We investigate the behavior of a homogeneous one-dimensional Bose gas composed of $N$ identical bosons experiencing attractive two-body and repulsive three-body interactions. Utilizing intermediate Hartree theory, we rigorously derive the homogeneous cubic-quintic nonlinear Schrödinger functional as the mean-field limit of the many-body Hamiltonian. Particular attention is given to the impact of the repulsive three-body term on ground state energy estimates and mass concentration propertiesWe investigate the behavior of a homogeneous one-dimensional Bose gas composed of $N$ identical bosons experiencing attractive two-body and repulsive three-body interactions. Utilizing intermediate Hartree theory, we rigorously derive the homogeneous cubic-quintic nonlinear Schrödinger functional as the mean-field limit of the many-body Hamiltonian. Particular attention is given to the impact of the repulsive three-body term on ground state energy estimates and mass concentration properties

arXiv:2608.29874Aug 30, 20260 citations

Ground-state properties of dilute Bose systems with synthetic dispersion laws

Eugene B. Kolomeisky

Experimental advances in synthesizing spin-orbit couplings in cold atomic Bose gases promise to create single-particle dispersion laws featuring energy minima that are degenerate on a ring or a sphere in momentum space. We show that for arbitrary space dimensionality the ground-state properties of a dilute system of spin-orbit-coupled Bose particles with such dispersion and short-range repulsive interactions are universal: the chemical potential exhibits a quadratic dependence on the particle density as found in a one-dimensional free Fermi gas.Experimental advances in synthesizing spin-orbit couplings in cold atomic Bose gases promise to create single-particle dispersion laws featuring energy minima that are degenerate on a ring or a sphere in momentum space. We show that for arbitrary space dimensionality the ground-state properties of a dilute system of spin-orbit-coupled Bose particles with such dispersion and short-range repulsive interactions are universal: the chemical potential exhibits a quadratic dependence on the particle density as found in a one-dimensional free Fermi gas.

arXiv:1803.09732Physical Review AJul 9, 20180 citations

Ground State Energy of Dilute Bose Gases in 1D

Johannes Agerskov, Robin Reuvers, Jan Philip Solovej

arXiv:2203.17183Communications in Mathematical PhysicsJan 11, 20253 citations

Ground state energy of the dilute Bose-Hubbard gas on Bravais lattices

Norbert Mokrzański, Marcin Napiórkowski, Jacek Wojtkiewicz

We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that, in the dilute limit $ρ\to 0$ , the ground state energy density satisfies $e_0(ρ) = 4πa ρ^2 \big(1+O(ρ^{1/6})\big),$ where $a$ is the lattice scattering length defined through the corresponding two-body problem. This establishes the analogue of the Dyson and Lieb-Yngvason theorems for the Bose-Hubbard gas. Our result shows that the leading-order energy is universal: although the lattice geometry affects the microscopic dispersion relation, it enters the leading order asymptotics only through the scattering length. In particular, it is independent of other features of the underlying Bravais lattice.We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that, in the dilute limit $ρ\to 0$, the ground state energy density satisfies $$e_0(ρ) = 4πa ρ^2 \big(1+O(ρ^{1/6})\big),$$ where $a$ is the lattice scattering length defined through the corresponding two-body problem. This establishes the analogue of the Dyson and Lieb-Yngvason theorems for the Bose-Hubbard gas. Our result shows that the leading-order energy is universal: although the lattice geometry affects the microscopic dispersion relation, it enters the leading order asymptotics only through the scattering length. In particular, it is independent of other features of the underlying Bravais lattice.

arXiv:2602.16566Feb 18, 20260 citations

We investigate the behavior of a homogeneous one-dimensional Bose gas composed of

N

identical bosons experiencing attractive two-body and repulsive three-body interactions. Utilizing intermediate Hartree theory, we rigorously derive the homogeneous cubic-quintic nonlinear Schrödinger functional as the mean-field limit of the many-body Hamiltonian. Particular attention is given to the impact of the repulsive three-body term on ground state energy estimates and mass concentration properties

We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that, in the dilute limit

ρ\to 0

, the ground state energy density satisfies

e_0(ρ) = 4πa ρ^2 \big(1+O(ρ^{1/6})\big),

where

a

is the lattice scattering length defined through the corresponding two-body problem. This establishes the analogue of the Dyson and Lieb-Yngvason theorems for the Bose-Hubbard gas. Our result shows that the leading-order energy is universal: although the lattice geometry affects the microscopic dispersion relation, it enters the leading order asymptotics only through the scattering length. In particular, it is independent of other features of the underlying Bravais lattice.