Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Crystallization of quantum hard spheres. A density functional approach

P. Nielaba

Published Jan 1, 1992• 0 citations
Publisher

Abstract

At zero temperature Bose hard sphere systems are in the fluid phase at low densities and in the solid phase at high densities. The fluid‐solid transition in this quantum system is discribed by density functional methods (modified weighted density functional theory). Predictions for solid‐phase energies and for freezing parameters are in good agreement with available simulation data.

DOI
10.1063/1.41934

Related papers

Fluid-Solid Phase Transition of a Hard-Sphere Bose System

Jean-Pierre Hansen, D. Levesque, Daniel Schiff

The ground-state energy of a system of hard-sphere bosons of diameter $\ensuremath{\sigma}$ is calculated by a variational method using a Jastrow wave-function for the fluid phase and a "localized" Jastrow times a Gaussian wave function for the solid phase. The transition densities are ${\ensuremath{\rho}}_{\mathrm{fluid}}=0.23\ifmmode\pm\else\textpm\fi{}0.02$ particles/${\mathrm{\ensuremath{\sigma}}}^{3}$ and ${\ensuremath{\rho}}_{\mathrm{solid}}=0.25\ifmmode\pm\else\textpm\fi{}0.02$ particles/${\mathrm{\ensuremath{\sigma}}}^{3}$.

Physical Review A•Feb 1, 1971•59 citations

Quantum Monte Carlo study of the dynamic structure factor in the gas and crystal phase of hard-sphere bosons

R. Rota, F. Tramonto, Davide Emilio Galli +1 more

We investigate the dynamic structure factor of a system of Bose particles at zero temperature using quantum Monte Carlo methods. Interactions are modeled using a hard-sphere potential of size $a$ and simulations are performed for values of the gas parameter $n{a}^{3}$ ranging from the dilute regime up to densities $n$ where the thermodynamically stable phase is a solid. With increasing density, we observe a crossover of the dispersion of elementary excitations from a Bogoliubov-type spectrum to a phonon-maxon-roton curve and the emergence of a broad multiphonon contribution accompanying the single-quasiparticle peak. In particular, for $n{a}^{3}=0.2138$, which corresponds to superfluid ${}^{4}$He at equilibrium density, the extracted spectrum turns out to be in good agreement with the experimental energy-momentum dispersion relation in the roton region and for higher momenta. The behavior of the spectral function at the same density in the stable solid and metastable gas phase above the freezing point is also discussed.

arXiv:1310.1753•Physical Review B•Dec 6, 2013•20 citations

Low-Temperature Behavior of a Dilute Bose System of Hard Spheres. I. Equilibrium Properties

T. D. Lee, Chongming Yang

By a generalization of the method used in a previous paper the distribution of energy levels of a dilute Bose system of hard spheres is found. These energy levels are then used to compute the statistical properties for the system. A phase transition is found, and the transition point is calculated to the lowest order of $a$, the diameter of the hard spheres. Furthermore, the thermodynamical functions of the system in both the gas phase and the degenerate phase are obtained, provided $(\frac{a}{\ensuremath{\lambda}})\ensuremath{\ll}1$ and $\ensuremath{\rho}{a}^{3}\ensuremath{\ll}1$, where $\ensuremath{\lambda}$ is the thermal wavelength and $\ensuremath{\rho}$ is the particle density.

Physical Review•Dec 1, 1958•193 citations

Bose-Einstein Gas with Repulsive Interactions: Hard Spheres at High Density

K. A. Brueckner, K. Sawada

A method developed by the authors for treating Bose-Einstein particles at low temperature is specialized to the case of hard sphere interactions. It is shown that the integral equations determining the energy can in this case be replaced by an integral involving the unknown excitation spectrum. The energy is first determined as a power series in ${(\ensuremath{\rho}{a}^{3})}^{\frac{1}{2}}$, where $\ensuremath{\rho}$ is the density and $a$ the hard-sphere radius. This solution is shown to diverge badly at high density. A result is then obtained which is valid over the full range of density, reducing to the exact expressions at low density and to a good approximation at high density. The excitation spectrum of the system is shown to have a peculiar nonmonotonic relation between energy and momentum very similar to that deduced by Landau from the low-temperature properties of ${\mathrm{He}}^{4}$.

