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[[File:Quantum ergodicity.gif|thumb|360px|right|The eigenmode of a classically integrable ...y|chaotic]] in the sense of exponential sensitivity to initial conditions. Quantum ergodicity states, roughly, that in the high-energy limit, the probability ...

In [[quantum mechanics]], the '''quantum revival'''<ref> | title = Periodic spontaneous collapse and revival in a simple quantum model ...

...ough Borges' strongest links to mathematics are through [[Georg Cantor]]'s theory of infinite sets, outlined in "The Doctrine of Cycles" (''La doctrina de lo ...overing [[logic]], [[paradox]]es, infinity, [[topology]] and [[probability theory]]. He was also aware of the contemporary debates on the foundations of math ...

{{quantum mechanics | cTopic = Background }} ...bau_1922_p_364.png|thumb|5 electrons with the same principal and auxiliary quantum numbers, orbiting in sync. (<ref name=":1" /> page 364)]] ...

...dom trajectories appear and eventually consume the entire plot, indicating chaos.]] ...eory|chaos]] (the study of chaos in [[Hamiltonian system]]s) and [[quantum chaos]]. It describes a free rotating stick (with [[moment of inertia]] <math>I</ ...

* [[Sturm–Liouville theory]] of [[orthogonal polynomials]] and separable partial differential equation ===Dynamical systems and Chaos theory=== ...

...ds developed within [[control theory]], [[information theory]], [[systems theory]] and related areas: control design, [[estimation]], [[System identificatio ...ed in the 1990s when two new areas emerged: ''[[control of chaos]]'' and ''quantum control''. ...

* ''The Aim and Structure of Physical Theory'' by [[Pierre Maurice Marie Duhem]] (1914, English tr., 1954) * ''[[The Meaning of Relativity]]: Including the Relativistic Theory of the Non-Symmetric Field'' by [[Albert Einstein]] (1922) ...

In [[probability theory]], a branch of [[mathematics]], '''white noise analysis''', otherwise known ...[[tempered distributions]] has the [[Characteristic function (probability theory)|characteristic function]]<ref name=":0">{{Cite book|last1=Hida|first1=Take ...

{{Short description|Dissipation in quantum systems}} ...s many features with the subjects of [[quantum decoherence]] and [[quantum theory of measurement]]. ...

...ence tracking microscope''' (RTM) is a [[microscope]] that is based on the quantum recurrence phenomenon of an atomic wave packet. It is used to investigate t ...ef>{{cite journal | last=Saif | first=Farhan | title=Classical and quantum chaos in atom optics | journal=Physics Reports | publisher=Elsevier BV | volume=4 ...

...Institute for Gravitational Physics]], Nicolai was head of the department "Quantum Gravity and Unified Field Theories" and a director from 1997 to 2020, when ...en, from 1998 to 2003 the editor-in-chief of the journal ''[[Classical and Quantum Gravity]]'', and from 2006 to 2011 the editor-in-chief of the journal ''[[G ...

.../ref> Mathematically speaking, parity measurements are used to project a [[Quantum state|state]] into an [[eigenstate]] of an operator and to acquire its [[ei ...{{Cite book |last=Nielsen |first=Michael A. |title=Quantum computation and quantum information |date=2010 |publisher=Cambridge University Press |others=Isaac ...

{{Short description|Notion in network science of quantum information networks}} ...|date=2011 |title=Cascading dynamics in complex quantum networks |journal=Chaos: An Interdisciplinary Journal of Nonlinear Science |volume=21 |issue=2 |pag ...

...description|Peer-reviewed, consciousness-based research for understanding quantum entanglement and non-locality.}} ...[[Mind]] emerges to comprehend both [[Principle of locality|local]] and [[Quantum nonlocality|non-local]] realities through [[consciousness]]. ...

{{Short description|Model of quantum optics}} ...critical exponents|Ising universality class]] and was realized in [[cavity quantum electrodynamics]] experiments. Although the superradiant transition bears s ...

In the fields of [[dynamical system]]s and [[control theory]], a '''fractional-order system''' is a dynamical system that can be modele ...With the introduction of fractional-order systems, some researchers study chaos in the system of total order less than 3.<ref>{{Cite book |doi = 10.1109/ET ...

{{Short description|Hypothesis of quantum systems and when equilibrium statistical mechanics describes them accuratel ...[[thermodynamic system]] through the mechanism of [[Chaos theory|dynamical chaos]], as is done in [[classical mechanics]], one should instead examine the pr ...

...t the output is statistically close to uniform.<ref>{{cite web| url=http://theory.stanford.edu/~trevisan/pubs/extractor-full.pdf| title= Extractors and Pseud ===Chaos machine=== ...

...ly by means of a [[stochastic differential equation]] of a [[Quantum field theory|field]]. ...niversity Press|oclc=939869413}}</ref><ref>{{Cite book|title=Quantum Field Theory|last=Zee|first=Anthony|publisher=Princeton University Press|year=2010|isbn= ...