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Journal of Low Temperature Physics

, Volume 149, Issue 1–2, pp 53–63 | Cite as

Two-Body Correlations and the Superfluid Fraction for Nonuniform Systems

  • W. M. Saslow
  • D. E. Galli
  • L. Reatto
Article

Abstract

We extend the one-body phase function upper bound on the superfluid fraction f s in a periodic solid (a spatially ordered supersolid) to include two-body phase correlations. The one-body current density is no longer proportional to the gradient of the one-body phase times the one-body density, but rather it becomes \(\vec{j}(\vec{r}_{1})=\rho_{1}(\vec{r}_{1})\frac{\hbar}{m}\vec{\nabla }_{1}\phi_{1}(\vec{r}_{1})+\frac{1}{N}\int d\vec{r}_{2}\rho_{2}(\vec{r}_{1},\vec{r}_{2})\frac{\hbar }{m}\vec{\nabla}_{1}\phi_{2}(\vec{r}_{1},\vec{r}_{2})\) . This expression therefore depends also on two-body correlation functions. The equations that simultaneously determine the one-body and two-body phase functions require a knowledge of one-, two-, and three-body correlation functions. The approach can also be extended to disordered solids. Fluids, with two-body densities and two-body phase functions that are translationally invariant, cannot take advantage of this additional degree of freedom to lower their energy.

Keywords

Superfluidity Supersolid Correlation functions 

PACS

67.80.-s 67.90.+z 67.57.De 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of PhysicsTexas A&M UniversityCollege StationUSA
  2. 2.Dipartimento di FisicaUniversità degli Studi di MilanoMilanoItaly

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