ALGEBRAIC CONDITIONS FOR CONVERGENCE OF A QUANTUM MARKOV SEMIGROUP TO A STEADY STATE
2008 ◽
Vol 11
(03)
◽
pp. 467-474
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Keyword(s):
Let [Formula: see text] be a uniformly continuous quantum Markov semigroup on [Formula: see text] with generator represented in a standard GKSL form [Formula: see text] and a faithful normal invariant state ρ. In this note we give new algebraic conditions for proving that [Formula: see text] converges towards a steady state, possibly different from ρ. Indeed, we show that this happens whenever the commutator of [Formula: see text] (i.e. its fixed point algebra) coincides with the commutator of [Formula: see text] (where δH(X) = [H, X]) for some n ≥ 1. As an application we discuss the convergence to the unique invariant state of a spin chain model.
2015 ◽
Vol 18
(04)
◽
pp. 1550027
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2010 ◽
Vol 13
(03)
◽
pp. 413-433
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Keyword(s):
2021 ◽
Vol 10
(11)
◽
pp. 3491-3504
Keyword(s):
2016 ◽
Vol 14
(03)
◽
pp. 1650018
◽
Keyword(s):
2021 ◽
Vol 126
◽
pp. 114455
Keyword(s):