论文标题
在特殊点上的非热性干扰墓地
Interference of non-Hermiticity with Hermiticity at exceptional points
论文作者
论文摘要
A family of non-Hermitian but ${\cal PT}-$symmetric $2J$ by $2J$ toy-model tridiagonal-matrix Hamiltonians $H^{(2J)}=H^{(2J)}(t)$ with $J=K+M=1,2,\ldots$ and $t<J^2$ is studied, for which a real but non-Hermitian $ 2K $ x $ 2k $ tridiagonal-submatrix组件$ c（t）$ the hamiltonian的$ c耦合到其其他两个复合体，但Hermitian $ m $ by $ m $ tridiagonal-submatrix components $ a（t）$ a（t）$和$ b（t）$。通过施工，（i）所有子膜的分解为$ t = t_m = m \，（2J-m）$，$ m = 1,2，\ ldots，j $; （ii）在所有参数上，$ t = t_m $，$ m = j-k = 0,1，\ ldots，j-1 $ hamiltonian不再是可对角线的，表现出Kato的非凡订单订单的特殊点$ 2K $; （iv）当$ t \ leq t_ {j-1} = j^2-1 $时，系统的$ {\ cal pt} - $对称会自发折断。
A family of non-Hermitian but ${\cal PT}-$symmetric $2J$ by $2J$ toy-model tridiagonal-matrix Hamiltonians $H^{(2J)}=H^{(2J)}(t)$ with $J=K+M=1,2,\ldots$ and $t<J^2$ is studied, for which a real but non-Hermitian $2K$ by $2K$ tridiagonal-submatrix component $C(t)$ of the Hamiltonian is assumed coupled to its other two complex but Hermitian $M$ by $M$ tridiagonal-submatrix components $A(t)$ and $B(t)$. By construction, (i) all of the submatrices get decoupled at $t=t_M=M\,(2J-M)$ with $M=1,2,\ldots,J$; (ii) at all of the parameters $t=t_M$ with $M=J-K=0,1,\ldots,J-1$ the Hamiltonian ceases to be diagonalizable exhibiting the Kato's exceptional-point degeneracy of order $2K$; (iv) the system's ${\cal PT}-$symmetry gets spontaneously broken when $t\leq t_{J-1}=J^2-1$.
