Download Open Quantum Systems: An Introduction by Ángel Rivas, Susana F. Huelga PDF
By Ángel Rivas, Susana F. Huelga
In this quantity the elemental conception of open quantum platforms is revised within the gentle of recent advancements within the box. A unified method of the quantum evolution of open platforms is gifted via merging strategies and strategies typically hired by way of various groups, resembling quantum optics, condensed topic, chemical physics and mathematical physics.
The mathematical constitution and the final houses of the dynamical maps underlying open procedure dynamics are defined intimately. The microscopic derivation of dynamical equations, together with either Markovian and non-Markovian evolutions, is additionally mentioned. as a result of step by step causes, this paintings is an invaluable connection with rookies during this box. in spite of the fact that, skilled researches may also enjoy the presentation of modern results.
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Extra resources for Open Quantum Systems: An Introduction
Example text
N 2 − 1, the following operators, 1 F(t) = √ N G(t) = N 2 −1 a j N 2 (t)F j , j=1 1 aN 2 N 2 1+ F † (t) + F(t) , 2N 2 and H (t) = 1 F † (t) − F(t) , 2i which is self-adjoint. 2 Quantum Markov Evolution as a Differential Equation 37 N 2 −1 Lt (ρ) = −i[H (t), ρ] + {G(t), ρ} + a jk (t)F j ρ Fk† . j,k=1 Since the UDMs preserve trace for every density matrix ρ, ⎧⎡ ⎤ ⎫ N 2 −1 ⎨ ⎬ a jk (t)Fk† F j ⎦ ρ , 0 = Tr [Lt (ρ)] = Tr ⎣2G(t) + ⎩ ⎭ j, k=1 and therefore we conclude that 1 G(t) = − 2 N 2 −1 a jk (t)Fk† F j .
3. We should stress that one can construct Markovian models ad hoc which try to describe a system from a microscopic picture without involving these procedures; see for example [121, 122]. In this sense, these two cases are sufficient conditions to get a Markovian evolution, but not necessary. 2 Weak Coupling Limit As we said above, if we assume the weak coupling limit, the change of ρ(u) is negligible within the typical time τ B where the kernel K(t, u) is varying. To perform this limit, consider again Eq.
N 2 − 1, j, k = 1, . . , N 2 − 1, the following operators, 1 F(t) = √ N G(t) = N 2 −1 a j N 2 (t)F j , j=1 1 aN 2 N 2 1+ F † (t) + F(t) , 2N 2 and H (t) = 1 F † (t) − F(t) , 2i which is self-adjoint. 2 Quantum Markov Evolution as a Differential Equation 37 N 2 −1 Lt (ρ) = −i[H (t), ρ] + {G(t), ρ} + a jk (t)F j ρ Fk† . j,k=1 Since the UDMs preserve trace for every density matrix ρ, ⎧⎡ ⎤ ⎫ N 2 −1 ⎨ ⎬ a jk (t)Fk† F j ⎦ ρ , 0 = Tr [Lt (ρ)] = Tr ⎣2G(t) + ⎩ ⎭ j, k=1 and therefore we conclude that 1 G(t) = − 2 N 2 −1 a jk (t)Fk† F j .