ALGEBRAIC CONDITIONS FOR CONVERGENCE OF A QUANTUM MARKOV SEMIGROUP TO A STEADY STATE

DOI10.1142/S0219025708003142zbMath1165.46035OpenAlexW2030300841MaRDI QIDQ3548313

Franco Fagnola, Rolando Rebolledo Berroeta

Publication date: 11 December 2008

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025708003142

zbMATH Keywords

quantum Markov semigroupsapproach to equilibriumLindblad generatormultiple commutators

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Applications of operator theory in the physical sciences (47N50) Noncommutative dynamical systems (46L55) Quantum stochastic calculus (81S25) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10)

Related Items

Decomposition and Classification of Generic Quantum Markov Semigroups: The Gaussian Gauge Invariant Case ⋮ On the relationship between a quantum Markov semigroup and its representation via linear stochastic Schrödinger equations ⋮ Balance between quantum Markov semigroups ⋮ Support projection of state and a quantum Lévy–Austin–Ornstein theorem ⋮ Environment induced decoherence for Markovian evolutions ⋮ Quantum dynamical semigroups and stability ⋮ Decoherence free subspaces of a quantum Markov semigroup ⋮ The general structure of the decoherence-free subalgebra for uniformly continuous quantum Markov semigroups ⋮ G-Circulant Quantum Markov Semigroups ⋮ On the relationships between covariance and the decoherence-free subalgebra of a quantum Markov semigroup ⋮ Characterization of decoherence-free subsystems ⋮ Decoherence for quantum Markov semi-groups on matrix algebras ⋮ THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR ⋮ THE DECOHERENCE-FREE SUBALGEBRA OF A QUANTUM MARKOV SEMIGROUP WITH UNBOUNDED GENERATOR ⋮ Structure of uniformly continuous quantum Markov semigroups ⋮ Repeated interaction processes in the continuous-time limit, applied to quadratic fermionic systems ⋮ The induced semigroup of Schwarz maps to the space of Hilbert-Schmidt operators ⋮ Buzano's inequality in algebraic probability spaces ⋮ Hypercontractivity and logarithmic Sobolev inequality for non-primitive quantum Markov semigroups and estimation of decoherence rates ⋮ Decoherence for positive semigroups on M2(${\mathbb C}$C)

Cites Work

• Classification and decomposition of quantum Markov semigroups
• Long-time asymptotic properties of dynamical semigroups on W*-algebras
• Irreducible quantum dynamical semigroups
• Quantum dynamical semigroups and approach to equilibrium
• Stationary states of quantum dynamical semigroups
• Return to thermal equilibrium
• The Approach to Equilibrium of a Class of Quantum Dynamical Semigroups
• Subharmonic projections for a quantum Markov semigroup
• TWO-PHOTON ABSORPTION AND EMISSION PROCESS
• Unnamed Item