QUANTUM-MECHANICS, QUANTUM-CLASSICAL CORRESPONDENCE, THERMODYNAMICS, AND RESPONSE OF A SMALL ANHARMONIC PERIODIC CHAIN

The exact quantum states are obtained for a classically integrable anharmonic system, namely a three-particle periodic chain of equal masses interacting via nearest-neighbor harmonic and quartic potentials. Semiclassical quantization techniques are then used to establish connections between the quantum solutions and particular classical solutions, which are three-particle versions of the intrinsic localized modes and nonlinear sinusoidal waves that have recently been studied for general one-dimensional anharmonic periodic lattices. This constitutes a first step towards a full quantum-mechanical treatment of anharmonic modes in general lattices. The exact quantum heat capacity is computed and compared with the classical result. We then study the response to an externally applied sinusoidal driving force, comparing the quantum linear response with the classical response obtained within a rotating wave approximation. As the driving force is increased, we find that the classical response exhibits a family of solutions with displacement patterns of a symmetry different than that of the external driving force. © 1995 The American Physical Society.