Lindbladian

<p>In <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, the Gorini–Kossakowski–Sudarshan–Lindblad equation (GKSL equation, named after Vittorio Gorini, <a href="/facts/Andrzej_Kossakowski/ReN0xeWV">Andrzej Kossakowski</a>, <a href="/facts/E._C._George_Sudarshan/EVsFTkSR">George Sudarshan</a> and <a href="/facts/G%C3%B6ran_Lindblad_(physicist)/qmLTf9HT">Göran Lindblad</a>), master equation in Lindblad form, quantum Liouvillian, or Lindbladian is one of the general forms of <a href="/facts/Markov_process/5oP5hntk">Markovian</a> <a href="/facts/Quantum_master_equation/1anPCylx">master equations</a> describing open quantum systems. It generalizes the <a href="/facts/Schr%C3%B6dinger_equation/3csgSIWF">Schrödinger equation</a> to open quantum systems; that is, systems in contacts with their surroundings. The resulting dynamics are no longer unitary, but still satisfy the property of being <a href="/facts/Completely_positive_trace-preserving/o7DKPKJc">trace-preserving and completely positive</a> for any initial condition. 
</p><p>The <a href="/facts/Schr%C3%B6dinger_equation/3csgSIWF">Schrödinger equation</a> or, actually, the von Neumann equation, is a special case of the GKSL equation, which has led to some speculation that quantum mechanics may be productively extended and expanded through further application and analysis of the Lindblad equation.  The Schrödinger equation deals with <a href="/facts/Quantum_state/7jbxd7Dx">state vectors</a>, which can only describe <a href="/facts/Pure_quantum_state/7jbxd7Dx">pure quantum states</a> and are thus less general than <a href="/facts/Density_matrix/A1XdylJa">density matrices</a>, which can describe <a href="/facts/Mixed_state_(physics)/7jbxd7Dx">mixed states</a> as well.
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Lindbladian open-in-new

Lindbladian