Landauer current and mutual information in a bosonic quantum dot

TL;DR

This paper investigates quantum transport of bosons through a quantum dot connected to heat baths, deriving Landauer formulas for currents and analyzing mutual information growth, revealing logarithmic and quadratic relationships with boson number and current.

Contribution

It introduces a method to compute particle and heat currents in bosonic quantum dots using Landauer form and analyzes mutual information dynamics.

Findings

Mutual information grows logarithmically with boson number.

At low temperatures, mutual information can quadratically depend on steady-state current.

The study provides a framework for understanding quantum correlations in bosonic transport.

Abstract

We study the quantum transport of bosons through a quantum dot coupled to two macroscopic heat baths $L$ and $R$, held at fixed temperatures $T_{L}$ and $T_{R}$ respectively. We manage to cast the particle as well as the heat current into the Landauer form. Following the correlation matrix approach, we compute the time-dependent mutual information of the dot with the baths. We find that mutual information goes logarithmically as the number of bosons, and at low temperatures, it is possible to set up the parameters in such a way that in steady-state, the mutual information goes quadratically as a function of current.