Weak coupling, definition

Figure 7.17 (a) Magnetic properties of [LaTb] and [Tb2] in the form of yT versus T plot per mole of Tb(lll). (b) Schematic representation of the qubit definition, weak coupling and asymmetry, as derived from magnetic and heat capacity data. 

The studies on [LaTb], [TbLu], [LaEr] and [CeY] established that the individual ions ofthe molecules [Tb2(HL)2(H2L)Cl(py)(H20)] and [CeEr(HL)2(H2L)(N03) (py)(H20)] exhibit isolated, well-defined ground state doublets, thus leading to proper definitions of qubit states. The next step is to prove the existence of a weak coupling within each molecule conducive to the appropriate energy level spectrum for the realization of quantum gate operations. 

No divergences and dependence on the contact parameters Ti 2 remain in the form for r. It shows the transmittance function (at least in the weak-coupling limit) is indeed a well-defined molecular quantity. We can rewrite equation (38), taking into account the definition of 6 (see equation (35)) and the definition of the Chebyshev polynomials of the second kind U (cos 6) — sin[(n +l)0]/sin 6 as... 

Therefore we may eliminate the correlations in many ways. A different definition of the physical quantity 0R corresponds to each %. Equation (51) already looks like the average, Eq. (47), taken in a weakly coupled system with p0 replaced by p and O by 0R. There still remains a difference. We have as yet no relation between p and the entropy. If we could find a p such that the quantity of Boltzmann would be given by... 

Bolometers are just thermometers weakly coupled to a thermal bath by a conductance G. Radiation is focussed on the bolometer causing its temperature to rise by AT = P/G (see Figure 9.17). The thermal time constant of a bolometer is given by t = C/G where C = dQ/dT is the heat capacity of the bolometer in ergs/K. From the definition of entropy S = k In G with Q being the state density, and dS = dQ/T, we find that... 

The vector model cannot be interpreted in such a simple way in the case of a spin system with more than one nucleus. For weakly coupled spin systems, the single spin vector model may be applied for each nucleus, one after the other. Thus the coupling with the other nuclei can be incorporated into its precession frequency, since the definition of the weak coupling (J -C vM v,/1) means that the transitions of a nucleus only depend on the spin states of the other nuclei in the first order. The detected signal is the sum of the sine curves provided by the individual environment of the nuclei. 

The linearized dispersion equation (27) leads to the same definition of the Fermi surface E(k) = EF as that of Eq. (26) provided that f x t lta, with vF 2ata. We have neglected the dispersion along the c direction of very weak coupling. 

Spin echo spectroscopy is a definitive technique for determining the binding of imidazole to copper complexes. Detection of spin echo signals is based on the weak coupling of the electron to the unbound imidazole nitrogen, rather than the bound... 

Here, e and refer to the electron number density and electron Debye length, respectively. The meaning of the plasma parameter is clear if it is large, then the Debye sphere is heavily populated (this is the case of the weakly coupled plasma), whereas if it is small, then the Debye sphere is only sparsely poptilated and the plasma is strongly coupled. Some authors define the plasma parameter as 1/3 of the value in O Eq. (6.12). In this case, the plasma parameter is exactly the number of particles inside the Debye sphere, whereas in the definition given by O Eq. (6.12), it is only proportional to it. The plasma parameter is defined for the electrons only. One could, in principle, define a plasma parameter for the ions also, but that is not common. 

Fig. 9.15 shows four ENDOR spectra as detected via the ESR transitions (a), (b), (c), and (d), respectively. Four protons i = 1, 2, 3, and 4, respectively, are clearly separated from the free proton frequency vp. In the vicinity of vp a large number of weakly coupled protons are visible. They also have been resolved by expansion of the NMR frequency scale. For a few strongly coupled protons we are able to detect all five NMR transitions (1) to (5). This is a further and definite proof that we do observe quintet states. 

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