We consider a system of $N$ bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form $N^{3β-1} v (N^βx)$ for $β\in (0,1)$ . We prove the next order correction to Bogoliubov theory for the ground state and the ground state energy.We consider a system of $N$ bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form $N^{3β-1} v (N^βx)$ for $β\in (0,1)$. We prove the next order correction to Bogoliubov theory for the ground state and the ground state energy.

arXiv:2309.12233Sep 21, 20230 citations

Quantum states of interacting Bose gases in 1D random potentials

Pierre Lugan, David Clément, Philippe Bouyer +3 more

Jun 1, 20070 citations

Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential

Armando Relaño, J. Dukelsky, P. Pérez-Fernández +1 more

The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.

arXiv:1406.6833Physical Review EOct 27, 201422 citations

We consider a system of

N

bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form

N^{3β-1} v (N^βx)

for

β\in (0,1)

. We prove the next order correction to Bogoliubov theory for the ground state and the ground state energy.