The microscopic study of the two-body density matrix ${\mathrm{\ensuremath{\rho}}}_{2}$( ${\mathbf{r}}_{1}$ , ${\mathbf{r}}_{2}$ ,${\mathbf{r}}_{1}^{\ensuremath{'}}$,${\mathbf{r}}_{2}^{\ensuremath{'}}$) initiated for uniform Bose fluids in an earlier paper is continued for the Fermi case. We present formal results on the structure of the generalized momentum distribution n(p,q)=${\mathrm{\ensuremath{\Sigma}}}_{\mathbf{k}\mathbf{\^{}}}$〈\ensuremath{\Psi}|${\mathrm{a}}_{\mathbf{k}\mathbf{\^{}}+\mathbf{q}}^{\mathrm{\ifmmode\dagger\else\textdagger\fi{}}}$${\mathrm{a}}_{\mathbf{p}\mathbf{\^{}}\mathrm{\ensuremath{-}}\mathbf{q}}^{\mathrm{\ifmmode\dagger\else\textdagger\fi{}}}$ ${\mathrm{a}}_{\mathbf{p}\mathbf{\^{}}}$ ${\mathrm{a}}_{\mathbf{k}\mathbf{\^{}}}$ |\ensuremath{\Psi}〉, and its Fourier inverse ${\mathrm{\ensuremath{\rho}}}_{2}$( ${\mathbf{r}}_{1}$ , ${\mathbf{r}}_{2}$ ,${\mathbf{r}}_{1}^{\ensuremath{'}}$, ${\mathbf{r}}_{2}$ )\ensuremath{\equiv}${\mathrm{\ensuremath{\rho}}}_{2}$( ${\mathbf{r}}_{1}$ , ${\mathbf{r}}_{2}$ ,${\mathbf{r}}_{1}^{\ensuremath{'}}$), based on a variational ground-state wave function of Jastrow-Slater form. The structural relations are inferred from the cluster expansions of these objects, from the asymptotic condition relating ${\mathrm{\ensuremath{\rho}}}_{2}$( ${\mathbf{r}}_{1}$ , ${\mathbf{r}}_{2}$ ,${\mathbf{r}}_{1}^{\ensuremath{'}}$) to the particle density and the one-body density matrix ${\mathrm{\ensuremath{\rho}}}_{1}$( ${\mathbf{r}}_{1}$ ,${\mathbf{r}}_{1}^{\ensuremath{'}}$), and from formal diagrammatic connections with the Bose problem. The two-body density-matrix elements ${\mathrm{\ensuremath{\rho}}}_{2}$( ${\mathbf{r}}_{1}$ , ${\mathbf{r}}_{2}$ ,${\mathbf{r}}_{1}^{\ensuremath{'}}$) are thereby expressed in closed form in terms of certain sums of irreducible cluster diagrams. Some of these diagram sums are familiar from the analogous theory of the one-body density matrix; all can be evaluated quantitatively by solving a set of Fermi-hypernetted-chain (FHNC) equations. Upon invoking the sequential relation between ${\mathrm{\ensuremath{\rho}}}_{2}$( ${\mathbf{r}}_{1}$ , ${\mathbf{r}}_{2}$ ,${\mathbf{r}}_{1}^{\ensuremath{'}}$) and ${\mathrm{\ensuremath{\rho}}}_{1}$( ${\mathbf{r}}_{1}$ ,${\mathbf{r}}_{1}^{\ensuremath{'}}$), the corresponding result for the generalized momentum distribution n(p,q) effects a resolution into contributions from various scattering processes occurring in the many-body medium, specified by form factors that are susceptible to FHNC evaluation. This decomposition is comparable to that derived earlier for the Bose-fluid ground state but is complicated by contributions from exchange scattering and by a dynamically dressed Pauli kinematic correction. Silver has proposed a simple expression for the generalized momentum distribution n(p,q), a function which plays an essential role in his theory of final-state effects in deep-inelastic neutron scattering from the helium liquids. Based on the present microscopic treatment, the quality of Silver's estimate is assessed for the case of normal liquid ${\mathrm{He}}^{3}$ , by evaluating the necessary distribution functions and form factors within the FHNC/0 