Bosonic quantum transport with power-law coupling: single-particle versus many-body treatment
Marisa Ulfa (1), Donny Dwiputra (2,3)

(1) Department of Physics, Faculty of Mathematics and Natural Science, Jakarta State University, East Jakarta 13220, Indonesia
(2) Research Center for Quantum Physics, National Research and Innovation Agency (BRIN), South Tangerang 15314, Indonesia
(3) Asia Pacific Center for Theoretical Physics, Pohang Science and Technology University, Pohang 37673, South Korea

Abstract

Simulating boundary-driven quantum transport in open systems is quadratically more complex compared to an isolated quantum systems, which is already contains exponentially growing time-complexity as number of the sites grow. To efficiently solve the Lindblad master equation, we may restrict our attention to the single-excitation sector, effectively mapping the problem to a tight-binding model, or keeping the many-body possibility by working with the covariance matrix via the Lyapunov equation. We show numerically for bosonic systems that they do not agree, except in a specific limit that is rarely stated explicitly. Remarkably, we find that qualitative behaviors---whether the particle current grows monotonically as a function of power-law parameter---also depends on specific particle sectors being considered. We aim for a practical guide for when each method is trustworthy and when results should be cross-checked.

Keywords: Quantum transport, Lindblad master equation, power-law hopping, long-range interactions

Topic: Theory, Nuclear, and Particle Physics