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Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation

Journal Article · · Quantum
 [1]
  1. Georgia Inst. of Technology, Atlanta, GA (United States); Georgia Institute of Technology
+ Show Author Affiliations
Here we present a Lindblad master equation that approximates the Redfield equation, a well known master equation derived from first principles, without significantly compromising the range of applicability of the Redfield equation. Instead of full-scale coarse-graining, this approximation only truncates terms in the Redfield equation that average out over a time-scale typical of the quantum system. The first step in this approximation is to properly renormalize the system Hamiltonian, to symmetrize the gains and losses of the state due to the environmental coupling. In the second step, we swap out an arithmetic mean of the spectral density with a geometric one, in these gains and losses, thereby restoring complete positivity. This completely positive approximation, GAME (geometric-arithmetic master equation), is adaptable between its time-independent, time-dependent, and Floquet form. In the exactly solvable, three-level, Jaynes-Cummings model, we find that the error of the approximate state is almost an order of magnitude lower than that obtained by solving the coarse-grained stochastic master equation. As a test-bed, we use a ferromagnetic Heisenberg spin-chain with long-range dipole-dipole coupling between up to 25-spins, and study the differences between various master equations. We find that GAME has the highest accuracy per computational resource.
Research Organization:
Georgia Inst. of Technology, Atlanta, GA (United States)
Sponsoring Organization:
Georgia Tech Quantum Alliance (GTQA); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
Grant/Contract Number:
FG02-06ER46281
OSTI ID:
1666137
Journal Information:
Quantum, Journal Name: Quantum Vol. 4; ISSN 2521-327X
Publisher:
Quantum Science Open CommunityCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Energy Transfer
Quantum Dynamics