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Qualitative properties of coupled parabolic systems of evolution equations

Stefano Cardanobile, Delio Mugnolo (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of sesquilinear mappings. We apply our results to parabolic problems of different nature: a coupled diffusive system arising in neurobiology, a strongly damped wave equation, and a heat equation with dynamic boundary conditions.

Quantum detailed balance conditions with time reversal: the finite-dimensional case

Franco Fagnola, Veronica Umanità (2011)

Banach Center Publications

We classify generators of quantum Markov semigroups on (h), with h finite-dimensional and with a faithful normal invariant state ρ satisfying the standard quantum detailed balance condition with an anti-unitary time reversal θ commuting with ρ, namely t r ( ρ 1 / 2 x ρ t 1 / 2 ( y ) ) = t r ( ρ 1 / 2 θ y * θ ρ t 1 / 2 ( θ x * θ ) ) for all x,y ∈ and t ≥ 0. Our results also show that it is possible to find a standard form for the operators in the Lindblad representation of the generators extending the standard form of generators of quantum Markov semigroups satisfying the usual...

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