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The Ground State Energy of a Dilute Bose Gas
Mathematical Physics · Submitted 20 Oct 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This result, which is important for the theoretical description of current experiments on Bose-Einstein condensation, has recently been established rigorously for the first time.
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The abstract, sentence by sentence
According to a formula that was put forward many decades ago the ground state energy per particle of an interacting, dilute Bose gas at density $\rho$ is $2\pi\hbar^2\rho a/m$ to leading order in $\rho a^3\ll 1$, where $a$ is the scattering length of the interaction potential and $m$ the particle mass. This result, which is important for the theoretical description of current experiments on Bose-Einstein condensation, has recently been established rigorously for the first time. We give here an account of the proof that applies to nonnegative, spherically symmetric potentials decreasing faster than $1/r^3$ at infinity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | According to a formula that was put forward many decades ago the ground state energy per particle of an interacting, dilute Bose gas at density $\rho$ is $2\pi\hbar^2\rho a/m$ to leading order in $\rho a^3\ll 1$, where $a$ is the scattering length of the interaction potential and $m$ the particle mass. | background 0.99 | 0.03 | 0.21 | asserted 1.00 |
| s1 | This result, which is important for the theoretical description of current experiments on Bose-Einstein condensation, has recently been established rigorously for the first time. | background 0.34 | 0.26 | 0.54 | asserted 1.00 |
| s2 | We give here an account of the proof that applies to nonnegative, spherically symmetric potentials decreasing faster than $1/r^3$ at infinity. | contribution 0.85 | 0.90 | 0.11 | asserted 0.98 |
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Original abstract
According to a formula that was put forward many decades ago the ground state energy per particle of an interacting, dilute Bose gas at density $\rho$ is $2\pi\hbar^2\rho a/m$ to leading order in $\rho a^3\ll 1$, where $a$ is the scattering length of the interaction potential and $m$ the particle mass. This result, which is important for the theoretical description of current experiments on Bose-Einstein condensation, has recently been established rigorously for the first time. We give here an account of the proof that applies to nonnegative, spherically symmetric potentials decreasing faster than $1/r^3$ at infinity.
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States the same result 1 paper
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The correct asymptotic formula has recently been obtained by us and this work will be presented.
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