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We have studied the ground-state properties of para-hydrogen in one dimension and in quasione-dimensional configurations using the path integral ground state Monte Carlo method. This method produces zero-temperature exact results for a given interaction and geometry. The quasione-dimensional setup has been implemented in two forms: the inner channel inside a carbon nanotube coated with H2 and a harmonic confinement of variable strength. Our main result is the dependence of the Luttinger parameter on the density within the stable regime. Going from one dimension to quasi-one dimension, keeping the linear density constant, produces a systematic increase of the Luttinger parameter. This increase is however not enough to reach the superfluid regime and the system always remain in the quasi-crystal regime, according to Luttinger liquid theory.

Liquid 4He becomes superfluid and flows without resistance below temperature 2.17 K. Superfluidity has been a subject of intense studies and notable advances were made in elucidating the phenomenon by experiment and theory. Nevertheless, details of the microscopic state, including dynamic atom–atom correlations in the superfluid state, are not fully understood. Here using a technique of neutron dynamic pair-density function (DPDF) analysis we show that 4He atoms in the Bose–Einstein condensate have environment significantly different from uncondensed atoms, with the interatomic distance larger than the average by about 10%, whereas the average structure changes little through the superfluid transition. DPDF peak not seen in the snap-shot pair-density function is found at 2.3 Å, and is interpreted in terms of atomic tunnelling. The real space picture of dynamic atom–atom correlations presented here reveal characteristics of atomic dynamics not recognized so far, compelling yet another look at the phenomenon.

We report the quantum phase diagram of a one-dimensional Coulomb wire obtained using the path integral Monte Carlo (PIMC) method. The exact knowledge of the nodal points of this system permits us to find the energy in an exact way, solving the sign problem which spoils fermionic calculations in higher dimensions. The results obtained allow for the determination of the stability domain, in terms of density and temperature, of the one-dimensional Wigner crystal. At low temperatures, the quantum wire reaches the quantum-degenerate regime, which is also described by the diffusion Monte Carlo method. Increasing the temperature the system transforms to a classical Boltzmann gas which we simulate using classical Monte Carlo. At large enough density, we identify a one-dimensional ideal Fermi gas which remains quantum up to higher temperatures than in twoand three-dimensional electron gases. The obtained phase diagram as well as the energetic and structural properties of this system are relevant to experiments with electrons in quantum wires and to Coulomb ions in one-dimensional confinement.PACS numbers: 71.10. Pm, 71.10.Hf, 73.21.Hb Few systems are more universal than electron gases. Their study started long-time ago and the compilation of knowledge that we have now at hand is very wide, with impressive quantitative and qualitative results [1]. Phase diagrams for the electron gas in two and three dimensions appear now quite well understood thanks to progressively more accurate many-body calculations using mainly quantum Monte Carlo methods [2]. However, the theoretical knowledge of the electron gas in the onedimensional (1D) geometry is more scarce and a full determination of the density-temperature phase diagram is still lacking. The present work is intended as a contribution towards filling this gap by means of a microscopic approach based on the path integral Monte Carlo (PIMC) method.The quasiparticle concept introduced by Landau in his Fermi liquid theory is able to account for the excitations of the electron gas in two and three dimensions. This is not the case in one dimension where the enhancement of correlations makes all excitations, even at low energy, to be collective. The appropriate theoretical framework is an effective low-energy Tomonaga-Luttinger (TL) theory [3][4][5], properly modified by Schulz [6] to account for the long-range nature of the Coulomb interaction. Probably, the most noticeable prediction of the TL theory is the separation between spin and charge degrees of freedom, whose excitations are predicted to travel at different velocities. At the same time, a Coulomb wire is fundamentally different from other TL systems in that at low densities it forms a Wigner crystal, as manifested by the emergence of quasi-Bragg peaks [6]. Also the strongly repulsive nature of interactions might lead to a formation of a Coulomb Tonks-Girardeau gas [7]. In spite of the experimental difficulties in getting real 1D environments, strong evidences of having reached the TL liquid and the 1D Wigner crystal have...

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