0-dimensional systems

Physical models with no spatial extent, often representing a single site or degree of freedom while retaining internal dynamics.

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Degrees of freedom: Independent variables needed to specify the state of a physical system. A 0-dimensional model often retains only a few independent state variables.
Quantum harmonic oscillator: A quantum system with a particle bound by a potential proportional to the square of its displacement. It is a standard exactly solvable example with one dynamical coordinate and no spatial field.
Dynamical mean-field theory: A method that maps a lattice many-body problem to a self-consistent quantum impurity problem. Its central impurity problem is a 0-dimensional system embedded in a dynamical environment.
One-dimensional system: A system whose spatial variation occurs along one dimension. It restores spatial structure along one axis, unlike a 0-dimensional model.
State space: The set of all possible states of a system, represented by its independent variables. Its state space replaces spatial configuration as the model's description of possible states.
Two-level system: A quantum system whose state space has two independent basis states. Its internal state changes despite having no spatial extent.
Quantum impurity model: A localized quantum degree of freedom coupled to a continuum of surrounding states. It applies local dynamics to problems involving an impurity inside a larger material.
Zero-dimensional quantum field theory: A field theory with no spacetime coordinates, reduced to an integral over field variables. It is a mathematical zero-dimensional limit, distinct from a physical local system with time evolution.
Hamiltonian mechanics: A formulation of classical mechanics using generalized coordinates, conjugate momenta, and a Hamiltonian. It describes internal dynamics without requiring a spatially extended medium.
Spin dynamics: The time evolution of spin degrees of freedom under applied fields and interactions. A spin can evolve dynamically at a single site without spatial motion.