The perturbation theoretic procedure is developed for a system of strongly interacting particles, by replacing the singular potential with an equivalent operator. As an application of the method, an expression for the ground state energy of a Bose system, which corresponds to Lenz's formula for the hard-sphere system, is obtained for the Lennard-Jones potential. The cohesive energy of liquid He4 is calculated and is shown to be about twice as large as the experimentally observed one. Some difficulties arising from the negative value of the scattering length are discussed, and it is suggested that the assumption, usually taken for Bose system, that nearly all the particles are in the single particle state with momentum 0 should be altered for the actual liquid He4.The perturbation theoretic procedure is developed for a system of strongly interacting particles, by replacing the singular potential with an equivalent operator. As an application of the method, an expression for the ground state energy of a Bose system, which corresponds to Lenz's formula for the hard-sphere system, is obtained for the Lennard-Jones potential. The cohesive energy of liquid He4 is calculated and is shown to be about twice as large as the experimentally observed one. Some difficulties arising from the negative value of the scattering length are discussed, and it is suggested that the assumption, usually taken for Bose system, that nearly all the particles are in the single particle state with momentum 0 should be altered for the actual liquid He4.

Progress of Theoretical PhysicsJun 1, 19586 citations

IDEAL BOSE SYSTEMS

Raj K. Pathria

Elsevier eBooksJan 1, 19960 citations

Ideal Bose systems

Raj K. Pathria, Paul D. Beale

Elsevier eBooksFeb 21, 20210 citations

Bose-Einstein Condensation and the Lambda Transition for Interacting Lennard-Jones Helium-4

Phil Attard

An introduction to Bose-Einstein condensation and the $λ$ -transition is given. Results of quantum loop Monte Carlo simulations are presented for interacting Lennard-Jones helium-4. The optimum condensation fraction is found by minimizing the constrained free energy. The results show that approaching the transition the growth of pure position permutation loops and the consequent divergence of the heat capacity are enabled by the suppression of condensation and consequently of superfluidity. Condensation and superfluidity emerge at the peak of the heat capacity due to mixed position permutation chains.An introduction to Bose-Einstein condensation and the $λ$-transition is given. Results of quantum loop Monte Carlo simulations are presented for interacting Lennard-Jones helium-4. The optimum condensation fraction is found by minimizing the constrained free energy. The results show that approaching the transition the growth of pure position permutation loops and the consequent divergence of the heat capacity are enabled by the suppression of condensation and consequently of superfluidity. Condensation and superfluidity emerge at the peak of the heat capacity due to mixed position permutation chains.

arXiv:2504.07147Apr 9, 20250 citations

An introduction to Bose-Einstein condensation and the

λ

-transition is given. Results of quantum loop Monte Carlo simulations are presented for interacting Lennard-Jones helium-4. The optimum condensation fraction is found by minimizing the constrained free energy. The results show that approaching the transition the growth of pure position permutation loops and the consequent divergence of the heat capacity are enabled by the suppression of condensation and consequently of superfluidity. Condensation and superfluidity emerge at the peak of the heat capacity due to mixed position permutation chains.