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Preprint
An elementary construction of the GKSL master equation for N-level systems
arXiv.org
05 Sep 2024
Abstract
The GKSL master equation for N-level systems provides a necessary and
sufficient form for the generator of a quantum dynamical semigroup in the
Schrodinger picture where the underlying Hilbert space is $\mathbb{C}^N$. In
this paper we provide a detailed, self-contained, and elementary construction
of the GKSL master equation for an N-level system. We also provide necessary
and sufficient conditions for forms of generators of semigroups which have
some, but not all, of the defining properties of quantum dynamical semigroups.
We do this in such a way to illuminate how each defining property of a quantum
dynamical semigroup contributes to the form of the generators.
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Details
- Title
- An elementary construction of the GKSL master equation for N-level systems
- Creators
- Matthew Ziemke
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021902615504721