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17
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67650329000
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note
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In this effective Hamiltonian is written in terms of the IRF electric field. One can show using the Lorentz force equation (under the assumption that nonelectromagnetic causes of the acceleration are negligible) that these two forms are equivalent.
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19
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67650307442
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This is just a change in basis of the standard polarization directions and should not be confused with the creation or annihilation operators which are obtained by separating the field into positive and negative frequencies.
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This is just a change in basis of the standard polarization directions and should not be confused with the creation or annihilation operators which are obtained by separating the field into positive and negative frequencies.
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-
-
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20
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84869370191
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These magnetic modes are related to photon modes through B□ =□× A□.
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These magnetic modes are related to photon modes through B□ =□× A□.
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-
-
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23
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67650316680
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Since the spin-field coupling strength is small, a perturbative expansion is acceptable.
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Since the spin-field coupling strength is small, a perturbative expansion is acceptable.
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-
-
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24
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84869364509
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TrB [V (τ) ρB] =-μ σi TrB (Bi† ρB) and since Bi = Bi+ + Bi-, where Bi± are the positive and negative frequencies, then as long as the field is not in a squeezed state (we assume ρB is not) TrB (Bi± ρB) =0.
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TrB [V (τ) ρB] =-μ σi TrB (Bi† ρB) and since Bi = Bi+ + Bi-, where Bi± are the positive and negative frequencies, then as long as the field is not in a squeezed state (we assume ρB is not) TrB (Bi± ρB) =0.
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-
-
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25
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67650307443
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note
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Where the choice of -i appropriate Green's function for this two-point correlation function (see for a discussion on the analytic properties of the Green's functions).en made to recover the appropriate Green's function for this two-point correlation function (see for a discussion on the analytic properties of the Green's functions).
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-
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26
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84869362400
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Note that B± (x) □ = Bx (x) Bx (x′) + By (x) By (x′) =2G (x, x′).
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Note that B± (x) B□ (x′) = Bx (x) Bx (x′) + By (x) By (x′) =2G (x, x′).
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27
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84869370190
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A. J. Fisher, Graduate course on open quantum systems, 2004, URL: www.cmmp.ucl.ac.uk/ajf/course-notes.pdf.
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(2004)
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Fisher, A.J.1
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30
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33645297114
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10.1103/PhysRevLett.96.124801
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A. Gover, Phys. Rev. Lett. 96, 124801 (2006). 10.1103/PhysRevLett.96. 124801
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Gover, A.1
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31
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67650295106
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note
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In practice one could observe a loss of concurrence before this time, however, defining the time scale in this way is preferred since it is more meaningful to speak of the time taken for the spins to completely disentangle from each other as opposed to the time taken for them to evolve to some arbitrary value of concurrence.
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-
-
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32
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84869354468
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We note for completeness that the time taken for the concurrence to decay to the value C is given by τC = 3π 8 ln (3 2C+1) □
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We note for completeness that the time taken for the concurrence to decay to the value C is given by τC = 3π 8 ln (3 2C+1) c6 μ2 a3.
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-
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34
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84869370186
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However notice the slight difference in notation, d β□ ′ →Δβ.
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However notice the slight difference in notation, d β□ ′ →Δβ.
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35
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84869370184
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See Eq. (11.117) of although note the typographical error in the argument of the last boost which should read Aboost (Δβ) instead of Aboost (δβ). This error has been confirmed via private correspondence with
-
See Eq. (11.117) of although note the typographical error in the argument of the last boost which should read Aboost (Δβ) instead of Aboost (δβ). This error has been confirmed via private correspondence with J. D. Jackson.
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-
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Jackson, J.D.1
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