论文标题
频谱等效的时间依赖性双井和不稳定的非谐振荡器
Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
论文作者
论文摘要
我们构建了一个时间依赖的双井潜力，作为与具有时间依赖性质量项的显式相关的负四分之一振荡器等效的精确光谱。首先，将不稳定的Anharmonic振荡器Hamiltonian定义在下半部分的复合面上的轮廓上，由此产生的时间依赖性的非热汉密尔顿人首先是由时间依赖性的Dyson方程的精确溶液映射到时间依赖性的Hermitian Hamiltonian定义在真实轴心上的。当统一转换，缩放和傅立叶变换时，我们从下面获得了时间相关的双重势能。所有转换都是非扰动进行的，以便在此过程中所有汉密尔顿人在频谱上都完全等效，因为它们具有相同的瞬时能量特征值。
We construct a time-dependent double well potential as an exact spectral equivalent to the explicitly time-dependent negative quartic oscillator with a time-dependent mass term. Defining the unstable anharmonic oscillator Hamiltonian on a contour in the lower-half complex plane, the resulting time-dependent non-Hermitian Hamiltonian is first mapped by an exact solution of the time-dependent Dyson equation to a time-dependent Hermitian Hamiltonian defined on the real axis. When unitary transformed, scaled and Fourier transformed we obtain a time-dependent double well potential bounded from below. All transformations are carried out non-perturbatively so that all Hamiltonians in this process are spectrally exactly equivalent in the sense that they have identical instantaneous energy eigenvalue spectra.
