Northern (Arctic) Federal University, nab. Severnoi Dviny 17, 163002, Arkhangelsk, Russia.
Phys Rev E. 2018 Apr;97(4-1):042203. doi: 10.1103/PhysRevE.97.042203.
A system of two coupled quantum harmonic oscillators with the Hamiltonian H[over ̂]=1/2(1/m_{1}p[over ̂]{1}^{2}+1/m{2}p[over ̂]{2}^{2}+Ax{1}^{2}+Bx_{2}^{2}+Cx_{1}x_{2}) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H[over ̂]Ψ=iℏ∂Ψ/∂t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.
一个由两个耦合量子谐振子组成的系统，其哈密顿量为 H[over ̂]=1/2(1/m_{1}p[over ̂]{1}^{2}+1/m{2}p[over ̂]{2}^{2}+Ax{1}^{2}+Bx_{2}^{2}+Cx_{1}x_{2})，可以在量子和非线性物理、分子化学和生物物理的许多应用中找到。这样的系统的定态波函数是已知的，但是由于计算施密特模式的复杂性，它在量子纠缠分析中的应用受到了限制。此外，对于这样的动力系统，非定态薛定谔方程 H[over ̂]Ψ=iℏ∂Ψ/∂t 和施密特模式没有精确的解析解。在本文中，我们找到了非定态薛定谔方程的解；我们还以解析形式找到了定态和动力问题的施密特模式的解。基于施密特模式，分析了所考虑系统的量子纠缠。结果表明，对于系统的某些参数，量子纠缠可以非常大。
