The Born-Green-Yvon (BGY) equations for two-body distribution functions of fermion-Jastrow many-body trial functions are derived using a diagrammatic method. Also derived are the Jackson-Feenberg and Pandharipande-Bethe expressions for the kinetic energy of this function in terms of partial two- and three-body distribution functions. Simple approximations for these three-body functions are then used in the BGY equations and the kinetic energies and are solved for the ground state of liquid $^{3}\mathrm{He}$ .The Born-Green-Yvon (BGY) equations for two-body distribution functions of fermion-Jastrow many-body trial functions are derived using a diagrammatic method. Also derived are the Jackson-Feenberg and Pandharipande-Bethe expressions for the kinetic energy of this function in terms of partial two- and three-body distribution functions. Simple approximations for these three-body functions are then used in the BGY equations and the kinetic energies and are solved for the ground state of liquid $^{3}\mathrm{He}$.

Physical review. B, Condensed matterFeb 1, 198214 citations

THEORY OF FERMI--BOSE QUANTUM FLUIDS.

Isaac M. Khalatnikov

Jan 1, 19680 citations

Generalized Bogoliubov-Born-Green-Kirkwood-Yvon Hierarchy for Near-Integrable Dynamics

Leonardo Biagetti, Maciej Łebek, Miłosz Panfil +1 more

We study quantum and classical many-body Hamiltonian systems that combine integrable contact interactions with generic long-range two-body potentials. Starting from an ansatz for the state at time t , which we call the correlated fluid-cell ensemble, we show that the dynamics of local observables at macroscopic times and length scales can be cast into a generalized Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy formulated in terms of the quasiparticle densities of the underlying integrable model and their correlations. We derive this hierarchy and validate these predictions against microscopic molecular-dynamics simulations, finding perfect agreement. At late times, the one-particle distribution relaxes via a Boltzmann-type scattering integral encoding the interplay between integrable contact processes and long-range collisions, whereas higher-point correlations remain strongly nonthermal on thermalization timescales, indicative of a form of incomplete or generalized thermalization. Focusing on long-range dipolar quantum gases, where the relevant matrix elements can be obtained explicitly, we show that our collision integral reduces exactly to the Fermi golden rule result and provide a complete theoretical account of the experimental observations of Tang []. More broadly, our framework extends the BBGKY program to regimes with strong local interactions and applies to a wide class of experimentally relevant systems, from one-dimensional dipolar cold-atom gases to Lennard-Jones molecular fluids.We study quantum and classical many-body Hamiltonian systems that combine integrable contact interactions with generic long-range two-body potentials. Starting from an ansatz for the state at time t , which we call the correlated fluid-cell ensemble, we show that the dynamics of local observables at macroscopic times and length scales can be cast into a generalized Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy formulated in terms of the quasiparticle densities of the underlying integrable model and their correlations. We derive this hierarchy and validate these predictions against microscopic molecular-dynamics simulations, finding perfect agreement. At late times, the one-particle distribution relaxes via a Boltzmann-type scattering integral encoding the interplay between integrable contact processes and long-range collisions, whereas higher-point correlations remain strongly nonthermal on thermalization timescales, indicative of a form of incomplete or generalized thermalization. Focusing on long-range dipolar quantum gases, where the relevant matrix elements can be obtained explicitly, we show that our collision integral reduces exactly to the Fermi golden rule result and provide a complete theoretical account of the experimental observations of Tang []. More broadly, our framework extends the BBGKY program to regimes with strong local interactions and applies to a wide class of experimentally relevant systems, from one-dimensional dipolar cold-atom gases to Lennard-Jones molecular fluids.

arXiv:2408.00593Physical Review XMay 20, 20262 citations

Theory of Quantum Fluids

Pure and applied physicsJan 1, 19690 citations

^{3}\mathrm{He}