Number-non-conserving terms in quadratic bosonic Hamiltonians can induce unwanted dynamical instabilities. By exploiting the pseudo-Hermitian structure built in to these Hamiltonians, we show that as long as dynamical stability holds, one may always construct a non-trivial dual (unitarily equivalent) number-conserving quadratic bosonic Hamiltonian. We exemplify this construction for a gapped harmonic chain and a bosonic analogue to Kitaev's Majorana chain. Our duality may be used to identify local number-conserving models that approximate stable bosonic Hamiltonians without the need for parametric amplification and to implement non-Hermitian ##IMG## [http://ej.iop.org/images/0295-5075/131/4/40006/epl20263ieqn1.gif] {$\mathcal{P}\mathcal{T}$} -symmetric dynamics in non-dissipative number-conserving bosonic systems. Implications for computing topological invariants are addressed.

中文翻译：

---

用对偶性恢复二次玻色子哈密顿量的数守恒

二次玻色子哈密顿量中的非守恒项会引起不希望的动力学不稳定性。通过利用内置在这些哈密顿量中的伪-Hermitian结构，我们表明，只要保持动力学稳定性，就可以始终构造一个非平凡的对偶（单位等价）数守恒的二次玻色子哈密顿量。我们举例说明了有间隙的谐波链和Kitaev的Majorana链的玻色类似物的这种构造。我们的对偶性可用于识别近似稳定的玻色子哈密顿量的局部数守恒模型，而无需参数放大，并用于实现非埃尔米特数## IMG ## /131/4/40006/epl20263ieqn1.gif] {$ \ mathcal {P} \ mathcal {T} $}-非耗散数守恒Bosonic系统中的对称动力学。