Quantum mechanics

Density matrix

Lindblad equation

Mathematical physics

Boundary (topology)

Boundary value problem

Mathematical optimization

Hamiltonian (control theory)

Classical mechanics

Dissipation

Physics

Periodic boundary conditions

Mathematics

Mathematical analysis

Quantum

Combinatorics

Topology (electrical circuits)

Master equation

Hermitian matrix

Dissipative system

Physical Review Research

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 boundary condition (OBC) and periodic boundary condition (PBC). 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 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 differs in the effective non-Hermitian Hamiltonian limit and the full master equation framework.

Liouvillian skin effect in an exactly solvable model