SciPost Phys. 7, 012 (2019) ·
published 25 July 2019

· pdf
We study the reduced timeevolution of open quantum systems by combining
quantuminformation and statistical field theory. Inspired by prior work [EPL
102, 60001 (2013) and Phys. Rev. Lett. 111, 050402 (2013)] we establish the
explicit structure guaranteeing the complete positivity (CP) and
tracepreservation (TP) of the realtime evolution expansion in terms of the
microscopic systemenvironment coupling.
This reveals a fundamental twostage structure of the coupling expansion:
Whereas the first stage defines the dissipative timescales of the system
before having integrated out the environment completely the second stage
sums up elementary physical processes described by CP superoperators. This
allows us to establish the nontrivial relation between the (NakajimaZwanzig)
memorykernel superoperator for the density operator and novel memorykernel
operators that generate the Kraus operators of an operatorsum. Importantly,
this operational approach can be implemented in the existing Keldysh realtime
technique and allows approximations for general timenonlocal quantum master
equations to be systematically compared and developed while keeping the CP and
TP structure explicit.
Our considerations build on the result that a Kraus operator for a physical
measurement process on the environment can be obtained by 'cutting' a group of
Keldysh realtime diagrams 'in half'. This naturally leads to Kraus operators
lifted to the system plus environment which have a diagrammatic expansion in
terms of timenonlocal memorykernel operators. These lifted Kraus operators
obey coupled timeevolution equations which constitute an unraveling of the
original Schr\"odinger equation for system plus environment. Whereas both
equations lead to the same reduced dynamics, only the former explicitly encodes
the operatorsum structure of the coupling expansion.
Prof. Wegewijs: "We thank the referee for caref..."
in Report on Densityoperator evolution: Complete positivity and the Keldysh realtime expansion