approximation.The microscopic study of the two-body density matrix ${\mathrm{\ensuremath{\rho}}}_{2}$(${\mathbf{r}}_{1}$,${\mathbf{r}}_{2}$,${\mathbf{r}}_{1}^{\ensuremath{'}}$,${\mathbf{r}}_{2}^{\ensuremath{'}}$) initiated for uniform Bose fluids in an earlier paper is continued for the Fermi case. We present formal results on the structure of the generalized momentum distribution n(p,q)=${\mathrm{\ensuremath{\Sigma}}}_{\mathbf{k}\mathbf{\^{}}}$〈\ensuremath{\Psi}|${\mathrm{a}}_{\mathbf{k}\mathbf{\^{}}+\mathbf{q}}^{\mathrm{\ifmmode\dagger\else\textdagger\fi{}}}$${\mathrm{a}}_{\mathbf{p}\mathbf{\^{}}\mathrm{\ensuremath{-}}\mathbf{q}}^{\mathrm{\ifmmode\dagger\else\textdagger\fi{}}}$${\mathrm{a}}_{\mathbf{p}\mathbf{\^{}}}$${\mathrm{a}}_{\mathbf{k}\mathbf{\^{}}}$|\ensuremath{\Psi}〉, and its Fourier inverse ${\mathrm{\ensuremath{\rho}}}_{2}$(${\mathbf{r}}_{1}$,${\mathbf{r}}_{2}$,${\mathbf{r}}_{1}^{\ensuremath{'}}$,${\mathbf{r}}_{2}$)\ensuremath{\equiv}${\mathrm{\ensuremath{\rho}}}_{2}$(${\mathbf{r}}_{1}$,${\mathbf{r}}_{2}$,${\mathbf{r}}_{1}^{\ensuremath{'}}$), based on a variational ground-state wave function of Jastrow-Slater form. The structural relations are inferred from the cluster expansions of these objects, from the asymptotic condition relating ${\mathrm{\ensuremath{\rho}}}_{2}$(${\mathbf{r}}_{1}$,${\mathbf{r}}_{2}$,${\mathbf{r}}_{1}^{\ensuremath{'}}$) to the particle density and the one-body density matrix ${\mathrm{\ensuremath{\rho}}}_{1}$(${\mathbf{r}}_{1}$,${\mathbf{r}}_{1}^{\ensuremath{'}}$), and from formal diagrammatic connections with the Bose problem. The two-body density-matrix elements ${\mathrm{\ensuremath{\rho}}}_{2}$(${\mathbf{r}}_{1}$,${\mathbf{r}}_{2}$,${\mathbf{r}}_{1}^{\ensuremath{'}}$) are thereby expressed in closed form in terms of certain sums of irreducible cluster diagrams. Some of these diagram sums are familiar from the analogous theory of the one-body density matrix; all can be evaluated quantitatively by solving a set of Fermi-hypernetted-chain (FHNC) equations. Upon invoking the sequential relation between ${\mathrm{\ensuremath{\rho}}}_{2}$(${\mathbf{r}}_{1}$,${\mathbf{r}}_{2}$,${\mathbf{r}}_{1}^{\ensuremath{'}}$) and ${\mathrm{\ensuremath{\rho}}}_{1}$(${\mathbf{r}}_{1}$,${\mathbf{r}}_{1}^{\ensuremath{'}}$), the corresponding result for the generalized momentum distribution n(p,q) effects a resolution into contributions from various scattering processes occurring in the many-body medium, specified by form factors that are susceptible to FHNC evaluation. This decomposition is comparable to that derived earlier for the Bose-fluid ground state but is complicated by contributions from exchange scattering and by a dynamically dressed Pauli kinematic correction. Silver has proposed a simple expression for the generalized momentum distribution n(p,q), a function which plays an essential role in his theory of final-state effects in deep-inelastic neutron scattering from the helium liquids. Based on the present microscopic treatment, the quality of Silver's estimate is assessed for the case of normal liquid ${\mathrm{He}}^{3}$, by evaluating the necessary distribution functions and form factors within the FHNC/0 approximation.

