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Non-Hermitian adiabatic transport in spaces of exceptional points
Physical Review A ( IF 2.6 ) Pub Date : 2020-09-16 , DOI: 10.1103/physreva.102.032216
J. Höller , N. Read , J. G. E. Harris

We consider the space of n×n non-Hermitian Hamiltonians (n=2, 3, ...) that are equivalent to a single n×n Jordan block. We focus on adiabatic transport around a closed path (i.e., a loop) within this space, in the limit as the time scale T=1/ɛ taken to traverse the loop tends to infinity. We show that, for a certain class of loops and a choice of initial state, the state returns to itself and acquires a complex phase that is ɛ1 times an expansion in powers of ɛ1/n. The exponential of the term of nth order (which is equivalent to the “geometric” or Berry phase modulo 2π) is thus independent of ɛ as ɛ0; it depends only on the homotopy class of the loop and is an integer power of e2πi/n. One of the conditions under which these results hold is that the state being transported is, for all points on the loop, that of slowest decay.

中文翻译:

特殊地点空间中的非赫米特绝热运输

我们考虑的空间 ñ×ñ 非埃尔米特哈密顿量(ñ=2,3,...)相当于一个 ñ×ñ乔丹街区。我们专注于围绕该空间的闭合路径(即环路)的绝热运输,其极限是时间尺度Ť=1个/ɛ遍历循环趋于无穷大。我们表明,对于特定类型的循环和初始状态的选择,状态会返回自身并获得一个复杂的相位,即ɛ-1个 倍增权力 ɛ1个/ñ。项的指数ñ 阶(等效于“几何”或贝里相位模 2π)因此独立于 ɛɛ0; 它仅取决于循环的同伦类,并且是Ë2π一世/ñ。这些结果成立的条件之一是,对于环路上的所有点,传输的状态都是最慢的衰减状态。
更新日期:2020-09-16
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