A generic quantum Markov semigroup T of a d-level quantum open system with a faithful normal invariant state ρ admits a dual semigroup with respect to the scalar product induced by ρ. We show that the difference of the generator L and its adjoint can be written as the sum of a derivation 2i[H, ·] and a weighted difference of automorphisms. The formula we prove allows us to represent the deviation from equilibrium (in a “small” time interval) as the superposition of cycles of the system where the difference between the forward and backward evolution is written as the difference of a reversible evolution and its time reversal. Moreover, it generalises cycle decomposition of Markov jump processes. We also find a similar formula with partial isometries instead of unitaries.
GENERIC QUANTUM MARKOV SEMIGROUPS, CYCLE DECOMPOSITION AND DEVIATION FROM EQUILIBRIUM
FAGNOLA, FRANCO;
2012-01-01
Abstract
A generic quantum Markov semigroup T of a d-level quantum open system with a faithful normal invariant state ρ admits a dual semigroup with respect to the scalar product induced by ρ. We show that the difference of the generator L and its adjoint can be written as the sum of a derivation 2i[H, ·] and a weighted difference of automorphisms. The formula we prove allows us to represent the deviation from equilibrium (in a “small” time interval) as the superposition of cycles of the system where the difference between the forward and backward evolution is written as the difference of a reversible evolution and its time reversal. Moreover, it generalises cycle decomposition of Markov jump processes. We also find a similar formula with partial isometries instead of unitaries.File | Dimensione | Formato | |
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