论文标题
量子准系统：属性和应用
Quantum quasi-Lie systems: properties and applications
论文作者
论文摘要
Lie系统是一个非自主系统的普通微分方程的非自主系统，描述了$ t $依赖性的向量场的积分曲线，该曲线在矢量字段的有限维谎言代数中采用值。 Lie Systems已在文献中被推广，以处理由特定类别的$ t $依赖性的汉密尔顿运营商，量子Lie Systems和其他微分方程通过所谓的Quasi-lie方案确定的$ t $依赖的schrödinger方程。这项工作扩展了准级方案和量子谎言系统，以应对与此处称为Quantum Quasi-lie Systems相关的$ t $依赖性schrödinger方程。为了说明我们的方法，我们提出和研究了Perelomov搜索的经典非线性振荡器的量子类似物，并分析了诱捕电势的量子一维流体以及量子$ t $依赖性的smorodinsky--Winternitz振荡器。
A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised in the literature to deal with $t$-dependent Schrödinger equations determined by a particular class of $t$-dependent Hamiltonian operators, the quantum Lie systems, and other differential equations through the so-called quasi-Lie schemes. This work extends quasi-Lie schemes and quantum Lie systems to cope with $t$-dependent Schrödinger equations associated with the here called quantum quasi-Lie systems. To illustrate our methods, we propose and study a quantum analogue of the classical nonlinear oscillator searched by Perelomov and we analyse a quantum one-dimensional fluid in a trapping potential along with quantum $t$-dependent Smorodinsky--Winternitz oscillators.
