论文标题
跨非高米人$ \ Mathcal {pt} $ - 对称量子点和梯子
Transmission across non-Hermitian $\mathcal{PT}$-symmetric quantum dots and ladders
论文作者
论文摘要
连接到半侵蚀性赫米尔米尼晶格的非热区域作为源或水槽起作用，概率电流通常在散射中不保守。即使是$ \ Mathcal {P} \ Mathcal {T} $ - 包含源和水槽的对称区域也不会明显导致当前的保护。我们提出了一个模型，并研究了跨非热$ \ Mathcal {p} \ Mathcal {t} $ - 对称的两级量子点〜（qd），以特殊的方式连接到两个半偶然的一维晶格，以使可能性电流保留下来。 Aharonov-bohm类型阶段包含在模型中，该阶段是由磁性通量（$ \ hbarϕ_ {l} /e，〜\ hbarϕ_ {r} /e $）通过系统中的两个循环产生的。我们表明，当$ ϕ_l = ϕ_r $时，概率电流是保存的。我们发现，在$ \ Mathcal {p} \ Mathcal {t} $ - 不间断阶段（与孤立QD的真实特征力相对应）中，QD之间的传输可以是完美的，而传输在$ \ MATHCAL {p} \ MATHCAL {p} \ MATHCAL {t} $ prake a persigal（per）eig的eig pureige quential quential quential quential quential quential quential quential quential quential quential quential quential qureig pureig s p puroly Image，两个传输峰仅对于磁通的特殊值（是$π\ hbar/2e $）的宽度相同。在破碎的相中，透射峰不令人惊讶地在零能量下。我们通过四个站点的玩具模型深入了解此功能。我们将模型扩展到$ \ MATHCAL {P} \ MATHCAL {T} $ - 对称梯子连接到两个半侵入晶格。我们表明，由于Fabry-Pérot型干扰，可以通过调整化学势来控制梯子的不间断阶段的传播。在梯子的破碎相中，传输被大大抑制。
A non-Hermitian region connected to semi-infinite Hermitian lattices acts either as a source or as a sink and the probability current is not conserved in a scattering typically. Even a $\mathcal{P}\mathcal{T}$-symmetric region that contains both a source and a sink does not lead to current conservation plainly. We propose a model and study the scattering across a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric two-level quantum dot~(QD) connected to two semi-infinite one-dimensional lattices in a special way so that the probability current is conserved. Aharonov-Bohm type phases are included in the model, which arise from magnetic fluxes ($\hbarϕ_{L} /e,~\hbarϕ_{R} /e$) through two loops in the system. We show that when $ϕ_L=ϕ_R$, the probability current is conserved. We find that the transmission across the QD can be perfect in the $\mathcal{P}\mathcal{T}$-unbroken phase (corresponding to real eigenenergies of the isolated QD) whereas the transmission is never perfect in the $\mathcal{P}\mathcal{T}$-broken phase (corresponding to purely imaginary eigenenergies of the QD). The two transmission peaks have the same width only for special values of the fluxes (being odd multiples of $π\hbar/2e$). In the broken phase, the transmission peak is surprisingly not at zero energy. We give an insight into this feature through a four-site toy model. We extend the model to a $\mathcal{P}\mathcal{T}$-symmetric ladder connected to two semi-infinite lattices. We show that the transmission is perfect in unbroken phase of the ladder due to Fabry-Pérot type interference, that can be controlled by tuning the chemical potential. In the broken phase of the ladder, the transmission is substantially suppressed.
