A simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy
Eric A. Carlen, Markus Holzmann, Ian Jauslin, Elliott H. Lieb
2020
Abstract
In 1963, a Simple Approach was developed to study the ground state energy of an interacting Bose gas. It consists in the derivation of an Equation, which is not based on perturbation theory, and which gives the exact expansion of the energy at low densities. This Equation is expressed directly in the thermodynamic limit, and only involves functions of 3 variables, rather than 3N. Here, we revisit this approach, and show that the Equation yields accurate predictions for various observables for all densities. Specifically, in addition to the ground state energy, we have shown that the Simple Approach gives predictions for the condensate fraction, twopoint correlation function, and momentum distribution. We have carried out a variety of tests by comparing the predictions of the Equation with Quantum Monte Carlo calculations, and have found remarkable agreement. We thus show that the Simple Approach provides a new theoretical tool to understand the behavior of the manybody Bose gas, not only in the small and large density ranges, which have been studied before, but also in the range of intermediate density, for which little is known.
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[CJL20]: Analysis of a simple equation for the ground state of the Bose gas II: Monotonicity, Convexity and Condensate Fraction
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[CJL19]: Analysis of a simple equation for the ground state energy of the Bose gas
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(published in Pure and Applied Analysis, volume 2, issue 3, pages 659684)
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Talks
This work has been presented at the following conferences:

[LMU21]: An effective equation to study Bose gases at all densities
Ludwig Maximilian University, Munich, Germany, Apr 28 2021
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[Ye21]: An effective equation to study Bose gases at all densities
Yeshiva University, New York, NY, USA, Apr 07 2021
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[Ja21]: An effective equation to study Bose gases at all densities
Jacobs University, Bremen, Germany, Apr 01 2021
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[Pe21]: An effective equation to study Bose gases at all densities
Penn State, University Park, Pennsylvania, USA, Mar 12 2021
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[MC21]: Many interacting quantum particles: open problems, and a new point of view on an old problem
Mathematical Conversations, Institute for Advanced Study, Princeton, NJ, USA, Mar 10 2021
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[Cop21]: An effective equation to study Bose gasses at all densities
University of Copenhagen, Denmark, Jan 13 2021
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[Rut20]: Analysis of a nonlinear, nonlocal PDE to study Bose gases at all densities
Rutgers University, New Brunswick, New Jersey, USA, Dec 16 2020
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[TAMU20b]: A new approach to the Mathematics of the Bose gas
Texas A&M, College Station, Texas, USA, Nov 30 2020
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