Quantum Lindblad Equation

Available identifiers

WikidataQ4476520 ScholiaQ4476520MaRDI QIDQ6534317

describes open system quantum dynamics including dissipation and/or decoherence

Description

Markovian quantum master equation for the evolution of quantum mechanical density matrices (pure or mixed states). 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.

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Defining Formula: $\frac{\mathrm{d}}{\mathrm{d}t}\rho =-\frac{\mathrm{i}}{\hslash }[H,\rho ]+\sum _{k=1}^{N^2-1}{\gamma }_k(L_k\rho L_k^{†}-\frac{1}{2}[L_k^{†}{L}_k,\rho {]}_{+})$

$H$ symbol represents Quantum Hamiltonian Operator

$L$ symbol represents Quantum Jump Operator

$\gamma >0$ symbol represents Quantum Damping Rate

$\hslash$ symbol represents Planck Constant

$\rho$ symbol represents Quantum Density Operator

$t$ symbol represents Time

$\mathrm{i}$ symbol represents imaginary unit

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Related URL

https://en.wikipedia.org/wiki/Lindbladian

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