Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
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DOI：
10.1016/j.physleta.2020.126530
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发表时间：
2020-07-27
影响因子：
2.6
通讯作者：
Tenney, Rebecca
中科院分区：
文献类型：
--
作者：
Fring, Andreas;Tenney, Rebecca
我们构造了一个含时双势垒势，作为一个精确的谱等价于带有含时质量项的显式含时负四次振子。在下半复平面的等高线上定义不稳定的非谐振子哈密顿量，所得到的含时非厄米哈密顿量首先通过含时Dyson方程的精确解映射到定义在实轴上的含时厄米哈密顿量。通过么正变换、定标变换和傅立叶变换，我们得到了含时双势垒势的下界。所有的变换都是非微扰地进行的，因此这个过程中的所有哈密顿量在光谱上是完全等价的，因为它们具有相同的瞬时能量本征值谱。(C)2020爱思唯尔B.V.保留所有权利。
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. (C) 2020 Elsevier B.V. All rights reserved.