In physics, quantum dynamics is the quantum version of
classical dynamics
In classical mechanics, analytical dynamics, also known as classical dynamics or simply dynamics, is concerned with the relationship between motion of bodies and its causes, namely the forces acting on the bodies and the properties of the bodies, ...
. 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
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
and
atomic optics Atom optics (or atomic optics) is the area of physics which deals with beams of cold, slowly moving neutral atoms, as a special case of a particle beam.
Like an optical beam, the atomic beam may exhibit diffraction and Interference (wave propagation ...
.
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 physi ...
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
Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his con ...
,
Stone
In geology, rock (or stone) is any naturally occurring solid mass or aggregate of minerals or mineraloid matter. It is categorized by the minerals included, its Chemical compound, chemical composition, and the way in which it is formed. Rocks ...
,
Hahn and
Hellinger Hellinger is a surname. Notable people with the surname include:
* Bert Hellinger (1925–2019), German psychotherapist
*Ernst Hellinger (1883–1950), German mathematician
**Hellinger distance, used to quantify the similarity between two probabil ...
worked in the field. Recently, mathematicians in the field have studied irreversible quantum mechanical systems on
von Neumann algebra
In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra.
Von Neumann algeb ...
s.
See also
*
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
*
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
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it.
The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'', ...
*
Pseudodifferential operators
In mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory, e.g. i ...
*
Brownian motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas).
This pattern of motion typically consists of random fluctuations in a particle's position insi ...
*
Dilation theory In mathematics, a dilation is a function f from a metric space M into itself that satisfies the identity
:d(f(x),f(y))=rd(x,y)
for all points x, y \in M, where d(x, y) is the distance from x to y and r is some positive real number.
In Euclidean sp ...
*
Quantum probability
The Born rule (also called Born's rule) is a key postulate of quantum mechanics which gives the probability that a measurement of a quantum system will yield a given result. In its simplest form, it states that the probability density of findin ...
*
Free probability Free probability is a mathematical theory that studies non-commutative random variables. The "freeness" or free independence property is the analogue of the classical notion of independence, and it is connected with free products.
This theory was in ...
References
Quantum mechanics
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