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26 April 2024 |
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Article overview
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Liouvillian Skin Effect in an Exactly Solvable Model | | Fan Yang
; Qing-Dong Jiang
; Emil J. Bergholtz
; | | Date: |
2 Mar 2022 | | Abstract: | The interplay between dissipation, topology and sensitivity to boundary
conditions has recently attracted tremendous amounts of attention at the level
of effective non-Hermitian descriptions. Here we exactly solve a quantum
mechanical Lindblad master equation describing a dissipative topological
Su-Schrieffer-Heeger (SSH) chain of fermions for both open and periodic
boundary conditions. We find that the extreme sensitivity on the boundary
conditions associated with the non-Hermitian skin effect is directly reflected
in the rapidities governing the time evolution of the density matrix giving
rise to a {it Liouvillian Skin Effect}. This leads to several intriguing
phenomena including boundary sensitive damping behavior, steady state currents
in finite periodic systems, and diverging relaxation times in the limit of
large systems. We illuminate how the role of topology in these systems differ
in the effective non-Hermitian Hamiltonian limit and the full master equation
framework. | | Source: | arXiv, 2203.01333 | | Services: | Forum | Review | PDF | Favorites | |
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