aqora

Constant-density thermodynamic perturbation theory for quantum fluids

B. Kumar, Nutan Chandra

Physica A Statistical Mechanics and its ApplicationsFeb 1, 19820 citations

Renormalization of the reduced density matrices for inhomogeneous quantum fluids. I

L. E. Reichl

The first of two papers in which a systematic scheme for renormalizing the reduced density matrices of an initially inhomogeneous quantum fluid is introduced. In this paper, an expression for the perturbation Liouville expansion of the n-particle reduced density matrix is formulated in the momentum representation using the grand ensemble. A generating function for the reduced density matrices is introduced and the theory is formulated in such a way that the binary Liouville expansion may easily be introduced in place of the perturbation expansion.The first of two papers in which a systematic scheme for renormalizing the reduced density matrices of an initially inhomogeneous quantum fluid is introduced. In this paper, an expression for the perturbation Liouville expansion of the n-particle reduced density matrix is formulated in the momentum representation using the grand ensemble. A generating function for the reduced density matrices is introduced and the theory is formulated in such a way that the binary Liouville expansion may easily be introduced in place of the perturbation expansion.

Bulletin de la Classe des sciencesJan 1, 19730 citations

Aspects of Quantum Fluids

WORLD SCIENTIFIC eBooksJun 1, 20080 citations

Thermodynamic perturbation theory of hard-core square-well bosons

C Keller, Valdir C. Aguilera-Navarro, MANUEL DE LLANO

The authors investigate the calculational scheme for an eventual first-principles description of the ground-state energy of the many-boson Schrodinger equation. They employ a model 4 He intermolecular pair potential consisting of a hard core surrounded by an attractive rectangular well. The study is based on the well known low-density expansion for such a system, where three coefficients are known. The first corrections to the fourth coefficient are determined on the basis of the rearranged series being a thermodynamic perturbation expansion, namely one representing perturbation not about the ideal gas but about the hard-sphere fluid. Pade approximants, and variations thereof, are employed to extrapolate to physical regimes in both resulting series, in density as well as in the attractive coupling constant.The authors investigate the calculational scheme for an eventual first-principles description of the ground-state energy of the many-boson Schrodinger equation. They employ a model 4 He intermolecular pair potential consisting of a hard core surrounded by an attractive rectangular well. The study is based on the well known low-density expansion for such a system, where three coefficients are known. The first corrections to the fourth coefficient are determined on the basis of the rearranged series being a thermodynamic perturbation expansion, namely one representing perturbation not about the ideal gas but about the hard-sphere fluid. Pade approximants, and variations thereof, are employed to extrapolate to physical regimes in both resulting series, in density as well as in the attractive coupling constant.

Journal of Physics A Mathematical and GeneralFeb 7, 19883 citations

Hard-core square-well fermions

George Allen Baker Jr., L. P. Benofy, Mauricio Fortes +3 more

Based on the well-known low-density expansion for the ground-state energy per particle of a many-fermion system interacting pairwise via a central potential we develop a perturbation scheme in which the zero-order state is that of the purely-repulsive-spheres fluid. For the hard-core plus square-well pair-interaction case we have deduced, for two-species fermion matter, perturbation formulas up to sixth order in the attractive coupling parameter. We explicitly report results up to fourth order here. Pad\'e-approximant analyses in the density are carried out in each order with the intent of providing the basis necessary for extensive equation-of-state calculations of various many-fermion systems. In particular, for zero order (the fermion hard-sphere fluid) we predict an uncertainty-principle divergence in the energy, and hence pressure, corresponding to the random close packing of spheres, at a density of about 0.5 times the recently obtained value for boson hard spheres and about 0.2 times the well-known empirical value for classical hard spheres.Based on the well-known low-density expansion for the ground-state energy per particle of a many-fermion system interacting pairwise via a central potential we develop a perturbation scheme in which the zero-order state is that of the purely-repulsive-spheres fluid. For the hard-core plus square-well pair-interaction case we have deduced, for two-species fermion matter, perturbation formulas up to sixth order in the attractive coupling parameter. We explicitly report results up to fourth order here. Pad\'e-approximant analyses in the density are carried out in each order with the intent of providing the basis necessary for extensive equation-of-state calculations of various many-fermion systems. In particular, for zero order (the fermion hard-sphere fluid) we predict an uncertainty-principle divergence in the energy, and hence pressure, corresponding to the random close packing of spheres, at a density of about 0.5 times the recently obtained value for boson hard spheres and about 0.2 times the well-known empirical value for classical hard spheres.

Physical Review ADec 1, 198230 citations

Recent Progress in the Theory of Highly Correlated Quantum Fluids

C. E. Campbell

Recent Progress in Many-Body TheoriesJan 1, 19952 citations

New perturbation scheme for quantum fluids based on low-density expansions

Related papers

New perturbation scheme for quantum fluids based on low-density expansions

Related papers