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.[1][2] 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.[3] 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, mathematicians in the field have studied irreversible quantum mechanical systems on von Neumann algebras.[4]

See also

Quantum Field Theory

Perturbation theory

Semigroups

Pseudodifferential operators

Brownian motion

Dilation theory

Quantum probability

Free probability

References

Joan Vaccaro (2008-06-26). "Centre for Quantum Dynamics, Griffith University". Quantiki. Archived from the original on 2009-10-25. Retrieved 2010-01-25.

Wyatt, Robert Eugene; Corey J. Trahan (2005). Quantum dynamics with trajectories. Springer. ISBN 9780387229645.

Teufel, Stefan (1821-01-01). Adiabatic perturbation theory in quantum dynamics. Springer. ISBN 9783540407232.

Price, Geoffrey L. (2003). Advances in quantum dynamics. AMS Bookstore. ISBN 9780821832158.

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Quantum mechanics

Background

Introduction History

timeline Glossary Classical mechanics Old quantum theory

Fundamentals

Bra–ket notation Casimir effect Coherence Coherent control Complementarity Density matrix Energy level

degenerate levels excited state ground state QED vacuum QCD vacuum Vacuum state Zero-point energy Hamiltonian Heisenberg uncertainty principle Pauli exclusion principle Measurement Observable Operator Probability distribution Quantum Qubit Qutrit Scattering theory Spin Spontaneous parametric down-conversion Symmetry Symmetry breaking

Spontaneous symmetry breaking No-go theorem No-cloning theorem Von Neumann entropy Wave interference Wave function

collapse Universal wavefunction Wave–particle duality

Matter wave Wave propagation Virtual particle

Quantum

quantum coherence annealing decoherence entanglement fluctuation foam levitation noise nonlocality number realm state superposition system tunnelling Quantum vacuum state

Mathematics

Equations

Dirac Klein–Gordon Pauli Rydberg Schrödinger

Formulations

Heisenberg Interaction Matrix mechanics Path integral formulation Phase space Schrödinger

Other

Quantum

algebra calculus

differential stochastic geometry group Q-analog

List

Interpretations

Bayesian Consistent histories Cosmological Copenhagen de Broglie–Bohm Ensemble Hidden variables Many worlds Objective collapse Quantum logic Relational Stochastic Transactional

Experiments

Afshar Bell's inequality Cold Atom Laboratory Davisson–Germer Delayed-choice quantum eraser Double-slit Elitzur–Vaidman Franck–Hertz experiment Leggett–Garg inequality Mach-Zehnder inter. Popper Quantum eraser Quantum suicide and immortality Schrödinger's cat Stern–Gerlach Wheeler's delayed choice

Science

Measurement problem QBism

Quantum

biology chemistry chaos cognition complexity theory computing

Timeline cosmology dynamics economics finance foundations game theory information nanoscience metrology mind optics probability social science spacetime

Technologies

Quantum technology

links Matrix isolation Phase qubit Quantum dot

cellular automaton display laser single-photon source solar cell Quantum well

laser

Extensions

Dirac sea Fractional quantum mechanics Quantum electrodynamics

links Quantum geometry Quantum field theory

links Quantum gravity

links Quantum information science

links Quantum statistical mechanics Relativistic quantum mechanics De Broglie–Bohm theory Stochastic electrodynamics

Related

Quantum mechanics of time travel Textbooks

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Emerging technologies

Fields

Quantum

algorithms amplifier bus cellular automata channel circuit complexity theory computing clock cryptography

post-quantum dynamics electronics error correction finite automata image processing imaging information key distribution logic logic gates machine machine learning metamaterial network neural network optics programming sensing simulator teleportation

Other

Anti-gravity Acoustic levitation Cloak of invisibility Digital scent technology Force field

Plasma window Immersive virtual reality Magnetic refrigeration Phased-array optics Thermoacoustic heat engine

Category Category List-Class article List

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