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.
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 tarball: 19cjl1.0.1.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).
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 arXiv preprint: arXiv:1912.04987.
 This article was peer reviewed for: Pure and Applied Analysis, Volume 2, Issue 3, pages 659684, 2020.
Numerical computations
The numerical computations in this paper were carried out using an early version of simplesolv. Note that this early version is not compatible with the version of simplesolv published on this website. The code is included with the LaTeX source, in the 'figs' directory.
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[Palermo24]: Nonperturbative behavior of interacting Bosons at intermediate densities
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[TXST23]: BoseEinstein condensation and the Simplified Approach to interacting Bosons
Texas State University, San Marcos, Texas, USA, Jul 24 2023

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[Ru23]: Interacting Bosons at intermediate densities
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[Mi22]: An effective equation to study Bose gases at all densities
University of Milan, Italy, Feb 21 2022
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[Tu22]: An effective equation to study Bose gases at all densities
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[Pe21]: An effective equation to study Bose gases at all densities
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[SIAM20]: An Effective Equation To Study Bose Gasses At All Densities
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[IAMP20]: An effective equation to study Bose gasses at all densities
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[TAMU20]: A simple equation to study interacting Bose gasses
Texas A&M, College Station, Texas, USA, May 15 2020
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[HaRM20]: A simplified approach to interacting Bose gases
Harvard University, Cambridge, Massachusetts, USA, Apr 01 2020
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[To20]: A simplified approach to interacting Bose gases
University of Toronto, Ontario, Canada, Mar 06 2020
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[Pr20]: A simplified approach to interacting Bose gases
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[VATech20]: A simplified approach to interacting Bose gases
VirginiaTech, Blacksburg, Virginia, USA, Feb 14 2020
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[Davis20]: A simplified approach to interacting Bose gases
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[GaTech20]: A simplified approach to interacting Bose gases
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[GLaMP19]: Lieb's simplified approach to interacting Bose gases
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