"A theory is developed to allow the systematic calculation of the properties of quantum fluids given the microscopic two-body potential. Physical arguments are used to construct a correlation operator that approximately transforms the states of a non-interacting system into the corresponding states of the interacting-system. The theory can be regarded as a microscopic realization of Landau's assumption of a one-to-one correspondence between the non-interacting and interacting states. It is variational since the correlation operator is determined by minimizing E(p) the expectation value of the ground-state energy. We first give a survey of various other many-body theories including the simpler Jastrow variational method. Differential equations are derived to calculate the correlation operator and the related Jastrow correlation"" function. A comparison of results in several Bose systems with various methods is given. The Fermi hypernetted chain integral equations are generalized to allow the calculation of E(p) in Fermi systems, using the correlation operator wave function. The method is applied to liquid 3He and the v2-model of nuclear matter. In 3He the correlation operator gives results in much closer agreement with experiment than that with the Jastrow wave function. A new set of hypernetted chain equations are then derived to allow the calculation of the excited st;ate energies in Bose systems. The theory is then applied to the calculation of the single quasi-particle excitation spectrum of liquid 4He. The spectrum is found to be a stringent test on the form of the correlation operator, deficiencies in the correlation operator giving corresponding errors in the spectrum. Good results are obtained for the density dependence of the roton energy. A variational principle for the free energy is used to generalize the correlation operator technique to finite temperatures. Results are given for the finite temperature properties of the v8-model of nuclear matter.""A theory is developed to allow the systematic calculation of the properties of quantum fluids given the microscopic two-body potential. Physical arguments are used to construct a correlation operator that approximately transforms the states of a non-interacting system into the corresponding states of the interacting-system. The theory can be regarded as a microscopic realization of Landau's assumption of a one-to-one correspondence between the non-interacting and interacting states. It is variational since the correlation operator is determined by minimizing E(p) the expectation value of the ground-state energy. We first give a survey of various other many-body theories including the simpler Jastrow variational method. Differential equations are derived to calculate the correlation operator and the related Jastrow correlation"" function. A comparison of results in several Bose systems with various methods is given. The Fermi hypernetted chain integral equations are generalized to allow the calculation of E(p) in Fermi systems, using the correlation operator wave function. The method is applied to liquid 3He and the v2-model of nuclear matter. In 3He the correlation operator gives results in much closer agreement with experiment than that with the Jastrow wave function. A new set of hypernetted chain equations are then derived to allow the calculation of the excited st;ate energies in Bose systems. The theory is then applied to the calculation of the single quasi-particle excitation spectrum of liquid 4He. The spectrum is found to be a stringent test on the form of the correlation operator, deficiencies in the correlation operator giving corresponding errors in the spectrum. Good results are obtained for the density dependence of the roton energy. A variational principle for the free energy is used to generalize the correlation operator technique to finite temperatures. Results are given for the finite temperature properties of the v8-model of nuclear matter."

Aug 1, 19790 citations

Microscopic Analysis of Interacting Elementary Excitations in Bose Systems.

Jorge Alberto Carballo

Jan 1, 19750 citations

Excitation Spectrum and Liquid-Structure Function of a Charged Bose Gas

A. Bhattacharyya, Chia-Wei Woo

The excitation spectrum of a charged Bose gas in the high-density limit is calculated to two orders in the expansion parameter ${r}_{s}^{\frac{3}{4}}$ by the method of correlated basis functions (CBF). To $O({r}_{s}^{\frac{3}{4}})$ , the result differs from that obtained variationally, but agrees with that obtained by Ma and Woo via diagrammatic perturbation theory. The choice of the basis functions is, however, not unique. By choosing an alternate set of CBF which employs the ground-state eigenfunction as a correlating factor, we find it possible to extract from the excitation spectrum an expression for the liquid-structure function, also to two orders in ${r}_{s}^{\frac{3}{4}}$ , which represents a new result. This new facet of CBF helps to demonstrate the flexibility of the method and the ease with which it can be applied to calculating properties of many-particle systems, model as well as realistic.The excitation spectrum of a charged Bose gas in the high-density limit is calculated to two orders in the expansion parameter ${r}_{s}^{\frac{3}{4}}$ by the method of correlated basis functions (CBF). To $O({r}_{s}^{\frac{3}{4}})$, the result differs from that obtained variationally, but agrees with that obtained by Ma and Woo via diagrammatic perturbation theory. The choice of the basis functions is, however, not unique. By choosing an alternate set of CBF which employs the ground-state eigenfunction as a correlating factor, we find it possible to extract from the excitation spectrum an expression for the liquid-structure function, also to two orders in ${r}_{s}^{\frac{3}{4}}$, which represents a new result. This new facet of CBF helps to demonstrate the flexibility of the method and the ease with which it can be applied to calculating properties of many-particle systems, model as well as realistic.

