Trace preserving quantum dynamics using a novel reparametrization-neutral summation-by-parts difference operator
| Autor: | Oskar Ålund, Jan Nordström, Takahiro Miura, Fredrik Laurén, Yukinao Akamatsu, Alexander Rothkopf |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Density matrix
Trace (linear algebra) Dissipative systems Physics and Astronomy (miscellaneous) Nuclear Theory Beräkningsmatematik Quantum dynamics FOS: Physical sciences 010103 numerical & computational mathematics 01 natural sciences Initial boundary value problems Open quantum systems Nuclear Theory (nucl-th) High Energy Physics - Phenomenology (hep-ph) Master equation Time integration 0101 mathematics Physics Numerical Analysis Summation by parts Summation-by-parts operators Applied Mathematics Operator (physics) Computational mathematics Computational Physics (physics.comp-ph) Mimetic operator Computer Science Applications 010101 applied mathematics Computational Mathematics High Energy Physics - Phenomenology Classical mechanics Modeling and Simulation Dissipative system Physics - Computational Physics |
| Popis: | We develop a novel numerical scheme for the simulation of dissipative quantum dynamics following from two-body Lindblad master equations. All defining continuum properties of the Lindblad dynamics, hermiticity, positivity and in particular trace conservation of the evolved density matrix are preserved. The central ingredient is a new spatial difference operator, which not only fulfils the summation by parts (SBP) property but also implements a continuum reparametrization property. Using the time evolution of a heavy-quark anti-quark bound state in a hot thermal medium as an explicit example, we show how the reparametrization neutral summation-by-parts (RN-SBP) operator preserves the continuum properties of the theory. 34 pages, 7 figures, open-access code available via https://doi.org/10.5281/zenodo.3744460 |
| Databáze: | OpenAIRE |
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