GKSL generators and digraphs: computing invariant states
Abstract
In recent years, digraph induced generators of quantum dynamical semigroups have been introduced and studied, particularly in the context of unique relaxation and invariance. In this article we define the class of pair block diagonal generators, which allows for additional interaction coefficients but preserves the main structural properties. Namely, when the basis of the underlying Hilbert space is given by the eigenbasis of the Hamiltonian (for example the generic semigroups), then the action of the semigroup leaves invariant the diagonal and off-diagonal matrix spaces. In this case, we explicitly compute all invariant states of the semigroup.
- Publication:
-
Journal of Physics A Mathematical General
- Pub Date:
- July 2019
- DOI:
- 10.1088/1751-8121/ab27f6
- arXiv:
- arXiv:1810.05933
- Bibcode:
- 2019JPhA...52D5201A
- Keywords:
-
- quantum dynamical semigroups;
- invariant states;
- generic semigroups;
- pair block diagonal generators;
- graph induced generators;
- generator induced digraphs;
- Mathematical Physics;
- Quantum Physics;
- 81S22 (Primary) 46L57;
- 47D06;
- 47D07;
- 82C20 (Secondary)
- E-Print:
- doi:10.1088/1751-8121/ab27f6