Vibron-phonon coupling strength in a finite size lattice of H-bonded peptide units

An attempt is made to measure the vibron-phonon coupling strength in a finite size lattice of H-bonded peptide units. Within a finite temperature density matrix approach, we compare separately the influence of both the vibron-phonon coupling and the dipole-dipole interaction on the coherence between the ground state and a local one-vibron state. Due to the confinement, it is shown that the vibron-phonon coupling yields a series of dephasing-rephasing mechanisms that prevents the coherence to decay. Similarly, the dipole-dipole interaction gives rise to quantum recurrences for specific revival times. Nevertheless, intense recurrences are rather rare events so that the coherence behaves as a random variable whose most probable value vanishes. By comparing the degree of the coherence for each interaction, a critical coupling ${\chi }^{\ast }\left(L\right)$ is defined to discriminate between the weak and the strong coupling limits. Its size dependence indicates that the smaller the lattice size is, the weaker the vibron-phonon coupling relative to the dipole-dipole interaction is.

Figure 1

Time evolution of (a) $K\left(t\right)$ and (b) $\gamma \left(t\right)$ for $\chi =30\text{pN}$, $T=310\text{K}$, and $L=22$. Gray lines correspond to the Debye model (see the text).

Figure 2

Time evolution of the decoherence factor for $T=310\text{K}$ and for (a) $\chi =10\text{pN}$ and (b) $\chi =30\text{pN}$. Black lines correspond to $L=12$, whereas gray lines refer to $L=22$.

Figure 3

Time evolution of the decoherence factor for $T=310\text{K}$ and $L=22$. (a) $\chi =10\text{pN}$ and (b) $\chi =30\text{pN}$.

Figure 4

Distribution of the decoherence factor for $T=310\text{K}$. (a) $\chi =10\text{pN}$ and (b) $\chi =30\text{pN}$. The simulation has been carried out over 5000 ps with $5\times {10}^5$ time steps.

Figure 5

Time evolution of the survival probability $P\left(t\right)={\left|G_{x_0{x}_0}\left(t\right)\right|}^2$ for $L=16$.

Figure 6

Distribution of the survival probability for (a) $L=12$ and (b) $L=16$. The simulation has been carried out over 5000 ps with $5\times {10}^5$ time steps.

Figure 7

Size dependence of the critical coupling ${\chi }^{\ast }\left(L\right)$.