The diffusion Monte Carlo (DMC) method is used to analyze various properties of the three-dimensional plasma of charged bosons in the homogeneous fluid regime, over the density range 1\ensuremath{\le} ${\mathit{r}}_{\mathit{s}}$ \ensuremath{\le}160 extending from the so-called uniform limit (${\mathit{r}}_{\mathit{s}} $1) to the crystalline phase ($ {\mathit{r}}_{\mathit{s}}$\ensuremath{\gtrsim}160). The data on the static density response function \ensuremath{\chi}(k) extend to intermediate and high wave number k the work of Sugiyama, Bowen, and Alder [Phys. Rev. B 46, 13 042 (1992)] and allow us to extract the static local-field factor G(k) for exchange and correlation. The DMC results for the momentum distribution n(k) show that the condensate fraction decreases with increasing coupling strength from 83% at ${\mathit{r}}_{\mathit{s}}$ =1 to less than 1% at ${\mathit{r}}_{\mathit{s}}$ =160. We also present results for the ground-state energy ${\mathit{E}}_{\mathit{g}}$ ( ${\mathit{r}}_{\mathit{s}}$ ) and for the structure factor S(k). The results for ${\mathit{E}}_{\mathit{g}}$ ( ${\mathit{r}}_{\mathit{s}}$ ), n(k), and \ensuremath{\chi}(k) are summarized in analytic interpolation formulas embodying the known asymptotic behaviors. A rigorous upper bound on the plasmon dispersion curve is obtained from the DMC data through a sum-rule argument. \textcopyright{} 1996 The American Physical Society.The diffusion Monte Carlo (DMC) method is used to analyze various properties of the three-dimensional plasma of charged bosons in the homogeneous fluid regime, over the density range 1\ensuremath{\le}${\mathit{r}}_{\mathit{s}}$\ensuremath{\le}160 extending from the so-called uniform limit (${\mathit{r}}_{\mathit{s}}$1) to the crystalline phase (${\mathit{r}}_{\mathit{s}}$\ensuremath{\gtrsim}160). The data on the static density response function \ensuremath{\chi}(k) extend to intermediate and high wave number k the work of Sugiyama, Bowen, and Alder [Phys. Rev. B 46, 13 042 (1992)] and allow us to extract the static local-field factor G(k) for exchange and correlation. The DMC results for the momentum distribution n(k) show that the condensate fraction decreases with increasing coupling strength from 83% at ${\mathit{r}}_{\mathit{s}}$=1 to less than 1% at ${\mathit{r}}_{\mathit{s}}$=160. We also present results for the ground-state energy ${\mathit{E}}_{\mathit{g}}$(${\mathit{r}}_{\mathit{s}}$) and for the structure factor S(k). The results for ${\mathit{E}}_{\mathit{g}}$(${\mathit{r}}_{\mathit{s}}$), n(k), and \ensuremath{\chi}(k) are summarized in analytic interpolation formulas embodying the known asymptotic behaviors. A rigorous upper bound on the plasmon dispersion curve is obtained from the DMC data through a sum-rule argument. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterApr 15, 199630 citations

Equilibrium statistical mechanics of quantum fluids

Bijoy Kumar

Jan 1, 19680 citations

Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid

N. D. Drummond, Richard J. Needs

We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair-correlation function, static structure factor, and momentum density of the ground state of the two-dimensional (2D) homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair-correlation function, static structure factor, and momentum density of the ground state of the two-dimensional (2D) homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.

arXiv:1002.2122Physical Review BFeb 13, 200940 citations

Static response, collective frequencies, and ground-state thermodynamical properties of spin-saturated two-component cold atoms and neutron matter

