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Bimodal energy relaxations in quasi-one-dimensional systems

We show that the low temperature ($T<0.5$ K) time dependent non-exponential energy relaxation of quasi-one-dimensional (quasi-1D) compounds strongly differ according to the nature of their modulated ground state. For incommensurate ground states, such as in (TMTSF)$_2$PF$_6$ the relaxation time distribution is homogeneously shifted to larger time when the duration of the heat input is increased, and exhibits in addition a scaling between the width and the position of the peak in the relaxation time distribution, $w^{2}\sim\ln{(τ_{m})}$. For a commensurate ground state, as in (TMTTF)$_2$PF$_6$, the relaxation time spectra show a bimodal character with a weight transfer between well separated slow and fast entities. Our interpretation is based on the dynamics of defects in the modulated structure, which depend crucially on the degree of commensurability.