Nonlinear Physics Seminar :"Kapitza resistance in one dimension: basic models and classes of universality"

Wed, 20/01/2021 - 12:00 to 13:30

Lecturer: O.V.Gendelman, Faculty of Mechanical engineering, Technion – Israel Institute of Technology

It is commonly accepted today, that one-dimenisonal lattice models can belong to three
universality classes with respect to the bulk heat conduction. The first class (e.g. lattices with
linear interactions) is characterized by heat flux that is proportional to temperature difference
rather than to the temperature gradient. The second class includes models with size-dependent heat conduction coefficient (e.g. Fermi-Pasta-Ulam model and similar nonlinear
chains with conserved momentum). The third class includes the chains that can be
characterized by well-defined convergent heat conduction coefficient in the thermodynamic
limit (e.g. Frenkel – Kontorova model or chain of rotators). There exist some quarrels and
contradictions on classification of various exotic chain models, but the universality classes
seem well-established.
The talk will address, in a sense, the opposite limit case with respect to a transport in the
homogeneous bulk – Kapitza, or boundary, thermal resistance (KR). This phenomenon (sharp
step in the temperature profile) readily reveals itself if one considers either isolated isotopic
or link defect in the homogeneous chain, or interface between two chain fragments with
different characteristics. Linear chain model with isolated defect allows exact analytic solution
for the KR – so, contrary to the bulk conductivity, the resistance has well-defined value also in
the linear chain. However, the result strongly depends on the model of thermostat –
therefore, the anomaly still is well articulated.
Account of nonlinearity demonstrates that the KR properties are related to the universality
class with respect to the heat conduction, to which the considered chain model belongs. In
linear chains, the KR does not depend on the chain length in the thermodynamic limit, but
substantially depends on the characteristics of thermostats used in the simulations. In the
models with size-dependent heat conduction coefficient, the KR also is substantially size-dependent, despite strong localization of the Kapitza step. Finally, in the models with normal
heat conductivity the KR is also normal, i.e. size- and thermostat-independent in the
thermodynamical limit.