Physical review. B, Condensed matterMay 1, 199011 citations

Correlations in bose fluids

L. Reatto

Lecture notes in physicsJan 1, 19810 citations

Superfluidity, Bose-Einstein condensation, and structure in one-dimensional Luttinger liquids

Leandra Vranješ Markić, Hrvoje Vrcan, Z. Zuhrianda +1 more

We report diffusion Monte Carlo (DMC) and path integral Monte Carlo (PIMC) calculations of the properties of a one-dimensional (1D) Bose quantum fluid. The equation of state, the superfluid fraction ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$, the one-body density matrix $n(x)$ , the pair distribution function $g(x)$ , and the static structure factor $S(q)$ are evaluated. The aim is to test Luttinger liquid (LL) predictions for 1D fluids over a wide range of fluid density and LL parameter $K$ . The 1D Bose fluid examined is a single chain of $^{4}\mathrm{He}$ atoms confined to a line in the center of a narrow nanopore. The atoms cannot exchange positions in the nanopore, the criterion for 1D. The fluid density is varied from the spinodal density where the 1D liquid is unstable to droplet formation to the density of bulk liquid $^{4}\mathrm{He}$ . In this range, $K$ varies from $K>2$ at low density, where a robust superfluid is predicted, to $K<0.5$ , where fragile 1D superflow and solidlike peaks in $S(q)$ are predicted. For uniform pore walls, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ scales as predicted by LL theory. The $n(x)$ and $g(x)$ show long range oscillations and decay with $x$ as predicted by LL theory. The amplitude of the oscillations is large at high density (small $K)$ and small at low density (large $K)$ . The $K$ values obtained from different properties agree well verifying the internal structure of LL theory. In the presence of disorder, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ does not scale as predicted by LL theory. A single ${v}_{J}$ parameter in the LL theory that recovers LL scaling was not found. The one body density matrix (OBDM) in disorder is well predicted by LL theory. The ``dynamical'' superfluid fraction, ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$, is determined. The physics of the deviation from LL theory in disorder and the ``dynamical'' ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$ are discussed.We report diffusion Monte Carlo (DMC) and path integral Monte Carlo (PIMC) calculations of the properties of a one-dimensional (1D) Bose quantum fluid. The equation of state, the superfluid fraction ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$, the one-body density matrix $n(x)$, the pair distribution function $g(x)$, and the static structure factor $S(q)$ are evaluated. The aim is to test Luttinger liquid (LL) predictions for 1D fluids over a wide range of fluid density and LL parameter $K$. The 1D Bose fluid examined is a single chain of $^{4}\mathrm{He}$ atoms confined to a line in the center of a narrow nanopore. The atoms cannot exchange positions in the nanopore, the criterion for 1D. The fluid density is varied from the spinodal density where the 1D liquid is unstable to droplet formation to the density of bulk liquid $^{4}\mathrm{He}$. In this range, $K$ varies from $K>2$ at low density, where a robust superfluid is predicted, to $K<0.5$, where fragile 1D superflow and solidlike peaks in $S(q)$ are predicted. For uniform pore walls, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ scales as predicted by LL theory. The $n(x)$ and $g(x)$ show long range oscillations and decay with $x$ as predicted by LL theory. The amplitude of the oscillations is large at high density (small $K)$ and small at low density (large $K)$. The $K$ values obtained from different properties agree well verifying the internal structure of LL theory. In the presence of disorder, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ does not scale as predicted by LL theory. A single ${v}_{J}$ parameter in the LL theory that recovers LL scaling was not found. The one body density matrix (OBDM) in disorder is well predicted by LL theory. The ``dynamical'' superfluid fraction, ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$, is determined. The physics of the deviation from LL theory in disorder and the ``dynamical'' ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$ are discussed.

Physical review. B./Physical review. BJan 19, 201819 citations

On the three-particle structure function of bose fluids

Srećko Kilić

The European Physical Journal BMar 1, 19781 citation

The microscopic study of the two-body density matrix ${\mathrm{\ensuremath{\rho}}}_{2}$(

{\mathbf{r}}_{1}

{\mathbf{r}}_{2}

,${\mathbf{r}}_{1}^{\ensuremath{'}}$,${\mathbf{r}}_{2}^{\ensuremath{'}}$) initiated for uniform Bose fluids in an earlier paper is continued for the Fermi case. We present formal results on the structure of the generalized momentum distribution n(p,q)=${\mathrm{\ensuremath{\Sigma}}}_{\mathbf{k}\mathbf{\^{}}}$〈\ensuremath{\Psi}|${\mathrm{a}}_{\mathbf{k}\mathbf{\^{}}+\mathbf{q}}^{\mathrm{\ifmmode\dagger\else\textdagger\fi{}}}$${\mathrm{a}}_{\mathbf{p}\mathbf{\^{}}\mathrm{\ensuremath{-}}\mathbf{q}}^{\mathrm{\ifmmode\dagger\else\textdagger\fi{}}}$

