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<p>Replace raw Quantum Collection backlink with BT backlink template</p> <p><b>New page</b></p><div>{{Short description|Operator describing collisions in quantum kinetic theory}}<br /> <br /> {{Quantum methods backlink|Plasma and kinetic methods}}<br /> <br /> [[File:Quantum_field_theory_dependency_map.png|250px|right]]<br /> <br /> &#039;&#039;&#039;Quantum collision operator&#039;&#039;&#039; is an operator used in [[Physics:Quantum kinetic theory]] to describe how interactions between particles change a quantum distribution function or density matrix over time. It represents the collisional part of a kinetic equation, separating scattering, relaxation, and redistribution processes from free motion and external-field evolution.<br /> <br /> In plasma, condensed-matter, and many-body systems, collision operators are used to model effects such as particle scattering, energy exchange, decoherence, damping, and transport. They provide a bridge between microscopic quantum dynamics and macroscopic quantities such as conductivity, diffusion, viscosity, and relaxation rates.<br /> <br /> == Role in kinetic equations ==<br /> <br /> A quantum kinetic equation often separates evolution into a reversible part and a collision part. Schematically,<br /> <br /> :&lt;math&gt;\frac{\partial f}{\partial t} + \text{transport terms} = C[f],&lt;/math&gt;<br /> <br /> where &lt;math&gt;f&lt;/math&gt; is a distribution function and &lt;math&gt;C[f]&lt;/math&gt; is the collision operator.<br /> <br /> The collision operator accounts for interactions that change the occupation of quantum states. Depending on the system, these may include electron-electron collisions, electron-phonon scattering, particle-wave interactions, or collisions between charged particles in a plasma.<br /> <br /> == Quantum features ==<br /> <br /> Unlike a purely classical collision term, a quantum collision operator may include:<br /> <br /> * Pauli blocking for fermions;<br /> * Bose enhancement for bosons;<br /> * transition probabilities from quantum scattering amplitudes;<br /> * coherence and off-diagonal density-matrix effects;<br /> * detailed balance between quantum states.<br /> <br /> These features are important when the occupation of states, wave interference, or quantum statistics affect transport and relaxation.<br /> <br /> == Applications ==<br /> <br /> Quantum collision operators appear in:<br /> <br /> * [[Physics:Quantum kinetic theory]];<br /> * [[Physics:Quantum Vlasov equation]];<br /> * [[Physics:Quantum Transport theory]];<br /> * nonequilibrium quantum field theory;<br /> * semiconductor transport;<br /> * dense plasma physics;<br /> * quantum hydrodynamic and many-body models.<br /> <br /> They are especially useful when a system is not in thermal equilibrium but still requires a statistical description.<br /> <br /> =See also=<br /> {{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also/Methods}}<br /> <br /> =References=<br /> {{reflist|3}}<br /> <br /> {{Author|Harold Foppele}}<br /> <br /> {{Sourceattribution|Collision operator|1}}</div>

imported>WikiHarold