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Confinement and non-universality of anomalous heat transport and superdiffusion of energy in low-dimensional systems

We provide molecular dynamics simulation of heat transport and thermal energy diffusion in one-dimensional molecular chains with different interparticle pair potentials at zero and non-zero temperature. We model the thermal conductivity (TC) and energy diffusion in the coupled rotator chain and in the Lennard-Jones chain either without or with the confining parabolic interatomic potential. The considered chains without the confining potential have normal TC and energy diffusion, while the corresponding chains with the confining potential are characterized by anomalous (diverging with the system length) TC and superdiffusion of energy. We confirm in such a way that, surprisingly, the confinement makes both heat transport and energy diffusion anomalous in low-dimensional phononic systems. We show that the chain, which has a finite TC, is also characterized by the normal energy diffusion in the thermalized chain (at non-zero temperature), while the superdiffusion of thermal energy occurs in the thermalized chains with only anomalous TC. We present the arguments, supported by our simulations, that the scaling relation between the exponents in time dependence of the mean square displacement of thermal energy distribution and in length dependence of the anomalous TC is not universal and can be different, depending on the main mechanism of energy transport: by weakly-scattered waves or by noninteracting colliding particles performing Levy flights.