scholarly journals Area law for fixed points of rapidly mixing dissipative quantum systems

2015 ◽  
Vol 56 (10) ◽  
pp. 102202 ◽  
Author(s):  
Fernando G. S. L. Brandão ◽  
Toby S. Cubitt ◽  
Angelo Lucia ◽  
Spyridon Michalakis ◽  
David Perez-Garcia
Keyword(s):  
Fixed Points ◽  
Quantum Systems ◽  
Dissipative Quantum Systems ◽  
Area Law

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

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.

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 A tight nonlinear approximation theory for time dependent closed quantum systems

2019 ◽  
Vol 27 (3) ◽  
pp. 141-154
Author(s):  
Joseph W. Jerome
Keyword(s):  
Fixed Points ◽  
Nonlinear Approximation ◽  
Quantum Systems ◽  
Time Dependent ◽  
Projection Operators ◽  
Evolution Operators ◽  
Actual Application ◽  
Hartree Potential ◽  
Dependent Potential ◽  
External Time

Abstract The approximation of fixed points by numerical fixed points was presented in the elegant monograph of Krasnosel’skii et al. (1972). The theory, both in its formulation and implementation, requires a differential operator calculus, so that its actual application has been selective. The writer and Kerkhoven demonstrated this for the semiconductor drift-diffusion model in 1991. In this article, we show that the theory can be applied to time dependent quantum systems on bounded domains, via evolution operators. In addition to the kinetic operator term, the Hamiltonian includes both an external time dependent potential and the classical nonlinear Hartree potential. Our result can be paraphrased as follows: For a sequence of Galerkin subspaces, and the Hamiltonian just described, a uniquely defined sequence of Faedo–Galerkin solutions exists; it converges in Sobolev space, uniformly in time, at the maximal rate given by the projection operators.

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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