Antoine Boulet, Denis Lacroix A

The thermodynamical ground-state properties and static response in both cold atoms at or close to unitarity and neutron matter are determined using a recently proposed density functional theory (DFT) based on the $s$ -wave scattering length ${a}_{s}$ , effective range ${r}_{e}$ , and unitary gas limit. In cold atoms, when the effective range may be neglected, we show that the pressure, chemical potential, compressibility modulus, and sound velocity obtained with the DFT are compatible with experimental observations or exact theoretical estimates. The static response in homogeneous infinite systems is also obtained and a possible influence of the effective range on the response is analyzed. The neutron matter differs from unitary gas due to the noninfinite scattering length and to a significant influence of effective range, which affects all thermodynamical quantities as well as the static response. In particular, we show for neutron matter that the latter response recently obtained in auxiliary-field diffusion Monte Carlo (AFDMC) can be qualitatively reproduced when the $p$ -wave contribution is added to the functional. Our study indicates that the close similarity between the exact AFDMC static response and the free-gas response might stem from the compensation of the ${a}_{s}$ effect by the effective range and $p$ -wave contributions. We finally consider the dynamical response of both atoms or neutron droplets in anisotropic traps. Assuming the hydrodynamical regime and a polytropic equation of state, a reasonable description of the radial and axial collective frequencies in cold atoms is obtained. Following a similar strategy, we estimate the equivalent collective frequencies of neutron drops in anisotropic traps.The thermodynamical ground-state properties and static response in both cold atoms at or close to unitarity and neutron matter are determined using a recently proposed density functional theory (DFT) based on the $s$-wave scattering length ${a}_{s}$, effective range ${r}_{e}$, and unitary gas limit. In cold atoms, when the effective range may be neglected, we show that the pressure, chemical potential, compressibility modulus, and sound velocity obtained with the DFT are compatible with experimental observations or exact theoretical estimates. The static response in homogeneous infinite systems is also obtained and a possible influence of the effective range on the response is analyzed. The neutron matter differs from unitary gas due to the noninfinite scattering length and to a significant influence of effective range, which affects all thermodynamical quantities as well as the static response. In particular, we show for neutron matter that the latter response recently obtained in auxiliary-field diffusion Monte Carlo (AFDMC) can be qualitatively reproduced when the $p$-wave contribution is added to the functional. Our study indicates that the close similarity between the exact AFDMC static response and the free-gas response might stem from the compensation of the ${a}_{s}$ effect by the effective range and $p$-wave contributions. We finally consider the dynamical response of both atoms or neutron droplets in anisotropic traps. Assuming the hydrodynamical regime and a polytropic equation of state, a reasonable description of the radial and axial collective frequencies in cold atoms is obtained. Following a similar strategy, we estimate the equivalent collective frequencies of neutron drops in anisotropic traps.

arXiv:1709.05160Physical Review CJan 4, 201815 citations

Aspects of Quantum Fluids

WORLD SCIENTIFIC eBooksJun 1, 20080 citations

{\mathit{r}}_{\mathit{s}}

\ensuremath{\le}160 extending from the so-called uniform limit (${\mathit{r}}_{\mathit{s}}

1) to the crystalline phase (

{\mathit{r}}_{\mathit{s}}$\ensuremath{\gtrsim}160). The data on the static density response function \ensuremath{\chi}(k) extend to intermediate and high wave number k the work of Sugiyama, Bowen, and Alder [Phys. Rev. B 46, 13 042 (1992)] and allow us to extract the static local-field factor G(k) for exchange and correlation. The DMC results for the momentum distribution n(k) show that the condensate fraction decreases with increasing coupling strength from 83% at

{\mathit{r}}_{\mathit{s}}

=1 to less than 1% at

{\mathit{r}}_{\mathit{s}}

=160. We also present results for the ground-state energy

{\mathit{E}}_{\mathit{g}}

(

{\mathit{r}}_{\mathit{s}}

) and for the structure factor S(k). The results for

{\mathit{E}}_{\mathit{g}}

(

{\mathit{r}}_{\mathit{s}}

), n(k), and \ensuremath{\chi}(k) are summarized in analytic interpolation formulas embodying the known asymptotic behaviors. A rigorous upper bound on the plasmon dispersion curve is obtained from the DMC data through a sum-rule argument. \textcopyright{} 1996 The American Physical Society.

s

-wave scattering length

{a}_{s}

, effective range

{r}_{e}

, and unitary gas limit. In cold atoms, when the effective range may be neglected, we show that the pressure, chemical potential, compressibility modulus, and sound velocity obtained with the DFT are compatible with experimental observations or exact theoretical estimates. The static response in homogeneous infinite systems is also obtained and a possible influence of the effective range on the response is analyzed. The neutron matter differs from unitary gas due to the noninfinite scattering length and to a significant influence of effective range, which affects all thermodynamical quantities as well as the static response. In particular, we show for neutron matter that the latter response recently obtained in auxiliary-field diffusion Monte Carlo (AFDMC) can be qualitatively reproduced when the

p

-wave contribution is added to the functional. Our study indicates that the close similarity between the exact AFDMC static response and the free-gas response might stem from the compensation of the

{a}_{s}

effect by the effective range and

p

-wave contributions. We finally consider the dynamical response of both atoms or neutron droplets in anisotropic traps. Assuming the hydrodynamical regime and a polytropic equation of state, a reasonable description of the radial and axial collective frequencies in cold atoms is obtained. Following a similar strategy, we estimate the equivalent collective frequencies of neutron drops in anisotropic traps.