Editing Coupling (physics)

{{Short description|Two systems are coupled if they are interacting with each other}}
{{Coupling in molecules}}

In [[physics]], <dfn>two objects are said </dfn>to be coupled when they are interacting with each other. In [[classical mechanics]], coupling is a connection between two [[Oscillation|oscillating]] systems, such as [[pendulum]]s connected by a spring. The connection affects the oscillatory pattern of both objects. In [[particle physics]], <dfn>two particles are coupled </dfn>if they are connected by <dfn>one of the four </dfn>[[Fundamental interaction|fundamental forces]].

==Wave mechanics==

=== Coupled harmonic oscillator ===
[[File:Coupled.svg|thumb|Coupled pendulums connected by a spring]]
If two [[Waves (physics)|waves]] are able to transmit [[energy]] to each other, then these waves are said to be "coupled." This normally occurs when the waves share a common component. An example of this is two pendulums connected by a [[Spring (device)|spring]]. If the pendulums are identical, then their equations of motion are given by
<math display="block">m\ddot{x} = -mg\frac{x}{l_1} - k(x-y)</math>
<math display="block">m\ddot{y} = -mg \frac{y}{l_2} + k(x-y)</math>

These equations represent the [[simple harmonic motion]] of the pendulum with an added coupling factor of the spring.<ref name=":0">{{Cite book|title=The Physics of Vibrations and Waves | edition = Fourth | last=Pain|first=H.J.| publisher=Wiley | year=1993| isbn=0-471-93742-8|location=West Sussex, England}}</ref> This behavior is also seen in certain molecules (such as [[Carbon dioxide|CO<sub>2</sub>]] and H<sub>2</sub>O), wherein two of the atoms will vibrate around a central one in a similar manner.<ref name=":0" />

=== Coupled LC circuits ===
[[File:LC coupling.png|thumb|Two LC circuits coupled together.]]
In [[LC circuit]]s, charge oscillates between the [[capacitor]] and the [[inductor]] and can therefore be modeled as a simple harmonic oscillator. When the [[magnetic flux]] from <dfn>one inductor is able </dfn>to affect the [[inductance]] of an inductor in an unconnected LC circuit, the circuits are said to be coupled.<ref name=":0" /> The coefficient of coupling k defines how closely the <dfn>two circuits are coupled</dfn> and is given by the equation
<math display="block">\frac{M}{\sqrt{L_p L_s}} = k</math>
where M is the [[Mutual Inductance|mutual inductance]] of the circuits and L<sub>p</sub> and L<sub>s</sub> are the inductances of the primary and secondary circuits, respectively. If the flux lines of the primary inductor thread every line of the secondary one, then the coefficient of coupling is 1 and <math display="inline">M = \sqrt{L_p L_s}</math> In practice, however, there is of<dfn>ten leakage</dfn>, so most systems are not perfectly coupled.<ref name=":0" />[[File:1H NMR Ethyl Acetate Coupling shown - 2.png|thumb|Peaks in an NMR image of Ethyl Acetate.]]

==Chemistry==
=== Spin-spin coupling ===
[[Angular momentum coupling|Spin-spin coupling]] occurs when the [[magnetic field]] of <dfn>one atom affects the </dfn>magnetic field of another nearby atom. This is very common in [[Magnetic resonance imaging|NMR imaging]]. If the atoms are not coupled, then there will be <dfn>two individual peaks</dfn>, known as a doublet, representing the individual atoms. If coupling is present, then there will be a triplet, <dfn>one larger peak with two smaller ones to </dfn>either side. This occurs due to the [[Spin (physics)|spins]] of the individual atoms oscillating in tandem.<ref>{{Cite web|url=https://chem.libretexts.org/Textbook_Maps/Organic_Chemistry_Textbook_Maps/Map%3A_Organic_Chemistry_With_a_Biological_Emphasis_(Soderberg)/Chapter_05%3A_Structure_Determination_II/5.5%3A_Spin-spin_coupling|title=5.5 Spin-Spin Coupling|date=2015-07-21|website=Chemistry Libretexts|access-date=13 Apr 2017}}</ref>

==Astrophysics==

Objects in space which are coupled to each other are under the mutual influence of each other's [[gravity]]. For instance, the Earth is coupled to both the Sun and the Moon, as it is under the gravitational influence of both. Common in space are [[binary system]]s, two objects gravitationally coupled to each other. Examples of this are [[binary star]]s which circle each other. Multiple objects may also be coupled to each other simultaneously, such as with [[globular cluster]]s and [[galaxy group]]s. When smaller particles, such as dust, which are coupled together over time accumulate into much larger objects, [[Accretion (astrophysics)|accretion]] is occurring. This is the major process by which stars and planets form.<ref>{{Cite book|title=Universe, Second Edition|last=Kaufmann|first=William|publisher=W.H. Freeman and Company|year=1988|isbn=978-0-7167-1927-4|url-access=registration|url=https://archive.org/details/universe0002kauf}}</ref>

