In physics, quantum dynamics is the quantum version of
classical dynamics. Quantum dynamics deals with the motions, and energy and momentum exchanges of systems whose behavior is governed by the laws of
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
. Quantum dynamics is relevant for burgeoning fields, such as
quantum computing and
atomic optics.
In mathematics, quantum dynamics is the study of the mathematics behind
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
.
[
] Specifically, as a study of ''dynamics'', this field investigates how quantum mechanical
observables
In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum p ...
change over time. Most fundamentally, this involves the study of one-parameter automorphisms of the algebra of all bounded operators on the Hilbert space of observables (which are self-adjoint operators). These dynamics were understood as early as the 1930s, after
Wigner,
Stone,
Hahn and
Hellinger worked in the field. Recently, mathematicians in the field have studied irreversible quantum mechanical systems on
von Neumann algebras.
See also
*
Quantum Field Theory
*
Perturbation theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle ...
*
Semigroups
*
Pseudodifferential operators
*
Brownian motion
*
Dilation theory
*
Quantum probability
*
Free probability
References
Quantum mechanics
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