Lindbladian

In quantum mechanics, the Gorini–Kossakowski–Sudarshan–Lindblad equation (GKSL equation, named after Vittorio Gorini, Andrzej Kossakowski, George Sudarshan and Göran Lindblad), master equation in Lindblad form, quantum Liouvillian, or Lindbladian is one of the general forms of Markovian master equations describing open quantum systems. It generalizes the Schrödinger equation to open quantum systems; that is, systems in contacts with their surroundings. The resulting dynamics is no longer unitary, but still satisfies the property of being trace-preserving and completely positive for any initial condition.^[1]

The Schrödinger equation 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.^[2] The Schrödinger equation deals with state vectors, which can only describe pure quantum states and are thus less general than density matrices, which can describe mixed states as well.

^ Breuer, Heinz-Peter; Petruccione, F. (2002). The Theory of Open Quantum Systems. Oxford University Press. ISBN 978-0-1985-2063-4.
^ Weinberg, Steven (2014). "Quantum Mechanics Without State Vectors". Phys. Rev. A. 90 (4): 042102. arXiv:1405.3483. Bibcode:2014PhRvA..90d2102W. doi:10.1103/PhysRevA.90.042102. S2CID 53990012.

[BP-1] Breuer, Heinz-Peter; Petruccione, F. (2002). The Theory of Open Quantum Systems. Oxford University Press. ISBN 978-0-1985-2063-4.

[2] Weinberg, Steven (2014). "Quantum Mechanics Without State Vectors". Phys. Rev. A. 90 (4): 042102. arXiv:1405.3483. Bibcode:2014PhRvA..90d2102W. doi:10.1103/PhysRevA.90.042102. S2CID 53990012.

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