Quantum phonon fluctuations in mesoscopic dimerized systems

We describe quantitatively the structural change in finite Peierls chains, Full quantum mechanical calculations show: (i) how the smooth phase transit ion occurs by the continuous change of the ground state wave function which preserves the symmetry of the Hamiltonian; (ii) the structural change is a ccompanied by an anharmonicity which becomes very pronounced in the broad t ransition region; (iii) the dimerization is suppressed for sizes shorter th an a certain critical size, Quantum phonon fluctuations can make the latter sufficiently large (similar to 0.1-1 mu m) to be detected in mesoscopic sy stems (e.g. perylene radical cation salts) with weaker electron-phonon coup ling. As possible techniques for experimental observation, ne suggest the n onlinear optical absorption and the ultrasonic attenuation. Our calculation s are based on numerical diagonalization done exactly in small chains and w ithin the adiabatic ansatz for longer chains. We indicate how to test selfc onsistently the latter results and show: that the? are accurate up to mesos copic sizes in parameter ranges of relevance for real systems. We explain w hy. conventional many-body techniques are inappropriate to describe the Pei erls transition in finite chains.