scholarly journals Correction to: Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems

2020 ◽  
Vol 181 (6) ◽  
pp. 2432-2433
Author(s):  
Eric A. Carlen ◽  
Jan Maas
Keyword(s):  
Optimal Transport ◽  
Quantum Systems ◽  
Functional Inequalities ◽  
Dissipative Quantum Systems

scholarly journals Non-commutative Calculus, Optimal Transport and Functional Inequalities in Dissipative Quantum Systems

2019 ◽  
Vol 178 (2) ◽  
pp. 319-378 ◽  
Author(s):  
Eric A. Carlen ◽  
Jan Maas
Keyword(s):  
Spectral Gap ◽  
Optimal Transport ◽  
Quantum Systems ◽  
Sobolev Inequalities ◽  
Unified Framework ◽  
Logarithmic Sobolev Inequalities ◽  
Curvature Bounds ◽  
Finite Dimensional ◽  
Dissipative Quantum Systems ◽  
Entropy Inequalities

AbstractWe study dynamical optimal transport metrics between density matrices associated to symmetric Dirichlet forms on finite-dimensional $$C^*$$ C ∗ -algebras. Our setting covers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, and spectral gap estimates.

scholarly journals Effective quantum Zeno dynamics in dissipative quantum systems

2018 ◽  
Vol 98 (5) ◽  
Author(s):  
Vladislav Popkov ◽  
Simon Essink ◽  
Carlo Presilla ◽  
Gunter Schütz
Keyword(s):  
Quantum Systems ◽  
Quantum Zeno Dynamics ◽  
Dissipative Quantum Systems

The energy minimization problem for two-level dissipative quantum systems

2010 ◽  
Vol 51 (9) ◽  
pp. 092705 ◽  
Author(s):  
B. Bonnard ◽  
O. Cots ◽  
N. Shcherbakova ◽  
D. Sugny
Keyword(s):  
Minimization Problem ◽  
Energy Minimization ◽  
Quantum Systems ◽  
Dissipative Quantum Systems

scholarly journals Dynamical regimes of dissipative quantum systems

2013 ◽  
Vol 88 (24) ◽  
Author(s):  
D. M. Kennes ◽  
O. Kashuba ◽  
V. Meden
Keyword(s):  
Quantum Systems ◽  
Dynamical Regimes ◽  
Dissipative Quantum Systems
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