Energy exchange, localization, and transfer in nanoscale systems (weak-coupling approximation)

It is shown that both an adequate understanding and effective analysis of energy exchange, localization, and transfer in nanoscale systems is closely related to important aspects of the “wave-particle” duality, one of the key concepts of quantum mechanics. Due to the revealed similarities between the mathematical description of weakly coupled classical oscillators and multilevel quantum systems, this relation turns out to be essential for classical physics as well. Although the development of quantum field theory led, in fact, to the abolition of the wave-particle duality at the fundamental level, putting into the forefront the oscillatory field in the vacuum and imparting to quantized particles the status of field excitations, the wave-particle dilemma continues to be a powerful heuristic principle of theoretical analysis in quantum and classical physics. Within the framework of this approach, it is possible to identify two limiting cases that allow a natural interpretation as applied to polymer physics. In the continuum approximation, very long macromolecules in polymer crystals and other ordered polymer systems (e.g., in the DNA double helix), although considerably more complex in structure than spatially one-dimensional models of nonlinear physics, are ideal objects for the application of ideas and methods of classical nonlinear field theory,. Depending on the conditions of operation, these systems feature both wavelike (normal vibrations and waves) and solitonlike (particlelike) excitation of the nonlinear field, or some combination thereof. The main difficulties to be overcome here are associated with an asymptotic reduction of realistic models of polymer chains and crystals to analytically solvable models. However, for oligomers, with relatively short chains, and nanostructures (second limiting case), it became necessary to develop a fundamentally new approach, since in this case, the formation of localized nonlinear excitations and irreversible energy transfer are preceded (in the level of excitation) by the stage of intense energy exchange between certain groups of particles, referred to as effective particles. Most intense energy transfer is described in terms of limiting phase trajectories, a notion alternative to classical nonlinear normal modes and quantum stationary states. The possibility of introducing effective particles becomes apparent when the initial molecular chain is reduced (in a certain range of its frequencies) to a system of weakly coupled nonlinear oscillators, which is described by the same equations as the multilevel quantum system. With increasing excitation energy, a threshold is reached at which intense energy transfer gives way to the localization of energy on the initially excited effective particle or to its transfer along the chain. In view of the quantum-classical analogy, the analysis of classical linear and nonlinear oscillator models of nanoscale systems is applicable to multilevel quantum systems. In both cases, the asymptotic nature of the wave-particle duality manifests itself, which makes it possible to clarify the relationship between the existing interpretations of it.