Energy Transport in the Disordered Harmonic Chain and the Correlation-Function Formula

Amirali Hannani

Bruce N. Miller, Peter M. Larson

The methods of information theory are applied to the problem of describing the transport of internal energy along a linear harmonic chain in a stationary state. It is shown that the average energy flux along the chain is a constant of the motion which can be directly incorporated into the canonical formalism. The classical probability distribution in phase space is constructed and used to evaluate the partition function in the thermodynamic limit. Thermodynamic relationships between the undetermined multipliers and the given information are explicitly determined, as are the singlet- and pair-distribution functions in configuration and momentum space and the correlation of the momentum of a specific particle in time. For a given system energy there is an upper bound for the mean rate of energy transport. As this limit is closely approached, both the range and duration of correlations become large. This behavior, as well as some other features of the model, is reminiscent of that near a critical point.

L. P. Gor’kov, O. N. Dorokhov, Fedor V. Prigara

Tanausú Hernández Yanes

Niaz Ali Khan, João M. Viana Parente Lopes, J. P. Santos Pires +1 more

We investigate the spectral function of Bloch states in a one-dimensional tight-binding non-interacting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the single-particle spectral function based on the Kernel polynomial method, which has an [Formula: see text] computational complexity. These results are then confirmed by analytical calculations, where precise conditions were obtained for the appearance of a classical limit in a single-band lattice system. Spatial correlations in the disordered potential give rise to non-perturbative spectral functions shaped as the probability distribution of the random on-site energies, even at low disorder strengths. In the case of disordered potentials with an algebraic power-spectrum, [Formula: see text] [Formula: see text], we show that the spectral function is not self-averaging for [Formula: see text].

Manoj Kumar, Anupam Kundu, Manas Kulkarni +2 more

We explore transport properties in a disordered nonlinear chain of classical harmonic oscillators, and thereby identify a regime exhibiting behavior analogous to that seen in quantum many-body-localized systems. Through extensive numerical simulations of this system connected at its ends to heat baths at different temperatures, we computed the heat current and the temperature profile in the nonequilibrium steady state as a function of system size N, disorder strength Δ, and temperature T. The conductivity κ_{N}, obtained for finite length (N), saturates to a value κ_{∞}>0 in the large N limit, for all values of disorder strength Δ and temperature T>0. We show evidence that for any Δ>0 the conductivity goes to zero faster than any power of T in the (T/Δ)→0 limit, and find that the form κ_{∞}∼e^{-B|ln(CΔ/T)|^{3}} fits our data. This form has earlier been suggested by a theory based on the dynamics of multioscillator chaotic islands. The finite-size effect can be κ_{N}<κ_{∞} due to boundary resistance when the bulk conductivity is high (the weak disorder case), or κ_{N}>κ_{∞} due to direct bath-to-bath coupling through bulk localized modes when the bulk is weakly conducting (the strong disorder case). We also present results on equilibrium dynamical correlation functions and on the role of chaos on transport properties. Finally, we explore the differences in the growth and propagation of chaos in the weak and strong chaos regimes by studying the classical version of the out-of-time-ordered commutator.