Weak coupling region

Fig. 13.2. Crossover diagram in the w — / plane (uncritical surface). The shaded parts indicate regions dominated by asymptotic power law behavior. Weak coupling region (/ < 1) Long dashes lines of fixed z (— 300 1, from above). Short dashes lines of fixed sfz (= 0,01 1, from above). Dotted lines of fixed s = (0-02 0,8, from above). In the strong coupling region a line of fixed z = 300 is shown...

Now consider the weak coupling region / < 1. Prom Eq. (13.33 ii) we find that q2 —v g2, z fixed, implies,/ — 0. From Eqs. (13,24), (14.16) we then find the trivial limiting behavior Ja(q) 1/q2, in accord with the temperature blob model. For a system close to the excluded volume limit for large q we first may find some region described by the law (14.17), the trivial behavior developing only for extreme values of the momentum (see Fig. 14.2),... 

Let us start with the E e JT polaron in the weak-coupling region (or for the case of small gEigie), in which the perturbation approach in momentum representation is useful. The thermal one-electron Green s function Gkya(ico ) with co the fermion Matsubara frequency is defined at temperature T by... 

In the weak-coupling region, the AFO response is largest, as expected from the result of T = 1 for the first-excited state (see Fig. 9) and the electrons form local singlet states with either the total-pseudospin-zero state (PO) described by... 

Pair A24 shows very little coupling, as evidenced by the absence of frequency differences between homoisotopic and heteroisotopic pairs. The small difference in intensity ratio of A2 to A4 between 12C02 and 13C02 regions reveals a weak coupling of about 0.5 cm-1 for this pair. 

In the superohmic case at 7 = 0, the system exhibits weakly damped coherent oscillations characterized by the damping coefficient rjTLS from (2.44), but with A0 replaced by Aeff. In the region lexponential decay, in accordance with our weak-coupling predictions. 

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