quantum dynamics
{{Short description|Study of quantum systems changing with time}}
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.{{Cite web
|url=http://www.quantiki.org/content/centre-quantum-dynamics-griffith-university
|title=Centre for Quantum Dynamics, Griffith University
|author=Joan Vaccaro
|date=2008-06-26
|work=Quantiki
|access-date=2010-01-25
|archive-url=https://web.archive.org/web/20091025092158/http://www.quantiki.org/content/centre-quantum-dynamics-griffith-university
|archive-date=2009-10-25
|url-status=dead
{{Cite book
| publisher = Springer
| isbn = 9780387229645
| last = Wyatt
| first = Robert Eugene
| author-link = Robert E. Wyatt
|author2=Corey J. Trahan
| title = Quantum dynamics with trajectories
| year = 2005
}} 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.
{{Cite book
| publisher = Springer
| isbn = 9783540407232
| last = Teufel
| first = Stefan
| title = Adiabatic perturbation theory in quantum dynamics
| date = 1821-01-01
}} Specifically, as a study of dynamics, this field investigates how quantum mechanical observables 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,{{when|reference is a quarter-century old|date=April 2025}} mathematicians in the field have studied irreversible quantum mechanical systems on von Neumann algebras.{{cite book | last=Price | first=Geoffrey | title=Advances in quantum dynamics : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Advances in Quantum Dynamics, June 16-20, 2002, Mount Holyoke College, South Hadley, Massachusetts | publisher=American Mathematical Society | publication-place=Providence, R.I | year=2003 | isbn=0-8218-3215-8 | oclc=52901091 | page=}}
Relation to classical dynamics
Equations to describe quantum systems can be seen as equivalent to that of classical dynamics on a macroscopic scale, except for the important detail that the variables don't follow the commutative laws of multiplication.{{Cite journal |date=1927 |title=The physical interpretation of the quantum dynamics |journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character |language=en |volume=113 |issue=765 |pages=621–641 |doi=10.1098/rspa.1927.0012 |issn=0950-1207|doi-access=free |bibcode=1927RSPSA.113..621D |last1=Dirac |first1=P. A. M. }} Hence, as a fundamental principle, these variables are instead described as "q-numbers", conventionally represented by operators or Hermitian matrices on a Hilbert space.{{Cite journal |last=Kuypers |first=Samuel |date=2022 |title=The quantum theory of time: a calculus for q-numbers |journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |language=en |volume=478 |issue=2263 |doi=10.1098/rspa.2021.0970 |issn=1364-5021 |pmc=9326976 |pmid=35909420|arxiv=2108.02771 |bibcode=2022RSPSA.47810970K }} Indeed, the state of the system in the atomic and subatomic scale is described not by dynamic variables with specific numerical values, but by state functions that are dependent on the c-number time. In this realm of quantum systems, the equation of motion governing dynamics heavily relies on the Hamiltonian, also known as the total energy. Therefore, to anticipate the time evolution of the system, one only needs to determine the initial condition of the state function |Ψ(t) and its first derivative with respect to time.{{Cite book |last=Tang |first=Chung Liang |title=Fundamentals of quantum mechanics: for solid state electronics and optics |date=2005 |publisher=Cambridge Univ. Press |isbn=978-0-521-82952-6 |location=Cambridge}}
For example, quasi-free states and automorphisms are the Fermionic counterparts of classical Gaussian measures{{Cite book |last1=Alicki |first1=Robert |title=Quantum dynamical systems |last2=Fannes |first2=Mark |date=2001 |publisher=Oxford University Press |isbn=978-0-19-850400-9 |edition=1. publ |location=Oxford |pages=103–121}} (Fermions' descriptors are Grassmann operators).
See also
References
{{Quantum mechanics topics}}
{{emerging technologies|quantum=yes|other=yes}}{{More categories|date=October 2024}}