Semiclassical physics, or simply semiclassical refers to a theory in which one part of a system is described quantum-mechanically whereas the other is treated classically. For example, external fields will be constant, or when changing will be classically described. In general, it incorporates a development in powers of Planck's constant, resulting in the classical physics of power 0, and the first nontrivial approximation to the power of (−1). In this case, there is a clear link between the quantum-mechanical system and the associated semi-classical and classical approximations, as it is similar in appearance to the transition from physical optics to geometric optics.
Three examples of a semiclassical approximation include:
- WKB approximation: electrons in classical external electromagnetic fields
- semiclassical gravity: quantum field theory within a classical curved gravitational background (see general relativity)
- quantum chaos
In quantum field theory, in the semiclassical approximation only Feynman diagrams with at most a single closed loop (see for example one-loop Feynman diagram) are considered, this corresponds to the powers of Planck's constant. In chaos theory, the observation semiclassical approximations is a topic of current research. The relationship between quantum physics and semi-classical approximation in this field of research, with applications in solid-state physics, was treated in a 2011 work of two authors in the Physik-Journal.
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