# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 43: Poster: Quantum Dynamics and Many-Body Systems

### DY 43.14: Poster

### Donnerstag, 30. März 2023, 13:00–16:00, P1

**Explicit expressions for stationary states of the Lindblad equation for a finite state space** — •Bernd Michael Fernengel — TU Darmstadt, Darmstadt, Germany

The Gorini-Kossakowski-Sudarshan-Lindblad Equation is a quantum master equation describing the time evolution of quantum mechanical states. It is used to model open quantum systems. We give explicit expressions of stationary solutions of the Lindblad equation in the case of a finite state space, using the concept of state transition networks of Markov chains. Our treatment is based on the so-called quantum-jump unravelling, which is an ensembles of stochastic quantum trajectories, compatible with the Lindblad equation. A single such trajectory is a piecewise deterministic process, which is interrupted by stochastic jumps. We discuss differences to the classical case and conditions, under which the Lindblad equation is asymptotically stable.