Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator＇s Wave Functions

We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.     

Magnetic and Elastic Vibrations in Manganese–Zinc Spinel Crystals as the Functions of Anisotropy Constant

The amplitudes of magnetic and elastic vibrations for Mn_0.61Zn_0.35Fe_2.04O₄ spinel crystalline slab are calculated by solving the equations describing the magnetic and elastic dynamics. The anisotropy constants, magnetization, second-order elastic constants and magnetoelastic coupling constants for a studied crystal are expressed as the functions of temperature. The magnetization vector and elastic shear components are found as the functions of the first magnetic anisotropy constant at different values of an external constant magnetic field greater than a saturation field. The procession patterns for normally and tangentially magnetized slabs are displayed for two values of the first anisotropy constant. High absolute values of the first anisotropy constant are shown to refer to reorientation of the magnetization vector.     

Microstructure and Mechanical Properties of Multilayer α-AlN/α-BCN Coating as Functions of the Current Density during Sputtering of a B<Subscript>4</Subscript>C Target

Multilayer AlN/BCN coating of nanometer scale have been prepared by magnetron sputtering of Al and B₄C targets in an argon–nitrogen atmosphere during deposition on a Si substrate. These coating have an X-ray amorphous structure and the maximum Knoop hardness of 27 GPa (at the current density 100 mA). The first-principle molecular dynamics calculations show that the B4–BN layer is dynamically unstable; thus, it will not be epitaxial and will be amorphous or have a structure different from the B4–BN structure. The thermal vacuum annealing from 600 to 800°C of samples with multilayer nanosized coating leads to the decrease in the Knoop hardness to 18 GPa; however, the coating structure is retained X-ray amorphous.