Physical Review•Jun 15, 1957•95 citations

Freezing of soft-core bosons at zero temperature: A variational theory

Santi Prestipino, Alessandro Sergi, Ezio Bruno

The properties of a macroscopic assembly of weakly repulsive bosons at zero temperature are well described by Gross-Pitaevskii mean-field theory. According to this formalism the system exhibits a quantum transition from superfluid to cluster supersolid as a function of pressure. We develop a thermodynamically rigorous treatment of the different phases of the system by adopting a variational formulation of the condensate wave function---represented as a sum of Gaussians---that is amenable to exact manipulations. Not only is this description quantitatively accurate, but it is also capable to predict the order (and sometimes even the location) of the transition. We consider a number of crystal structures in two and three dimensions and determine the phase diagram. Depending on the lattice, the transition from fluid to solid can be first order or continuous, a lower coordination entailing a milder transition. In two dimensions, crystallization would occur at the same pressure on three distinct lattices (square, honeycomb, and stripes), all providing metastable phases with respect to the triangular crystal. A similar scenario holds in three dimensions, where the simple-cubic and diamond crystals also share a common melting point; however, the stable crystal at low pressure is typically fcc. Upon compression and depending on the shape of the potential, the fcc crystal may transform into hcp. We conclude by sketching a theory of the solid-fluid interface and of quantum nucleation of the solid from the fluid.

arXiv:1809.07515•Physical review. B./Physical review. B•Sep 10, 2018•26 citations

Many-body Bose systems and the hard-sphere model: dynamic properties from the weak to the strong interaction regime

R. Rota, F. Tramonto, Davide Emilio Galli +1 more

We obtain ab-initio estimations of the dynamic structure factor, S ( q ,ω), of Bose gases at zero temperature. More precisely, we use the Genetic Inversion via Falsification of Theories (GIFT) algorithm to perform analytic continuations of imaginary time correlation functions computed via an exact Path Integral projector method. Using the hard-sphere potential to model the two-body interactions between the atoms, we compute S ( q ,ω) changing the gas parameter from the dilute regime ( na 3 = 10 −4 ) up to the density corresponding to superfluid 4 He at equilibrium ( na 3 = 0.2138). With increasing density, we observe the emergence of a broad multiphonon contribution accompanying the quasiparticle peak and a crossover of the dispersion of elementary excitations from a Bogoliubov-like spectrum to a phonon-maxon- roton curve. Apart from the low wave vector region, for na 3 = 0.2138 the energy-momentum dispersion relation and the static density response function, χ( q ), turns out to be in good agreement with the superfluid 4 He experimental data at equilibrium density.

