Nonequilibrium stationary state of a harmonic crystal with alternating masses

Abstract

We analyze the non-equilibrium steady states (NESS) of a one dimensional harmonic chain of N atoms with alternating masses connected to heat reservoirs at unequal temperatures. We find that the temperature profile defined through the local kinetic energy T (j) ≡ < p 2 j >/m j , oscillates with period two in the bulk of the system. Depending on boundary conditions, either the heavier or the lighter particles in the bulk are hotter. We obtain exact expressions for the bulk temperature profile and steady state current in the limit N → ∞. These depend on whether N is odd or even.We also study similar temperature oscillations in the NESS of systems with noise in the dynamics.These die out as N → ∞.

Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions

“…However, there exist counterexamples of models with the three aforementioned conservation laws that depart from such universal behavior for different intrinsic reasons. For instance, integrable models, like a chain of harmonic oscillators and the Toda lattice, exhibit ballistic transport (i.e., κ ∼ N ), since energy is transmitted through the chain by the undamped propagation of eigenmodes (phonons and solitons, respectively [11,12]). Moreover, for systems in which the local symmetry of particle displacements with respect to the equilibrium position is restored, the exponent γ takes higher values, e.g., 2/5 or 1/2, depending on the model at hand.…”

Nonequilibrium generalised Langevin equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths

“…The introduction of configurational defects 24,25,39 or disorder 9,15,25,31,40 in harmonic systems can also lead to diffusive transport, with the build up of a temperature gradient across the system. Defects and disorder introduce some form of localisation of the vibration modes 27,28 which do not favour ballistic transport 27 .…”

“…In order to obtain a diffusive transport regime, one has to introduce any form of anharmonic effects in the system 10,[12][13][14]16,17,22,24,26,27,[29][30][31][32][33][34][35][36][37][38] . Diffusive transport is also obtained when extra local stochastic processes 9,10,15,17,18,26,32,41 or extra collision processes 42,43 are introduced. A vibrational mode coupling in classical systems 45 is also responsible for diffusive transport.…”

“…No temperature gradient is formed in the bulk of the system, since the dominating energy "carriers" are not scattered and propagate ballistically. A large variety of harmonic (integrable) classical [8][9][10][11][12][13][14][15][16][17] and quantum 10,13,[18][19][20][21][22][23] systems have been studied using analytical and/or numerical approaches. All these studies show that there is no temperature gradient inside the system (except for small regions in the vicinity of the contacts between the central system and the baths).…”

“…All these studies show that there is no temperature gradient inside the system (except for small regions in the vicinity of the contacts between the central system and the baths). One usually obtains a constanttemperature profile [8][9][10][11][12]15,[17][18][19][20][21][22][23] in the central system around the averaged temperature T av = (T L + T R )/2.…”