New Insights into the Obvious

The number of posts I publish here tends to rise around the holidays, when demands on my time temporarily wane, giving me time to think about interesting topics and reflect on life.  I reread a post from a while back, which talked about my frustrations with the hectic nature of my job and my desire to spend more time on deeper thought.  Click here for that post.  My goal was to understand some of the deeper consequences of quantum mechanics and how it underpins thermodynamics/statistical mechanics.

I have approached this goal over the last half decade by rethinking the most basic foundations of quantum mechanics; those topics that students quickly leapfrog to progress to the next stage of solving real research problems.  I find the need to build my intuition by mulling over these basics, perseverating over them until the meaning infuses my brain.  Once it becomes second nature, I can build on these foundations.

In the process skimming through typical textbooks, I found that the connection between quantum mechanics and density operators is not well made.  So, I wrote a simple two-page manuscript with a simple example that illustrates the important facts and submitted it to the American Journal of Physics.  One of the reviewers stated, “Reading this very short and sweet manuscript taught me something about density operators that I did not appreciate before; something that seems vitally important for both students -and- the general interested physicist to understand…

“The main thing I learned by reading this manuscript is that the apparent classical mixture form of the density matrix -always- originates from a purely quantum effect - entanglement with the environment. I almost cannot believe that I did not appreciate that before - interaction with the environment is certainly presented as the main issue to be solved in any open quantum system textbook. But the formalism obscures this, and I think I had come away with the impression that at least in some cases, the density matrix was really just used to represent a classical mixture. The use of the simple example here makes it extremely intuitive and obvious, which I think is just as the authors intended. However, I suggest three changes that I think will make this manuscript even better...”

I find AJP a wonderful journal, authored and read by people who enjoy learning and appreciate new insights or an unexpected twist on a well-worn topic.

At the other extreme, we just had a paper accepted that developed two different models of how light can affect the mechanical properties of matter and used these models to interpret experiments to determine the underlying mechanisms.

This break I plan on continuing my work on a new project related to quantum computing, which is particularly exciting to me because it will require learning a lot of new material.

Stay tuned!