Journal of Physics Conference Series•Aug 14, 2014•2 citations
At zero temperature Bose hard sphere systems are in the fluid phase at low densities and in the solid phase at high densities. The fluid‐solid transition in this quantum system is discribed by density functional methods (modified weighted density functional theory). Predictions for solid‐phase energies and for freezing parameters are in good agreement with available simulation data.
The ground-state energy of a system of hard-sphere bosons of diameter $\ensuremath{\sigma}$ is calculated by a variational method using a Jastrow wave-function for the fluid phase and a "localized" Jastrow times a Gaussian wave function for the solid phase. The transition densities are ${\ensuremath{\rho}}_{\mathrm{fluid}}=0.23\ifmmode\pm\else\textpm\fi{}0.02$ particles/${\mathrm{\ensuremath{\sigma}}}^{3}$ and ${\ensuremath{\rho}}_{\mathrm{solid}}=0.25\ifmmode\pm\else\textpm\fi{}0.02$ particles/${\mathrm{\ensuremath{\sigma}}}^{3}$.
We investigate the dynamic structure factor of a system of Bose particles at zero temperature using quantum Monte Carlo methods. Interactions are modeled using a hard-sphere potential of size aaa and simulations are performed for values of the gas parameter na3n{a}^{3}na3 ranging from the dilute regime up to densities nnn where the thermodynamically stable phase is a solid. With increasing density, we observe a crossover of the dispersion of elementary excitations from a Bogoliubov-type spectrum to a phonon-maxon-roton curve and the emergence of a broad multiphonon contribution accompanying the single-quasiparticle peak. In particular, for na3=0.2138n{a}^{3}=0.2138na3=0.2138, which corresponds to superfluid 4{}^{4}4He at equilibrium density, the extracted spectrum turns out to be in good agreement with the experimental energy-momentum dispersion relation in the roton region and for higher momenta. The behavior of the spectral function at the same density in the stable solid and metastable gas phase above the freezing point is also discussed.
By a generalization of the method used in a previous paper the distribution of energy levels of a dilute Bose system of hard spheres is found. These energy levels are then used to compute the statistical properties for the system. A phase transition is found, and the transition point is calculated to the lowest order of aaa, the diameter of the hard spheres. Furthermore, the thermodynamical functions of the system in both the gas phase and the degenerate phase are obtained, provided $(\frac{a}{\ensuremath{\lambda}})\ensuremath{\ll}1$ and $\ensuremath{\rho}{a}^{3}\ensuremath{\ll}1$, where $\ensuremath{\lambda}$ is the thermal wavelength and $\ensuremath{\rho}$ is the particle density.
A method developed by the authors for treating Bose-Einstein particles at low temperature is specialized to the case of hard sphere interactions. It is shown that the integral equations determining the energy can in this case be replaced by an integral involving the unknown excitation spectrum. The energy is first determined as a power series in ${(\ensuremath{\rho}{a}^{3})}^{\frac{1}{2}}$, where $\ensuremath{\rho}$ is the density and aaa the hard-sphere radius. This solution is shown to diverge badly at high density. A result is then obtained which is valid over the full range of density, reducing to the exact expressions at low density and to a good approximation at high density. The excitation spectrum of the system is shown to have a peculiar nonmonotonic relation between energy and momentum very similar to that deduced by Landau from the low-temperature properties of He4{\mathrm{He}}^{4}He4.
The properties of a macroscopic assembly of weakly repulsive bosons at zero temperature are well described by Gross-Pitaevskii mean-field theory. According to this formalism the system exhibits a quantum transition from superfluid to cluster supersolid as a function of pressure. We develop a thermodynamically rigorous treatment of the different phases of the system by adopting a variational formulation of the condensate wave function---represented as a sum of Gaussians---that is amenable to exact manipulations. Not only is this description quantitatively accurate, but it is also capable to predict the order (and sometimes even the location) of the transition. We consider a number of crystal structures in two and three dimensions and determine the phase diagram. Depending on the lattice, the transition from fluid to solid can be first order or continuous, a lower coordination entailing a milder transition. In two dimensions, crystallization would occur at the same pressure on three distinct lattices (square, honeycomb, and stripes), all providing metastable phases with respect to the triangular crystal. A similar scenario holds in three dimensions, where the simple-cubic and diamond crystals also share a common melting point; however, the stable crystal at low pressure is typically fcc. Upon compression and depending on the shape of the potential, the fcc crystal may transform into hcp. We conclude by sketching a theory of the solid-fluid interface and of quantum nucleation of the solid from the fluid.
We obtain ab-initio estimations of the dynamic structure factor, S ( q ,ω), of Bose gases at zero temperature. More precisely, we use the Genetic Inversion via Falsification of Theories (GIFT) algorithm to perform analytic continuations of imaginary time correlation functions computed via an exact Path Integral projector method. Using the hard-sphere potential to model the two-body interactions between the atoms, we compute S ( q ,ω) changing the gas parameter from the dilute regime ( na 3 = 10 −4 ) up to the density corresponding to superfluid 4 He at equilibrium ( na 3 = 0.2138). With increasing density, we observe the emergence of a broad multiphonon contribution accompanying the quasiparticle peak and a crossover of the dispersion of elementary excitations from a Bogoliubov-like spectrum to a phonon-maxon- roton curve. Apart from the low wave vector region, for na 3 = 0.2138 the energy-momentum dispersion relation and the static density response function, χ( q ), turns out to be in good agreement with the superfluid 4 He experimental data at equilibrium density.