Modern Physics Letters B

A quantum N-body problem with 2-component in (2 + 1) dimensions deduced from an integrable model in (2 + 1) dimensions is investigated. The Davey–Stewartson 1 (DS1) system⁹ is an integrable model in two dimensions. A quantum DS1 system with 2 color components in two dimensions has been formulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with 2 color components. The solutions of the two-dimensional problem under consideration has been constructed from the resulting problems in one dimension. For the latter with δ-function interactions and being solved by the Bethe–Yang ansatz, we introduce symmetrical and anti-symmetrical Young operators of the permutation group and obtain the exact solutions for the quantum DS1 system. The application of the solutions is discussed.

After 12 years of research on the thermodynamics of low-pressure diamond synthesis, a "bug" has been found hidden in classical thermodynamics for 150 years. On removing this bug, a new field of nonequilibrium nondissipative thermodynamics emerges, and the complete systematization of modern thermodynamics can be naturally obtained. It means that thermodynamics enters entirely into a new era: modern thermodynamics.

Artificial metal nanocluster crystals, (i.e. periodic lattices consisting of identical metal nanoclusters) were fabricated using a novel technique in which surface mediated magic clustering was used to achieve identical cluster size, while the Si(111)-7 × 7 surface was used as a template for ordering the clusters. The universality of this strategy was demonstrated by fabricating more than 10 different nanocluster arrays with different metals and alloys. The atomic structures, formation mechanism and stability of the nanoclusters were studied with in situ scanning tunneling microscopy combined with first-principles total energy calculations. Our study shows that delicate control of growth kinetics is extremely important for cluster crystal fabrication.

Exact analytical representations for W. Gordon's integral by means of Appell's functions are given. It is shown that they correlate between each other. But representation of this integral by means of Appell's function F₂ is more attractive.

The total relativistic kinetic energy of the Thomas–Fermi atom is E_kr = E_k + E_r, where E_k = κ_k ∫ ρ^5/3dv and E_r = -κ_r ∫ ρ^7/3dv + o(α²), . The minimum pressure of a relativistic degenerate electron gas is . In just the same way, the cases x = p_μ / mc = 1 and x > 1 are explicitly considered.

The evolutions of the von Neumann entropies of the low-lying states in two vertically coupled identical single-electron quantum dot systems with increasing magnetic field and inter-dot separation have been investigated. We show that both the external magnetic field and the inter-dot separation can induce the transition of the entropy of the system. Additionally, a suspicion (that is, the higher the excitation, the larger entropy) has been clarified and proven to be incorrect.

Powder X-ray diffraction structural studies on aluminum-doped lanthanum borates La_4-yAl_yB₄O₁₂ were carried out on samples with y = 1, 2 starting compositions heat-treated at temperatures between 860°C and 1200°C. The samples were prepared by the sol-gel method. The structural data were obtained by the Rietveld refinement of the XRD patterns.