Analysis of a simple equation for the ground state energy of the Bose gas
Eric Carlen, Ian Jauslin, Elliott H. Lieb
2019
Abstract
In 1963 a partial differential equation with a convolution nonlinearity was introduced in connection with a quantum mechanical manybody problem, namely the gas of bosonic particles.
This equation is mathematically interesting for several reasons.
(1) Although the equation was expected to be valid only for small values of the parameters, further investigation showed that predictions based on the equation agree well over the entire range of parameters with what is expected to be true for the solution of the true manybody problem.
(2) The novel nonlinearity is easy to state but seems to have almost no literature up to now.
(3) The earlier work did not prove existence and uniqueness of a solution, which we provide here along with properties of the solution such as decay at infinity.
Download
PDF:
LaTeX source:

tarball: 19cjl1.0.tar.gz

git repository: 19cjlgit (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).
Other releases
Related articles

[CJLL20]: On the convolution inequality f>f*f
Eric A. Carlen, Ian Jauslin, Elliott H. Lieb, Michael Loss, 2020
pdf, source

[CJL20]: Analysis of a simple equation for the ground state of the Bose gas II: Monotonicity, Convexity and Condensate Fraction
Eric A. Carlen, Ian Jauslin, Elliott H. Lieb, 2020
pdf, source
Talks
This work has been presented at the following conferences:

[SIAM20]: An Effective Equation To Study Bose Gasses At All Densities
SIAM TexasLouisiana Sectionnal Meeting, MiniSymposium on Spectral Theory and Mathematical Physics, Oct 17 2020
pdf,
source

[IAMP20]: An effective equation to study Bose gasses at all densities
International Association of Mathematical of Mathematical Physics, One World Seminars, Sep 22 2020
pdf,
source

[TAMU20]: A simple equation to study interacting Bose gasses
Texas A&M, College Station, Texas, USA, May 15 2020
pdf,
source

[HaRM20]: A simplified approach to interacting Bose gases
Harvard University, Cambridge, Massachusetts, USA, Apr 01 2020
pdf,
source

[To20]: A simplified approach to interacting Bose gases
University of Toronto, Ontario, Canada, Mar 06 2020
pdf,
source

[Pr20]: A simplified approach to interacting Bose gases
Princeton University, New Jersey, USA, Mar 03 2020
video,
pdf,
source

[VATech20]: A simplified approach to interacting Bose gases
VirginiaTech, Blacksburg, Virginia, USA, Feb 14 2020
pdf,
source

[Davis20]: A simplified approach to interacting Bose gases
UC Davis, California, USA, Feb 06 2020
pdf,
source

[GaTech20]: A simplified approach to interacting Bose gases
GeorgiaTech, Atlanta, Georgia, USA, Jan 21 2020
pdf,
source

[UBC20]: A simplified approach to interacting Bose gases
University of British Columbia, Vancouver, British Columbia, Canada, Jan 09 2020
pdf,
source

[GLaMP19]: Lieb's simplified approach to interacting Bose gases
Great Lakes Mathematical Physics Meeting 2019, Oberlin, Ohio, USA, Jun 29 2019
pdf,
source