# Coefficient of performance at maximum cooling power of a simplified quantum dot refrigerator model with resistance

## TL;DR

This paper presents an analytical model of a quantum dot refrigerator, deriving the maximum coefficient of performance at optimal cooling power and exploring its dependence on Carnot efficiency, aiding mesoscopic refrigerator design.

## Contribution

It introduces a simplified analytical model for a quantum dot refrigerator without spin or Coulomb effects, deriving performance limits analytically.

## Key findings

- Derived an analytical expression for maximum COP at optimal cooling power.
- Demonstrated the COP's dependence on Carnot efficiency numerically.
- Provided insights for designing mesoscopic refrigeration systems.

## Abstract

A simplified analytical model of single-level quantum dot (QD) refrigerator was studied without considering the electron spin and Coulomb interaction. Based on the ballistic transport of electrons between two reservoirs across the QD, the Joule heat of the system was assumed to be generated from the Ohmic contacts between the QD and reservoirs. By using the transition rate equation, the performance of the QD refrigerator was studied with respect to the electron transmission probability and the partition ratio (i.e., the fraction of Joule heat generated in the system that releases into the cold reservoir). The analytical expression of the maximum coefficient of performance was obtained under the exoreversible working condition. The Carnot-bound-dependent coefficient of performance at maximum cooling power of the QD system was also demonstrated numerically. The results of this work may provide some guidance for the design of mesoscopic refrigerators.

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Source: https://tomesphere.com/paper/1906.09009