==Plasma==
{{main|Frequency classification of plasmas}}

The coupling constant of a [[Plasma (physics)|plasma]] is given by the ratio of its average [[Coulomb interaction|Coulomb-interaction]] energy to its average [[kinetic energy]]—or how strongly the electric force of each atom holds the plasma together.<ref name=":1">{{Cite book|title=Plasma Physics|last=Ichimaru|first=Setsuo|publisher=Benjamin/Cumming Publishing Company|year=1986|isbn=978-0-8053-8754-4|location=Menlo Park, California}}</ref> Plasmas can therefore be categorized into weakly- and strongly-coupled plasmas depending upon the value of this ratio. Many of the typical classical plasmas, such as the plasma in the [[solar corona]], are weakly coupled, while the plasma in a [[white dwarf]] star is an example of a strongly coupled plasma.<ref name=":1" />

== Quantum mechanics ==
Two coupled quantum systems can be modeled by a [[Hamiltonian (quantum mechanics)|Hamiltonian]] of the form[[File:Spin orbit coupling dispersion relation.pdf|thumb|Dispersion relations for non-coupled, weakly-coupled, and strongly-coupled particles]]
<math display="block">\hat{H} = \hat{H}_a + \hat{H}_b + \hat{V}_{ab}</math>
which is the addition of the two Hamiltonians in isolation with an added interaction factor. In most simple systems, <math>\hat{H}_a</math> and <math>\hat{H}_b</math> can be solved exactly while <math>\hat{V}_{ab}</math> can be solved through [[Perturbation theory (quantum mechanics)|perturbation theory]].<ref name=":2">{{Cite book| title=Introductory Applied Quantum and Statistical Mechanics|last1=Hagelstein| first1=Peter| last2=Senturia|first2=Stephen| last3=Orlando|first3=Terry| publisher=Wiley |year=2004 |isbn=978-0-471-20276-9 |location=Hoboken, New Jersey}}</ref> If the two systems have similar total energy, then the system may undergo [[Rabi oscillation]].<ref name=":2" />

=== Angular momentum coupling ===
{{Main|Angular momentum coupling}}

When [[Angular momentum operator|angular momenta]] from two separate sources interact with each other, they are said to be coupled.<ref name=":3">{{Cite book| title=Quantum Mechanics | edition = Third |last=Merzbacher|first=Eugene |publisher=Wiley|year=1998 |isbn=978-0-471--88702-7}}</ref> For example, two [[electron]]s orbiting around the same [[Atomic nucleus|nucleus]] may have coupled angular momenta. Due to the [[Conservation of Angular Momentum|conservation of angular momentum]] and the nature of the [[angular momentum operator]], the total angular momentum is always the sum of the individual angular momenta of the electrons, or<ref name=":3" />
<math display="block">\mathbf{J}=\mathbf{J_1}+\mathbf{J_2}</math>
[[Spin–orbit interaction|Spin-Orbit interaction]] (also known as spin-orbit coupling) is a special case of angular momentum coupling. Specifically, it is the interaction between the [[Spin (physics)|intrinsic spin]] of a particle, '''S''', and its orbital angular momentum, '''L'''. As they are both forms of angular momentum, they must be conserved. Even if energy is transferred between the two, the total angular momentum, '''J''', of the system must be constant, <math>\mathbf{J}=\mathbf{L}+\mathbf{S}</math>.<ref name=":3" />

== Particle physics and quantum field theory ==
[[File:Gluon coupling.svg|thumb|Examples of gluon coupling]]
[[Particle]]s which interact with each other are said to be coupled. This interaction is caused by one of the fundamental forces, whose strengths are usually given by a dimensionless [[coupling constant]]. In [[quantum electrodynamics]], this value is known as the [[fine-structure constant]] α, approximately equal to 1/137. For [[quantum chromodynamics]], the constant changes with respect to the distance between the particles. This phenomenon is known as ''[[asymptotic freedom]].'' Forces which have a coupling constant greater than 1 are said to be "strongly coupled" while those with constants less than 1 are said to be "weakly coupled."<ref>{{Cite book|title=Elementary Particle-Second, Revised Edition|last=Griffiths|first=David|publisher=Wiley-VCH|year=2010|isbn=978-3-527-40601-2}}</ref>

== References ==
<references />

{{DEFAULTSORT:Coupling (Physics)}}
[[Category:Force]]
[[Category:Particle physics]]