutions of a nonlinear boson diffusion equation with suitable initial conditions that account for evaporative cooling of ultracold atoms, plus boundary conditions at the singularity are presented, and used to calculate the time-dependent entropy of a cold quantum gas.
DOI
10.1209/0295-5075/129/40006

Related papers

Solving a nonlinear analytical model for bosonic equilibration

N. Rasch, Georg Wolschin

An integrable nonlinear model for the time-dependent equilibration of a bosonic system that has been devised earlier is solved exactly with boundary conditions that are appropriate for a truncated Bose-Einstein distribution, and include the singularity at ε=μ. The buildup of a thermal tail during evaporative cooling, as well as the transition to the condensed state are accounted for. To enforce particle-number conservation during the cooling process with an energy-dependent density of states for a three-dimensional thermal cloud, a time-dependent chemical potential is introduced.

arXiv:1912.10851•Physics Open•Dec 18, 2019•10 citations

Time-dependent condensation of bosonic potassium

Anton Kabelac, Georg Wolschin

Abstract We calculate the time-dependent formation of Bose–Einstein condensates (BECs) in potassium vapours based on a previously derived exactly solvable nonlinear boson diffusion equation (NBDE). Thermalization following a sudden energy quench from an initial temperature $$T_\mathrm {i}$$ T i to a final temperature $$T_\mathrm {f}$$ T f below the critical value and BEC formation are accounted for using closed-form analytical solutions of the NBDE. The time-dependent condensate fraction is compared with available $$^{39}$$ 39 K data for various scattering lengths. Graphic Abstract

arXiv:2211.11845•The European Physical Journal D•Oct 1, 2022•7 citations

Time-dependent condensate formation in ultracold atoms with energy-dependent transport coefficients

M. Larsson, Georg Wolschin

Time-dependent Bose-Einstein condensate formation in ultracold atoms is investigated in a nonlinear diffusion model. For constant transport coefficients, the model has been solved analytically. Here, we extend it to include energy-dependent transport coefficients and numerically solve the nonlinear equation. Our results are compared with the earlier analytical model for constant transport coefficients, and with recent deep-quench data for $^{39}\mathrm{K}$ at various scattering lengths. Some nonphysical predictions from the constant-coefficient model are resolved using energy-dependent drift and diffusion.

arXiv:2407.14307•Physical Review A•Aug 6, 2024•1 citation

An exactly solvable model for equilibration in bosonic systems

Georg Wolschin

An analytical model for the kinetic equilibration of finite Bose systems is outlined. The corresponding transport equation is solved exactly through a nonlinear transformation. The model is applied to the equilibration of a cold quantum gas including implicitly the formation of a Bose-Einstein condensate through particle-number conservation.

Europhysics Letters (EPL)•Aug 24, 2018•7 citations

Unifying treatment of nonequilibrium and unstable dynamics of cold bosonic atom system with time-dependent order parameter in Thermo Field Dynamics

Y. Nakamura, Y. Yamanaka

arXiv:1007.1847•Annals of Physics•Dec 24, 2010•6 citations

The Mathematics of the Bose Gas and its Condensation

Élliott H. Lieb, Robert Seiringer, Jan Philip Solovej +1 more

This book surveys results about the quantum mechanical many-body problem of the Bose gas that have been obtained by the authors over the last seven years. These topics are relevant to current experiments on ultra-cold gases; they are also mathematically rigorous, using many analytic techniques developed over the years to handle such problems. Some of the topics treated are the ground state energy, the Gross-Pitaevskii equation, Bose-Einstein condensation, superfluidity, one-dimensional gases, and rotating gases. The book also provides a pedagogical entry into the field for graduate students and researchers.

arXiv:cond-mat/0610117•Birkhäuser-Verlag eBooks•Jan 1, 2005•334 citations
An integrable nonlinear model for the time-dependent equilibration of a bosonic system that has been devised earlier is solved exactly with boundary conditions that are appropriate for a truncated Bose-Einstein distribution, and include the singularity at ε=μ. The buildup of a thermal tail during evaporative cooling, as well as the transition to the condensed state are accounted for. To enforce particle-number conservation during the cooling process with an energy-dependent density of states for a three-dimensional thermal cloud, a time-dependent chemical potential is introduced.
Abstract We calculate the time-dependent formation of Bose–Einstein condensates (BECs) in potassium vapours based on a previously derived exactly solvable nonlinear boson diffusion equation (NBDE). Thermalization following a sudden energy quench from an initial temperature TiT_\mathrm {i}Ti​ T i to a final temperature TfT_\mathrm {f}Tf​ T f below the critical value and BEC formation are accounted for using closed-form analytical solutions of the NBDE. The time-dependent condensate fraction is compared with available 39^{39}39 39 K data for various scattering lengths. Graphic Abstract
Time-dependent Bose-Einstein condensate formation in ultracold atoms is investigated in a nonlinear diffusion model. For constant transport coefficients, the model has been solved analytically. Here, we extend it to include energy-dependent transport coefficients and numerically solve the nonlinear equation. Our results are compared with the earlier analytical model for constant transport coefficients, and with recent deep-quench data for 39K^{39}\mathrm{K}39K at various scattering lengths. Some nonphysical predictions from the constant-coefficient model are resolved using energy-dependent drift and diffusion.
This book surveys results about the quantum mechanical many-body problem of the Bose gas that have been obtained by the authors over the last seven years. These topics are relevant to current experiments on ultra-cold gases; they are also mathematically rigorous, using many analytic techniques developed over the years to handle such problems. Some of the topics treated are the ground state energy, the Gross-Pitaevskii equation, Bose-Einstein condensation, superfluidity, one-dimensional gases, and rotating gases. The book also provides a pedagogical entry into the field for graduate students and researchers.