PT-symmetric quantum Liouvillian dynamics

Abstract

We discuss a combination of unitary and anti-unitary symmetry of quantum Liouvillian dynamics, in the context of open quantum systems, which implies a D2 symmetry of the complex Liovillean spectrum. For sufficiently weak system-bath coupling it implies a uniform decay rate for all coherences, i.e. off-diagonal elements of the system's density matrix taken in the eigenbasis of the Hamiltonian. As an example we discuss symmetrically boundary driven open XXZ spin 1/2 chains.

Note [18] added with respect to a published version, explaining the symmetry of the matrix V [eq. (14)]

References in corpus (10)

• Making Sense of Non-Hermitian Hamiltonians
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• PT-Symmetric Wave Chaos
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Bypassing the bandwidth theorem with PT symmetry
• Negative differential conductivity in far-from-equilibrium quantum spin chains
• Universal routes to spontaneous PT-symmetry breaking in non-hermitian quantum systems