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User:Sckavassalis/Markov dissipative evolution

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Markov dissipative evolution is

Definition

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For an open system, where the total system is defined by a density operator , we assume it evolves according to the equation,

Where , acting on , and and are Schrödinger operators.

If we define a reduced density matrix for our system at time as,

,

which is given in terms of the partial trace of over the environment variables. If initially , we can define an evolution as,

This evolution is said to be dissipative if it satisfies these five properties:

(1) is linear.
(2) is positive.
(3) is trace preserving.
(4)
(4)Failed to parse (unknown function "\rhoV"): {\displaystyle \Beta_t(\rho)=\sum_n V_{nt}\rhoV^*_{nt}}


References

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