One-dimensional Oscillator System Research Articles

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

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.

Universality classes for thermal transport in one-dimensional oscillator systems.

Two universality classes for thermal transport in one-dimensional oscillator systems are proposed. In class A the asymptotic behavior of the frequency dependent thermal conductivity is κ(ω)∼ω-1/2, whereas the bulk viscosity is finite. In class B the asymptotic behavior of the thermal conductivity is κ∼ω-α, where α<0.4, and the frequency dependent bulk viscosity has the same asymptotic behavior as the thermal conductivity. It is further proposed that the criterion for membership in class A is that the ratio of specific heat capacities γ≡cP/cV=1. A one-dimensional cubic-plus-quartic coupled oscillator is examined at conditions for which γ=1 but P≠0. It is found that the system belongs to class A, in agreement with the proposed criterion. Additionally, it is proposed that examination of whether a system has a well-defined bulk Prandtl number is a more reliable way of determining whether a system is in class A or class B.

Predicting and identifying finite-size effects in current spectra of one-dimensional oscillator chains

The existence of a finite-size effect in one-dimensional oscillator systems causing the energy current power spectrum to saturate to a constant value at low frequencies is discussed. It is shown that a mode-coupling theory presented in earlier papers can be used to predict the frequency of onset of this finite-size effect. This can be used by researchers to plan simulations with large enough numbers of particles to avoid the presence of this finite-size effect.