Dimer formation by He atoms confined in a narrow tube is studied and the effect of adsorption potential is clarified. The results are well explained in terms of the effective radius <ρ> and the width of the single-particle ground-state wave function Δρ. For 3 He, adsorption potential promotes dimer formation when
⟨ρ⟩≲3 Å, but is unfavorable when
⟨ρ⟩≳3 Å. We discuss the recent experimental results for 3 He atoms confined in nanopores in light of the present results.
Low temperature structural and superfluid properties of
4He confined in cylindrical nanopores are theoretically investigated by means of first-principle quantum Monte Carlo (QMC) simulations. We vary the density of
4He inside the pore, as well as the pore diameter and the potential describing the interaction of each
4He atom with the pore surface. Accordingly, the
4He fluid inside the pore forms either a single channel along the axis, or a series of concentric cylindrical shells, with varying degrees of shell overlap. In the limit of pore length greatly exceeding its radius, the
4He fluid always displays markedly one-dimensional behavior, with no ``dimensional crossover'' above some specific pore radius and/or as multiple concentric shells form, in contrast to what was recently claimed by other authors [Phys. Rev. B 101, 104505 (2020)]. Indeed, the predicted robustness of one-dimensional physics suggests that this system may offer a broadly viable pathway to the experimental observation of exotic behavior of, e.g., junctions of interacting Tomonaga-Luttinger liquids, in an appropriately designed network of nanopores.
The (extended) lowest order constrained variational ((E) LOCV) method was used to calculate the ground state energy of liquid helium 3 (3He) droplets at zero temperature. Different types of density distribution profiles, such as the Gaussian, the Quasi-Gaussian and the Woods-Saxon were used. It was shown that at least, on average, near 20 3He atoms are needed to get the bound state for 3He liquid droplet. Depending on the choice of the density profiles and the atomic radius of 3He, the above estimate can increase to 300. Our calculated ground state energy and the number of atoms in liquid 3He droplet were compared with those of Variational Monte Carlo (VMC) method, Diffusion Monte Carlo (DMC) method and Density Functional Theory (DFT), for which a reasonable agreement was found.
As helium-4 is cooled below 2.17 K it undergoes a phase transition to a fundamentally quantum mechanical state of matter known as a superfluid which supports flow without viscosity. This type of dissipationless transport can be observed by forcing helium to travel through a narrow constriction that the normal liquid could not penetrate. Recent experiments have highlighted the feasibility of fabricating smooth pores with nanometer radii, that approach the truly one-dimensional limit where it is believed that a system of bosons (like helium-4) may have startlingly different behavior than in three dimensions. The one-dimensional system is predicted to have a linear hydrodynamic description known as Luttinger liquid (LL) theory, where no type of long range order can be sustained. In the limit where the pore radius is small, LL theory would predict that helium inside the channel behaves as a sort of quasi-supersolid with all correlations decaying as power-law functions of distance at zero temperature. We have performed large scale quantum Monte Carlo simulations of helium-4 inside nanopores of varying radii at low temperature with realistic helium–helium and helium-pore interactions. The results indicate that helium inside the nanopore forms concentric cylindrical shells surrounding a core that can be described via LL theory and provides insights into the exciting possibility of the experimental detection of this intriguing low-dimensional state of matter.
The ground-state properties of a system with a small number of interacting bosons over a wide range of densities are investigated. The system is confined in a two-dimensional isotropic harmonic trap, where the interaction between bosons is treated as a hard-core potential. By using variational Monte Carlo method, we diagonalize the one-body density matrix of the system to obtain the ground-state energy, condensate wavefunction and the condensate fraction. We find that in the dilute limit the depletion of central condensate in the 2D system is larger than in a 3D system for the same interaction strength; however as the density increases, the depletion at the centre of 2D trap will be equal to or even lower than that at the centre of 3D trap, which is in agreement with the anticipated in Thomas–Fermi approximation. In addition, in the 2D system the total condensate depletion is still larger than in a 3D system for the same scattering length.
Recent experiments on the flow of helium-4 fluid through nanopores with tunable pore radius provide a platform for studying the quasi-one-dimensional (quasi-1D) superfluid behaviors. In the extreme 1D limit, the helium atoms are localized by disordered small variations in the substrate potential provided by the pore walls. In the limit of wide pore radius, a solid layer of helium-4 is expected to coat the pore walls smoothing out the substrate potential, and superfluidity is observed in the central region. Building on earlier quantum Monte Carlo results, we propose a scenario for this crossover using a shell model of coupled Luttinger liquids. We find that a small-radius pore will always localize the helium atoms, but above a critical radius, a single 1D channel flows through the pore and can be described by Luttinger liquid theory.