Dissipative Solitons and Complex Currents in Active Lattices

Abstract

We first summarize features of free, forced and stochastic harmonic oscillations and, following an idea first proposed by Lord Rayleigh in 1883, we discuss the possibility of maintaining them in the presence of dissipation. We describe how phonons appear in a harmonic (linear) lattice and then use the Toda exponential interaction to illustrate solitonic excitations (cnoidal waves) in a one-dimensional nonlinear lattice. We discuss properties such as specific heat (at constant length/volume) and the dynamic structure factor, both over a broad range of temperature values. By considering the interacting Toda particles to be Brownian units capable of pumping energy from a surrounding heat bath taken as a reservoir we show that solitons can be excited and sustained in the presence of dissipation. Thus the original Toda lattice is converted into an active lattice using Lord Rayleigh's method. Finally, by endowing the Toda-Brownian particles with electric charge (i.e. making them positive ions) and adding free electrons to the system we study the electric currents that arise. We show that, following instability of the base linear Ohm(Drude) conduction state, the active electric Toda lattice is able to maintain a form of high-T supercurrent, whose characteristics we then discuss.

Bound states of electrons with soliton-like excitations in thermal systems - adiabatic approximations

“…After Davydov's pioneering work many investigations were performed for one-dimensional lattices with Morse interactions and imbedded electrons [19][20][21][22]. Here we shall follow this idea studying the systems with Morse interactions together with an appropriate electron-atom interaction.…”

Nonlinear Ionic Excitations, Dynamic Bound States, and Nonlinear Currents in a One‐dimensional Plasma

“…The effects of active friction force were investigated in [11,21,29] to model active Brownian particles that carry refillable energy depots (internal degrees of freedom). For the passive regime µ < 0 the deterministic dynamics has a single attractor at v = 0.…”

“…The thermal excitations in ring chains with Morse potentials (akin to the Lennard-Jones) and small particle number N were investigated in [19]. Here we report on new results on electrical transport under the influence of external fields [10,11] and hence situations far from equilibrium. As shown earlier, we may drive a nonlinear lattice away from equilibrium by applying dissipative forces [20][21][22] and excite "dissipative solitons" [23][24][25][26][27].…”

“…Here we are interested in analyzing dynamic bound states, created by deep local potential minima due non-linear excitations. We study the role of dynamic bound states between electrons and solitons (called "solectrons") [10,11]. These bound states are metastable in equilibrium systems and may lead to nonlinear conductance effects if appropriately maintained under nonequilibrium conditions.…”

Metastable states in the Morse–Rayleigh chain

“…Аналогичными свойствами обладает и цепочка Морзе -Рэлея, где силы взаимодействия между частицами задаются потенциалом Морзе, который при небольших смещениях ча-стиц подобен потенциалу Тоды [14,18,[20][21][22][23][24][25][26]. Однако было обнаружено, что если задаются случайные начальные возмущения скоростей частиц или их отклонения от положения рав-новесия, то в результате короткого переходного процесса возникает мода с неравномерным распределением максимумов плотности частиц, похожим на распределение частиц в муль-тисолитонной моде консервативной цепочки [2].…”