An Effect of the Space Dimension of Electron Fermi Gas upon the Spin Ordering in Clusters and Nanoparticles

Abstract

Herein, the collective effects of spin polarization in a degenerate electron gas of an arbitrary space dimension are discussed. We consider these low-dimensional systems in light of potential wells (rectangular or cylindrical), and as a two- or one-dimensional oscillator system with the second (and third) spatial dimension proportional to the oscillator’s length. The concept of “intermediate„ sizes ν = 6, 5, 4 corresponding to the quasi-low dimensions ν* = 0, 1, 2, contrary to “pure„ space dimensions ν = 1, 2 is introduced. A general effect of the space dimension upon the spontaneous polarization in electron Fermi gas is detected.

Keywords

• quasi-two
• quasi-one
• quasi-zero dimension Fermi system
• intermediate dimension of phase space
• polarized state
• critical parameter
• a general criterion for the spontaneous polarization