scholarly journals A thermodynamically consistent Markovian master equation beyond the secular approximation

2021 ◽  
Author(s):  
Patrick Potts ◽  
Alex Kalaee ◽  
Andreas Wacker
Keyword(s):  
Master Equation ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Memory Effects ◽  
Master Equations ◽  
Open Quantum ◽  
Laws Of Thermodynamics ◽  
Versatile Tool ◽  
Approximate Nature ◽  
Secular Approximation

Abstract Markovian master equations provide a versatile tool for describing open quantum systems when memory effects of the environment may be neglected. As these equations are of an approximate nature, they often do not respect the laws of thermodynamics when no secular approximation is performed in their derivation. Here we introduce a Markovian master equation that is thermodynamically consistent and provides an accurate description whenever memory effects can be neglected. The thermodynamic consistency is obtained through a rescaled Hamiltonian for the thermodynamic bookkeeping, exploiting the fact that a Markovian description implies a limited resolution for heat. Our results enable a thermodynamically consistent description of a variety of systems where the secular approximation breaks down.

scholarly journals Adiabatically steered open quantum systems: Master equation and optimal phase

2010 ◽  
Vol 82 (6) ◽  
Author(s):  
J. Salmilehto ◽  
P. Solinas ◽  
J. Ankerhold ◽  
M. Möttönen
Keyword(s):  
Master Equation ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Testing the Validity of the ‘Local’ and ‘Global’ GKLS Master Equations on an Exactly Solvable Model

2017 ◽  
Vol 24 (04) ◽  
pp. 1740010 ◽  
Author(s):  
J. Onam González ◽  
Luis A. Correa ◽  
Giorgio Nocerino ◽  
José P. Palao ◽  
Daniel Alonso ◽  
...  
Keyword(s):  
Master Equation ◽  
Open Quantum Systems ◽  
Solvable Model ◽  
Exact Result ◽  
Quantum Systems ◽  
Local Approach ◽  
Weakly Coupled ◽  
Exactly Solvable ◽  
Global And Local ◽  
Secular Approximation

When deriving a master equation for a multipartite weakly-interacting open quantum systems, dissipation is often addressed locally on each component, i.e. ignoring the coherent couplings, which are later added ‘by hand’. Although simple, the resulting local master equation (LME) is known to be thermodynamically inconsistent. Otherwise, one may always obtain a consistent global master equation (GME) by working on the energy basis of the full interacting Hamiltonian. Here, we consider a two-node ‘quantum wire’ connected to two heat baths. The stationary solution of the LME and GME are obtained and benchmarked against the exact result. Importantly, in our model, the validity of the GME is constrained by the underlying secular approximation. Whenever this breaks down (for resonant weakly-coupled nodes), we observe that the LME, in spite of being thermodynamically flawed: (a) predicts the correct steady state, (b) yields with the exact asymptotic heat currents, and (c) reliably reflects the correlations between the nodes. In contrast, the GME fails at all three tasks. Nonetheless, as the inter-node coupling grows, the LME breaks down whilst the GME becomes correct. Hence, the global and local approach may be viewed as complementary tools, best suited to different parameter regimes.

scholarly journals On Time-Local Generators of Quantum Evolution

2014 ◽  
Vol 21 (01n02) ◽  
pp. 1440004 ◽  
Author(s):  
Dariusz Chruściński
Keyword(s):  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Master Equations ◽  
Quantum Evolution ◽  
Completely Positive ◽  
Open Quantum ◽  
The Family

We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum evolutions. The analysis of Markovian and non-Markovian quantum dynamics is presented as well. The whole discussion is illustrated by the family of many instructive examples.

scholarly journals Post-Markov master equation for the dynamics of open quantum systems

2000 ◽  
Vol 265 (5-6) ◽  
pp. 331-336 ◽  
Author(s):  
Ting Yu ◽  
Lajos Diósi ◽  
Nicolas Gisin ◽  
Walter T. Strunz
Keyword(s):  
Master Equation ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum ◽  
Markov Master Equation

NON-MARKOVIAN OPEN QUANTUM SYSTEMS: SYSTEM–ENVIRONMENT CORRELATIONS IN DYNAMICAL MAPS

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1617-1634 ◽  
Author(s):  
CÉSAR A. RODRÍGUEZ-ROSARIO ◽  
E. C. G. SUDARSHAN
Keyword(s):  
Master Equation ◽  
Quantum Discord ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Complete Positivity ◽  
System Environment ◽  
Open Quantum ◽  
Mathematical Properties ◽  
Classical Correlations ◽  
The Relationship

We construct a non-Markovian dynamical map that accounts for systems correlated to the environment. We refer to it as a canonical dynamical map, which forms an evolution family. The relationship between inverse maps and correlations with the environment is established. The mathematical properties of complete positivity is related to classical correlations, according to quantum discord, between the system and the environment. A generalized non-Markovian master equation is derived from the canonical dynamical map.

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