Biomedical subjects

A A Shanenko

Publications and source records attributed to A A Shanenko.

2 recordsLinked to original sources

PubMed2001

Dilute Bose gas in two dimensions: density expansions and the Gross-Pitaevskii equation.

A dilute homogeneous two-dimensional (2D) Bose gas at zero temperature is studied with the method developed earlier by the authors. This method allows for considering renormalization of an arbitrary pairwise potential in a self-consistent manner, without the pseudopotential delta-function representation. Low-density expansions are derived for the chemical potential, ground-state energy, pair distribution function, kinetic and interaction energies. The expansion parameter is found to be a dimensionless in-medium scattering amplitude u obeying the equation 1/u+ln u=-ln(na(2)pi)-2gamma, where na(2) and gamma are the gas parameter and the Euler constant, respectively. It is shown that the ground-state energy is mostly kinetic in the low-density limit. This result does not depend on a specific form of the pairwise interaction potential, contrary to the 3D case. A new form of the 2D Gross-Pitaevskii equation is proposed within our scheme.

Journal Article↗

PubMed1999

Dilute Bose gas revised.

The well-known results concerning a dilute Bose gas with the short-range repulsive interaction should be reconsidered due to a thermodynamic inconsistency of the method being basic to much of the present understanding of this subject. The aim of our paper is to propose another way of treating the dilute Bose gas with an arbitrary strong interaction. Using the reduced density matrix of the second order and a variational procedure, this way allows us to escape the inconsistency mentioned and operate with singular potentials of the Lennard-Jones type. The derived expansion of the condensate depletion in powers of the boson density n=N/V reproduces the familiar result, while the expansion for the mean energy per particle is of the form epsilon=2 pi planck(2)an/m[1+128/(15 square root of [pi]) square root of [na(3)](1-5b/8a)+...], where a is the scattering length and b> or =0 stands for one more characteristic length depending on the shape of the interaction potential (in particular, for the hard spheres a=b). All the consideration concerns the zero temperature.

Journal Article↗