Physical Review AJan 1, 197311 citations

Formation of selfbound states in a one-dimensional nuclear model—a renormalization group based density functional study

Sandra Kemler, Martin Pospiech, Jens Braun

Abstract In nuclear physics, density functional theory (DFT) provides the basis for state-of-the art studies of ground-state properties of heavy nuclei. However, the direct relation of the density functional underlying these calculations and the microscopic nuclear forces is not yet fully understood. We present a combination of DFT and renormalization group (RG) techniques which allows to study selfbound many-body systems from microscopic interactions. We discuss its application with the aid of systems of identical fermions interacting via a long-range attractive and short-range repulsive two-body force in one dimension. We compute ground-state energies, intrinsic densities, and density correlation functions of these systems and compare our results to those obtained from other methods. In particular, we show how energies of excited states as well as the absolute square of the ground-state wave function can be extracted from the correlation functions within our approach. The relation between many-body perturbation theory and our DFT-RG approach is discussed and illustrated with the aid of the calculation of the second-order energy correction for a system of N identical fermions interacting via a general two-body interaction. Moreover, we discuss the control of spuriously emerging fermion self-interactions in DFT studies within our framework. In general, our approach may help to guide the development of energy functionals for future quantitative DFT studies of heavy nuclei from microscopic interactions.Abstract In nuclear physics, density functional theory (DFT) provides the basis for state-of-the art studies of ground-state properties of heavy nuclei. However, the direct relation of the density functional underlying these calculations and the microscopic nuclear forces is not yet fully understood. We present a combination of DFT and renormalization group (RG) techniques which allows to study selfbound many-body systems from microscopic interactions. We discuss its application with the aid of systems of identical fermions interacting via a long-range attractive and short-range repulsive two-body force in one dimension. We compute ground-state energies, intrinsic densities, and density correlation functions of these systems and compare our results to those obtained from other methods. In particular, we show how energies of excited states as well as the absolute square of the ground-state wave function can be extracted from the correlation functions within our approach. The relation between many-body perturbation theory and our DFT-RG approach is discussed and illustrated with the aid of the calculation of the second-order energy correction for a system of N identical fermions interacting via a general two-body interaction. Moreover, we discuss the control of spuriously emerging fermion self-interactions in DFT studies within our framework. In general, our approach may help to guide the development of energy functionals for future quantitative DFT studies of heavy nuclei from microscopic interactions.

arXiv:1606.04388Journal of Physics G Nuclear and Particle PhysicsDec 5, 201625 citations

Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum

Élliott H. Lieb

Springer eBooksJan 1, 200433 citations

The excitation spectrum of a charged Bose gas in the high-density limit is calculated to two orders in the expansion parameter

{r}_{s}^{\frac{3}{4}}

by the method of correlated basis functions (CBF). To

O({r}_{s}^{\frac{3}{4}})

, the result differs from that obtained variationally, but agrees with that obtained by Ma and Woo via diagrammatic perturbation theory. The choice of the basis functions is, however, not unique. By choosing an alternate set of CBF which employs the ground-state eigenfunction as a correlating factor, we find it possible to extract from the excitation spectrum an expression for the liquid-structure function, also to two orders in

{r}_{s}^{\frac{3}{4}}

, which represents a new result. This new facet of CBF helps to demonstrate the flexibility of the method and the ease with which it can be applied to calculating properties of many-particle systems, model as well as realistic.