Localization effects due to a random magnetic field on heat transport in a harmonic chain (original) (raw)

Role of pinning potentials in heat transport through disordered harmonic chains

Physical Review E, 2008

The role of quadratic onsite pinning potentials on determining the size (N) dependence of the disorder averaged steady state heat current , in a isotopically disordered harmonic chain connected to stochastic heat baths, is investigated. For two models of heat baths, namely white noise baths and Rubin's model of baths, we find that the N dependence of is the same and depends on the number of pinning centers present in the chain. In the absence of pinning, ~ 1/N^{1/2} while in presence of one or two pins ~ 1/N^{3/2}. For a finite (n) number of pinning centers with 2 <= n << N, we provide heuristic arguments and numerical evidence to show that ~ 1/N^{n-1/2}. We discuss the relevance of our results in the context of recent experiments.

Thermal conductance of one-dimensional disordered harmonic chains

Physical review, 2020

We study heat conduction mediated by longitudinal phonons in one dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find nontrivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that a system with strong disorder, characterized by a 'heavy-tailed' probability distribution, and with large impedance mismatch between the bath and the system satisfies Fourier's law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.

Thermal transport in out-of-equilibrium quantum harmonic chains

Physical Review E, 2015

We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the phenomenology of the transport process. We study in detail the behavior of thermodynamically relevant quantities such as heat currents and mean energies of the oscillators, establishing rigorous analytical conditions for the existence of a steady state, whose features we analyse carefully. In particular we assess the conditions that should be faced to recover trends reminiscent of the classical Fourier law of heat conduction and highlight how such a possibility depends on the environment linked to our system.

Heat Conduction in Chains of Nonlinear Oscillators

Physical Review Letters, 1997

We numerically study heat conduction in chains of nonlinear oscillators with time-reversible thermostats. A nontrivial temperature profile is found to set in, which obeys a simple scaling relation for increasing the number N of particles. The thermal conductivity diverges approximately as N 1͞2 , indicating that chaotic behavior is not enough to ensure the Fourier law. Finally, we show that the microscopic dynamics ensures fulfillment of a macroscopic balance equation for the entropy production. [S0031-9007(97)02611-2]

Heat transport and phonon localization in mass-disordered harmonic crystals

Physical Review B, 2010

We investigate the steady state heat current in two and three dimensional disordered harmonic crystals in a slab geometry, connected at the boundaries to stochastic white noise heat baths at different temperatures.The disorder causes short wavelength phonon modes to be localized so the heat current in this system is carried by the extended phonon modes which can be either diffusive or ballistic. Using ideas both from localization theory and from kinetic theory we estimate the contribution of various modes to the heat current and from this we obtain the asymptotic system size dependence of the current. These estimates are compared with results obtained from a numerical evaluation of an exact formula for the current, given in terms of a frequency transmission function, as well as from direct nonequilibrium simulations. These yield a strong dependence of the heat flux on boundary conditions. Our analytical arguments show that for realistic boundary conditions the conductivity is finite in three dimensions but we are not able to verify this numerically, except in the case where the system is subjected to an external pinning potential. This case is closely related to the problem of localization of electrons in a random potential and here we numerically verify that the pinned three dimensional system satisfies Fourier's law while the two dimensional system is a heat insulator. We also investigate the inverse participation ratio of different normal modes.

Heat Transport in an Ordered Harmonic Chain in Presence of a Uniform Magnetic Field

Journal of Statistical Physics, 2021

We consider heat transport across a harmonic chain of charged particles, with transverse degrees of freedom, in the presence of a uniform magnetic field. For an open chain connected to heat baths at the two ends we obtain the nonequilibrium Green's function expression for the heat current. This expression involves two different Green's functions which can be identified as corresponding respectively to scattering processes within or between the two transverse waves. The presence of the magnetic field leads to two phonon bands of the isolated system and we show that the net transmission can be written as a sum of two distinct terms attributable to the two bands. Exact expressions are obtained for the current in the thermodynamic limit, for the the cases of free and fixed boundary conditions. In this limit, we find that at small frequency ω, the effective transmission has the frequency-dependence ω 3/2 and ω 1/2 for fixed and free boundary conditions respectively. This is in contrast to the zero magnetic field case where the transmission has the dependence ω 2 and ω 0 for the two boundary conditions respectively, and can be understood as arising from the quadratic low frequency phonon dispersion.

Heat conduction in diatomic chains with correlated disorder

Physics Letters A

The paper considers heat transport in diatomic one-dimensional lattices, containing equal amounts of particles with different masses. Ordering of the particles in the chain is governed by single correlation parameter-the probability for two neighboring particles to have the same mass. As this parameter grows from zero to unity, the structure of the chain varies from regular staggering chain to completely random configuration, and then-to very long clusters of particles with equal masses. Therefore, this correlation parameter allows a control of typical cluster size in the chain. In order to explore different regimes of the heat transport, two interatomic potentials are considered. The first one is an infinite potential wall, corresponding to instantaneous elastic collisions between the neighboring particles. In homogeneous chains such interaction leads to an anomalous heat transport. The other one is classical Lennard-Jones interatomic potential, which leads to a normal heat transport. The simulations demonstrate that the correlated disorder of the particle arrangement does not change the convergence properties of the heat conduction coefficient, but essentially modifies its value. For the collision potential, one observes essential growth of the coefficient for fixed chain length as the limit of large homogeneous clusters is approached. The thermal transport in these models remains superdiffusive. In the Lennard-Jones chain the effect of correlation appears to be not monotonous in the limit of low temperatures. This behavior stems from the competition between formation of long clusters mentioned above, and Anderson localization close to the staggering ordered state.

Heat conduction in one-dimensional chains with random mass distribution

The paper considers heat conductivity in a set of one-dimensional lattice models, which contain particles with two different masses. First of all, we address recent findings concerning peculiar heat transport in a diatomic billiard close to the integrable limit. Our simulations demonstrate that the heat transport in this case remains superdiffusive, and the heat conductivity therefore is abnormal. Then, the effect of mass disorder on the heat transport in the diatomic system is explored both for systems with abnormal and normal heat conductivity. Two main characteristics of the disorder are addressed -- internal correlations in the disordered structure, and concentration of the "impurities" with different mass. We show that the disorder does not modify the convergency properties of the heat conduction coefficient in the thermodynamical limit. However, as one would expect, the disorder strongly effects the quantitative properties of the heat transport. Moreover, we demonstr...

Thermalization without chaos in harmonic systems

2021

Recent numerical results showed that thermalization of Fourier modes is achieved in short timescales in the Toda model, despite its integrability and the absence of chaos. Here we provide numerical evidence that the scenario according to which chaos is irrelevant for thermalization is realized even in the simplest of all classical integrable system: the harmonic chain. We study relaxation from an atypical condition given with respect to random modes, showing that a thermal state with equilibrium properties is attained in short times. Such a result is independent from the orthonormal base used to represent the chain state, provided it is random.