Browsing by Author "Fagnola, Franco"

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    Algebraic conditions for convergence of a quantum Markov semigroup to a steady state
    (WORLD SCIENTIFIC PUBL CO PTE LTD, 2008) Fagnola, Franco; Rebolledo, Rolando
    Let T be a uniformly continuous quantum Markov semigroup on B(h) with generator represented in a standard GKSL form L(x) = -1/2 Sigma(l)(L-l*L(l)x - 2L(l)*xL(l) + xL(l)*L-l) + i[H, x] and a faithful normal invariant state rho. In this note we give new algebraic conditions for proving that T converges towards a steady state, possibly different from rho. Indeed, we show that this happens whenever the commutator of {H, L-l, L-l*vertical bar l >= 1} (i.e. its fixed point algebra) coincides with the commutator of {L-l, L-l*, delta(H)(L-l), delta(H)(L-l*), ..., delta(n)(H)(L-l), delta(n)(H)(L-l*)vertical bar l >= 1} (where delta(H)(X) = [H,X]) for some n >= 1. As an application we discuss the convergence to the unique invariant state of a spin chain model.
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    THE DECOHERENCE-FREE SUBALGEBRA OF A QUANTUM MARKOV SEMIGROUP WITH UNBOUNDED GENERATOR
    (WORLD SCIENTIFIC PUBL CO PTE LTD, 2010) Dhahri, Ameur; Fagnola, Franco; Rebolledo, Rolando
    Let T be a quantum Markov semigroup on B(h) with a faithful normal invariant state.. The decoherence-free subalgebra N(T) of T is the biggest subalgebra of B(h) where the completely positive maps T(t) act as homomorphisms. When T is the minimal semigroup whose generator is represented in a generalised GKSL form L(x) = -1/2 Sigma(l)(L(l)*L(l)x-2L(l)*xL(l)+xL(l)*L(l))+i[H, x], with possibly unbounded H, L(l), we show that N(T) coincides with the generalised commutator of {e(-itH) L(l)e(itH), e(-itH) L(l)*e(itH) vertical bar l >= 1, t >= 0} under some natural regularity conditions.