Toward a microscopic picture of superfluid Helium-4

Taking inspiration from F. Bloch’s seminal work (PRA 7, 2187 (1973)), we investigate the quantum many-body states of superfluid 4 He, unveiling a novel characteristic in the system’s energy levels. Below the transition temperature, the thermally active low-energy levels exhibit a distinctive grouping behavior, with each level belonging exclusively to a single group. In a superflow state, the system establishes thermal equilibrium with its surroundings on a group-specific basis. Specifically, the levels within a chosen group, initially populated, undergo thermal redistribution, while the remaining groups of levels stay vacant due to absence of transitions between groups. The macroscopic properties of the system, such as its superflow velocity and thermal energy density, are statistically determined by the thermal distribution of the occupied group. Additionally, we infer that the thermal energy of a superflow has an unusual relationship with flow velocity, such that the larger the flow velocity, the smaller the thermal energy. This relationship is responsible for a range of intriguing phenomena, including the mechano-caloric effect and the fountain effect, which demonstrate a fundamental coupling between the thermal motion and hydrodynamic motion of the system. Furthermore, we present experimental evidence of a self-heating effect in 4 He superflows, confirming that a 4 He superflow carries significant thermal energy related to its velocity.