{\mathrm{a}}_{\mathbf{p}\mathbf{\^{}}}

{\mathrm{a}}_{\mathbf{k}\mathbf{\^{}}}

|\ensuremath{\Psi}〉, and its Fourier inverse ${\mathrm{\ensuremath{\rho}}}_{2}$(

{\mathbf{r}}_{1}

{\mathbf{r}}_{2}

,${\mathbf{r}}_{1}^{\ensuremath{'}}$,

{\mathbf{r}}_{2}

)\ensuremath{\equiv}${\mathrm{\ensuremath{\rho}}}_{2}$(

{\mathbf{r}}_{1}

{\mathbf{r}}_{2}

,${\mathbf{r}}_{1}^{\ensuremath{'}}$), based on a variational ground-state wave function of Jastrow-Slater form. The structural relations are inferred from the cluster expansions of these objects, from the asymptotic condition relating ${\mathrm{\ensuremath{\rho}}}_{2}$(

{\mathbf{r}}_{1}

{\mathbf{r}}_{2}

,${\mathbf{r}}_{1}^{\ensuremath{'}}$) to the particle density and the one-body density matrix ${\mathrm{\ensuremath{\rho}}}_{1}$(

{\mathbf{r}}_{1}

,${\mathbf{r}}_{1}^{\ensuremath{'}}$), and from formal diagrammatic connections with the Bose problem. The two-body density-matrix elements ${\mathrm{\ensuremath{\rho}}}_{2}$(

{\mathbf{r}}_{1}

{\mathbf{r}}_{2}

,${\mathbf{r}}_{1}^{\ensuremath{'}}$) are thereby expressed in closed form in terms of certain sums of irreducible cluster diagrams. Some of these diagram sums are familiar from the analogous theory of the one-body density matrix; all can be evaluated quantitatively by solving a set of Fermi-hypernetted-chain (FHNC) equations. Upon invoking the sequential relation between ${\mathrm{\ensuremath{\rho}}}_{2}$(

{\mathbf{r}}_{1}

{\mathbf{r}}_{2}

,${\mathbf{r}}_{1}^{\ensuremath{'}}$) and ${\mathrm{\ensuremath{\rho}}}_{1}$(

{\mathbf{r}}_{1}

,${\mathbf{r}}_{1}^{\ensuremath{'}}$), the corresponding result for the generalized momentum distribution n(p,q) effects a resolution into contributions from various scattering processes occurring in the many-body medium, specified by form factors that are susceptible to FHNC evaluation. This decomposition is comparable to that derived earlier for the Bose-fluid ground state but is complicated by contributions from exchange scattering and by a dynamically dressed Pauli kinematic correction. Silver has proposed a simple expression for the generalized momentum distribution n(p,q), a function which plays an essential role in his theory of final-state effects in deep-inelastic neutron scattering from the helium liquids. Based on the present microscopic treatment, the quality of Silver's estimate is assessed for the case of normal liquid

{\mathrm{He}}^{3}

, by evaluating the necessary distribution functions and form factors within the FHNC/0 approximation.

n(x)

, the pair distribution function

g(x)

, and the static structure factor

S(q)

are evaluated. The aim is to test Luttinger liquid (LL) predictions for 1D fluids over a wide range of fluid density and LL parameter

K

. The 1D Bose fluid examined is a single chain of

^{4}\mathrm{He}

atoms confined to a line in the center of a narrow nanopore. The atoms cannot exchange positions in the nanopore, the criterion for 1D. The fluid density is varied from the spinodal density where the 1D liquid is unstable to droplet formation to the density of bulk liquid

^{4}\mathrm{He}

. In this range,

K

varies from

K>2

at low density, where a robust superfluid is predicted, to

K<0.5

, where fragile 1D superflow and solidlike peaks in

S(q)

are predicted. For uniform pore walls, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ scales as predicted by LL theory. The

n(x)

and

g(x)

show long range oscillations and decay with

x

as predicted by LL theory. The amplitude of the oscillations is large at high density (small

K)

and small at low density (large

K)

. The

K

values obtained from different properties agree well verifying the internal structure of LL theory. In the presence of disorder, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ does not scale as predicted by LL theory. A single

{v}_{J}

parameter in the LL theory that recovers LL scaling was not found. The one body density matrix (OBDM) in disorder is well predicted by LL theory. The ``dynamical'' superfluid fraction, ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$, is determined. The physics of the deviation from LL theory in disorder and the ``dynamical'' ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$ are discussed.