My understanding of the processes involved in heat transfer has been expanding greatly in the past few weeks of research with Dr. Walczak. We are exploring quantum heat flux with the Landauer formula, which allows us to calculate thermal conductance. The Landauer formula along with the Fermi-Dirac distribution factors, for left and right heat reservoirs, follows.
We have employed a Taylor expansion with respect to temperature difference for this formula; allowing for a non-linear correction to heat flux in the quantum systems.
We are applying these and other functions so as to define the probability for electrons to be transferred via systems of coupled quantum dots. In such, we have employed different interference conditions which will affect electron transport. The particular couplings can be controlled by applied voltages by external gate terminals.
There are 8 differing configurations which we are analyzing currently. We are analyzing them with the aid of Mathematica and MATLAB, in which Dr. Walczak has created codes that allow for computation.
As our reasearch continues, we are working to create another code in MATLAB to integrate the convolutions of our transmission functions which will allow us to obtain the thermal conductance of samples. We aim to analyze all 8 configurations in depth and provide computation results and graphs within the final weeks of the summer.
Our research will examine the quantum processes of heat transfer. Specifically, we will examine these processes as carried by electrons tunneling via the system of coupled quantum dots. We will be using energy-dependent transmission functions and the calculation of quantum heat flux to understand the heat transfer process. Our goal is to develop models in which we can fit experimental data for the purpose of analysis. The analysis will include important conduction mechanisms, operational principles and nanoscale scattering processes.
By working with Dr. Walczak I hope to enhance my understanding of quantum interference by applying models specific to the heat transfer process. In order to be successful in applying such models, I intend to develop a deep understanding of the mathematical aspects of energy transfer processes, including the linear calculation of quantum heat flux and the quadratic correction available by use of Taylor Expansion.
Ultimately, we hope to present our findings at a conference and publish them in a peer-reviewed scientific journal. We believe that the conclusions of this research will have a significant impact upon our understanding of heat transfer phenomena.