New families of non-parity-time-symmetric complex potentials with all-real spectra
New families of non-parity-time-symmetric complex potentials with all-real spectra
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DOI：
10.1063/1.5124255
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发表时间：
2019-08
期刊：
影响因子：
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通讯作者：
B. Bagchi;Jianke Yang
中科院分区：
文献类型：
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作者：
B. Bagchi;Jianke Yang
利用超对称方法和伪厄米方法，导出了具有全实谱的非奇偶时对称复势族。利用超对称方法，我们找到了具有已知实谱的非奇偶时对称复伴势族，它们与基势具有相同的谱，如（复）Wadati势。与以往的实谱势的超对称推导不同，我们的推导没有利用基势的离散本征模。因此，我们的伙伴势具有包含自由函数的显式解析表达式。利用伪厄米方法，导出了一类具有自由函数和常数的非奇偶-时间对称复势，其特征值表现为共轭对。这种特征值对称性迫使谱在很大范围内选择这些函数和势中的常数时都是全实的。调整这些自由函数和常数，也可以诱导相变，其中在光谱中出现复特征值的共轭对。
New families of non-parity-time-symmetric complex potentials with all-real spectra are derived by the supersymmetry method and the pseudo-Hermiticity method. With the supersymmetry method, we find families of non-parity-time-symmetric complex partner potentials which share the same spectrum as base potentials with known real spectra, such as the (complex) Wadati potentials. Different from previous supersymmetry derivations of potentials with real spectra, our derivation does not utilize discrete eigenmodes of base potentials. As a result, our partner potentials feature explicit analytical expressions which contain free functions. With the pseudo-Hermiticity method, we derive a new class of non-parity-time-symmetric complex potentials with free functions and constants, whose eigenvalues appear as conjugate pairs. This eigenvalue symmetry forces the spectrum to be all-real for a wide range of choices of these functions and constants in the potential. Tuning these free functions and constants, phase transition can also be induced, where conjugate pairs of complex eigenvalues emerge in the spectrum.