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Investigating the generality of time-local master equations

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maldonado_mundo2014physreva042107.pdf (390.4Kb)
Date
08/10/2012
Author
Maldonado-Mundo, Daniel
Oehberg, Patrik
Lovett, Brendon W.
Andersson, Erika
Keywords
Dynamical semigroups
Quantum
QC Physics
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Abstract
Time-local master equations are more generally applicable than is often recognized, but at first sight, it would seem that they can only safely be used in time intervals where the time evolution is invertible. Using the Jaynes-Cummings model, we here construct an explicit example where two different Hamiltonians, corresponding to two different noninvertible and non-Markovian time evolutions, lead to arbitrarily similar time-local master equations. This illustrates how the time-local master equation, on its own in this case, does not uniquely determine the time evolution. The example is, nevertheless, artificial in the sense that a rapid change in (at least) one of the Hamiltonians is needed. The change must also occur at a very specific instance in time. If a Hamiltonian is known not to have such very specific behavior but is "physically well behaved," then one may conjecture that a time-local master equation also determines the time evolution when it is not invertible.
Citation
Maldonado-Mundo , D , Oehberg , P , Lovett , B W & Andersson , E 2012 , ' Investigating the generality of time-local master equations ' , Physical Review. A, Atomic, molecular, and optical physics , vol. 86 , no. 4 , 042107 . https://doi.org/10.1103/PhysRevA.86.042107
Publication
Physical Review. A, Atomic, molecular, and optical physics
Status
Peer reviewed
DOI
https://doi.org/10.1103/PhysRevA.86.042107
ISSN
1050-2947
Type
Journal article
Rights
© 2012. American Physical Society.
Description
We acknowledge helpful discussions with J. Cresser. D.M.-M. acknowledges support from the EPSRC CMDTC,P.O. acknowledges support from EPSRC Grant No. EP/J001392/1, B.W.L. thanks the Royal Society for a University Research Fellowship, and E.A. acknowledges partial support from EPSRC Grant No. EP/G009821/1.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/5201

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