QuantumCumulants.jl: A Julia framework for generalized mean-field
equations in open quantum systems
- URL: http://arxiv.org/abs/2105.01657v2
- Date: Mon, 27 Dec 2021 21:40:11 GMT
- Title: QuantumCumulants.jl: A Julia framework for generalized mean-field
equations in open quantum systems
- Authors: David Plankensteiner, Christoph Hotter, Helmut Ritsch
- Abstract summary: We present an open-source framework that fully automizes equations of motion of operators up to a desired order.
After reviewing the theory we present the framework and showcase its usefulness in a few example problems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A full quantum mechanical treatment of open quantum systems via a Master
equation is often limited by the size of the underlying Hilbert space. As an
alternative, the dynamics can also be formulated in terms of systems of coupled
differential equations for operators in the Heisenberg picture. This typically
leads to an infinite hierarchy of equations for products of operators. A
well-established approach to truncate this infinite set at the level of
expectation values is to neglect quantum correlations of high order. This is
systematically realized with a so-called cumulant expansion, which decomposes
expectation values of operator products into products of a given lower order,
leading to a closed set of equations. Here we present an open-source framework
that fully automizes this approach: first, the equations of motion of operators
up to a desired order are derived symbolically using predefined canonical
commutation relations. Next, the resulting equations for the expectation values
are expanded employing the cumulant expansion approach, where moments up to a
chosen order specified by the user are included. Finally, a numerical solution
can be directly obtained from the symbolic equations. After reviewing the
theory we present the framework and showcase its usefulness in a few example
problems.
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