Dynamical maps beyond Markovian regime
- URL: http://arxiv.org/abs/2209.14902v1
- Date: Thu, 29 Sep 2022 16:06:03 GMT
- Title: Dynamical maps beyond Markovian regime
- Authors: Dariusz Chru\'sci\'nski
- Abstract summary: We analyze quantum dynamics governed by time-local generators and/or non-local memory kernels.
Special attention is devoted to the concept of em divisibility which is often used as a definition of Markovianity.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Quantum dynamical maps provide suitable mathematical representation of
quantum evolutions. It is the very notion of complete positivity which provides
a proper mathematical representation of quantum evolution and gives rise to the
powerful generalization of unitary evolution of closed Hamiltonian systems. A
prominent example of quantum evolution of an open system is a Markovian
semigroup. In what follows, we analyze both the semigroups of positive and
completely positive maps. In the latter case the dynamics is governed by the
celebrated Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) Master Equation.
Markovian semigroups, however, provide only an approximate description of
general quantum evolution. The main topic of our analysis are dynamical maps
beyond this regime. Non-Markovian quantum evolution attracted a lot of
attention in recent years and there is a vast literature dedicated to it. In
this report we analyze quantum dynamics governed by time-local generators
and/or non-local memory kernels. A special attention is devoted to the concept
of {\em divisibility} which is often used as a definition of Markovianity. In
particular, the concept of so called CP-divisibility (in contrast to
P-divisibility) is widely accepted as a proper definition of quantum
Markovianity. We discuss a number of important physical implications of
divisibility. We also briefly discuss the notion of Markovianity beyond the
dynamical map, that is, when one has an access to the evolution of `system +
environment'. The entire exposition is concentrated more on the general
concepts and intricate connections between them than on studying particular
systems. We illustrate the analyzed concepts by paradigmatic models of open
quantum systems like the amplitude damping and phase damping models.
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