For an ideal D-dimensional Fermi gas under generic external confinement we derive the correcting coefficient (D − 2)/3D of the von Weizsacker term in the kinetic energy density. To obtain this coefficient we use the Kirzhnits semiclassical expansion of the number operator up to the second order in the Planck constant h̄. Within this simple and direct approach we determine the differential equati...

A relaxation method is employed to study a rotating dense Bose-Einstein condensate beyond Thomas-Fermi approximation. We use a slave-boson model to describe the strongly interacting condensate and derive a generalized non-linear Schrödinger equation with kinetic term for the rotating condensate. In comparison with previous calculations, based on Thomas-Fermi approximation, significant improveme...

Modeling of microbial inactivation by high hydrostatic pressure (HHP) requires a plot of the log microbial count or survival ratio versus time data under a constant pressure and temperature. However, at low pressure and temperature values, very long holding times are needed to obtain measurable inactivation. Since the time has a significant effect on the cost of HHP processing it may be reasona...

Our recent extended constrained-search theory @M. Higuchi and K. Higuchi, Phys. Rev. B 69, 035113 ~2004!# enables us to choose arbitrary quantities as the basic variables of density functional theory. In this paper, we apply it to several cases. In the case in which the occupation matrix of localized orbitals is chosen as a basic variable, we can obtain the single-particle equation which is equ...

We develop a general scheme for the use of Fermi operators within the framework of integrable systems. This enables us to read off a fermionic Hamiltonian from a given solution of the YangBaxter equation and to express the corresponding L-matrix and the generators of symmetries in terms of Fermi operators. We illustrate our approach through a number of examples. Our main example is the algebrai...

A model for the Fermi contact interaction is proposed in which the nuclear moment is represented as a magnetized spherical shell of radius ro. For a hydrogen-like system thus perturbed, the Schr6dinger equation is solvable without perturbation theory by use of the Coulomb Green's function. Approximation formulas are derived in terms of a quantum defect in the Coulombic energy formula. It is sho...

We derive a modification of the semiclassical Fermi Golden Rule collision operator based on quantum thermodynamic principles. The resulting operator is nonlocal in space and acknowledges the presence of steep potential gradients and potential barriers. The resulting quantum mechanical transport equation the Wigner quantum Boltzmann equation increases the corresponding quantum mechanical entropy...

We present theoretical predictions for the equation of state of a harmonically trapped Fermi gas in the unitary limit. Our calculations compare Monte Carlo results with the equation of state of a uniform gas using three distinct perturbation schemes. We show that in experiments the temperature can be usefully calibrated by making use of the entropy, which is invariant during an adiabatic conver...