Ground state energy of the low density Bose gas with three-body interactions

Abstract

We consider the low density Bose gas in the thermodynamic limit with a three-body interaction potential. We prove that the leading order of the ground state energy of the system is determined completely in terms of the scattering energy of the interaction potential. The corresponding result for two-body interactions was proved in seminal papers of Dyson (1957) and Lieb--Yngvason (1998).

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• Stabilization against collapse of 2D attractive Bose-Einstein condensates with repulsive, three-body interactions
• Microscopic derivation of a Schrödinger equation in dimension one with a nonlinear point interaction
• Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential
• Local Density Approximation and Other Limit Regimes for a Homogeneous Bose Gas with Repulsive Three-Body Interactions in Low-Dimensional Space
• Homogeneous attractive Bose-Einstein condensates with repulsive three-body interactions: the two-dimensional case