Review of nature-inspired position-dependent mass oscillator models applied in quantum systems

This review explores position-dependent mass (PDM) oscillators, naturally occurring in biological systems and relevant to engineered quantum devices. In nature, PDM oscillations appear in the bending of plant stems, fish swimming, bird flight, and the motion of limbs, as well as in the oscillatory behavior of organs like the heart and vocal cords. These phenomena inspired models of oscillators whose effective mass varies with position, simulating elastic structures attached to bodies of variable mass. Mathematically, such systems are captured by Li?nard equations with quadratic velocity terms. This review examines key features - motion type, period, and amplitude - of PDM oscillators, highlighting their versatility for describing spatially varying inertia and dynamic adaptation. Extend?ing these concepts to quantum systems, spatial variations in carrier mass arise in semiconductor nanostructures like quantum wells, wires, and dots, due to compositional inhomogeneities and structural gradients. Position-dependent mass models refine quantum mechanics, enabling more accurate energy-level and carrier-dynamics predictions. Such models are central to the design of advanced electronic and photonic devices, including quantum cascade lasers, high electron mobility transistors, and scanning tunneling microscopy. Bridging biology and quantum engineering, PDM oscillators offer a robust framework for innovation in adaptive materials and biologically inspired technologies. Future research should address nonlinear effects, anisotropic materials, and leverage data-driven optimization to fully realize the technological potential of PDM oscillators.