Ground State Energy for a Many Boson System: a New Microscopic Approach.
In order to understand a many-body liquid Bose system one must first determine the ground-state (absolute zero temperature) and the equilibrium density. In theory one need only solve the Schrodinger equation for the N -body system to determine these properties. In practice, however, the Schrodinger equation is exactly soluble for every few instances, mostly low-dimensional and/or with simplistic interactions. Therefore, some approximations must be used. Many theoretical approaches, both "perturbative" and "variational", have been applied to the liquid Bose system. Here we employ a perturbative approach, which is based not on the ideal gas as a reference unperturbed state but on the corresponding nontrivial fluid of repulsive particles. We begin with the non-analytic (i.e., non-power) series in the density and coupling obtained through infinite partial summation renormalization techniques for the energy -per-particle. Only the first three coefficients of this series have been determined and the series is initially valid only at small densities and weak coupling values. The original series is rearranged to become a power series in a coupling parameter of the attraction alone, with coefficients which are still non-power series in the density. The later series is extrapolated to higher (i.e., physical) densities with generalized Pade approximants. Standard Pade analyses are applied to the attractive coupling series. Good to excellent results are obtained for several intermolecular potentials in comparison with available computer simulations which essentially give "exact" results.
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- Physics: General