In physics, 0-dimensional systems are idealized models whose spatial extent is negligible compared with relevant length scales, such that all degrees of freedom are localized at a single point in space. They are described solely by time-dependent variables without spatial coordinates, leading to dynamical equations without spatial derivatives (e.g., ordinary rather than partial differential equations). Examples include point particles in classical mechanics, quantum dots approximated as zero-dimensional electronic systems, and single-site models in many-body theory. These systems serve as useful limits for studying localization, discrete spectra, and simplified interactions before extending to higher-dimensional, spatially extended systems.
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