Non-Hermitian adiabatic transport in spaces of exceptional points
| Autor: | Höller, J., Read, N., Harris, J. G. E. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Phys. Rev. A 102, 032216 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.102.032216 |
| Popis: | We consider the space of $n \times n$ non-Hermitian Hamiltonians ($n=2$, $3$, . . .) that are equivalent to a single $n\times n$ 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 $T=1/\varepsilon$ 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 $\varepsilon^{-1}$ times an expansion in powers of $\varepsilon^{1/n}$. The exponential of the term of $n$th order (which is equivalent to the "geometric" or Berry phase modulo $2\pi$), is thus independent of $\varepsilon$ as $\varepsilon\to0$; it depends only on the homotopy class of the loop and is an integer power of $e^{2\pi i/n}$. 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. Comment: 4+3 pages. v2: slight title change; 9 pages, now in regular article format; as published |
| Databáze: | arXiv |
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