Have you ever wondered how Fermi-Dirac statistics arises? I may have wondered during my bachelor degree studies, but now I only remember derivation done by the means of combinatorics. In this post I continue my wandering from a perspective of numerical simulation of a highly simplified system.

In the previous post we have built a model in which particles may freely jump between the energy levels (restricted only by the Pauli exclusion principle and Boltzmann statistics). This is not necessarily possible in real life systems. In semiconductors individual traps may have a single characteristic trap depth, or multiple depths which would not span full spectrum of available trap depths. In such case we need to assume existence of a conduction band energy level, which allows particles to travel between different traps.

Let us examine this particular case in this post.

Have you ever wondered how Fermi-Dirac statistics arises? I may have wondered during my bachelor degree studies, but now I only remember derivation done by the means of combinatorics. In this post let us allow Fermi-Dirac distribution to emerge from simulation of a simple particle system.

Research Council of Lithuania currently accepts student applications to do internship projects this summer at various institutions across Lithuania. One of the projects students could apply for is mine!

My project is called "Influence of the state interaction network on the statistical properties of the voter model". I would expect for the intern to take a look at the multi-state noisy voter model, and explore what happens when some of transitions between the states are forbidden (something similar was explored in AB model). You do not need to be familiar with sociophysics or opinion dynamics, though I would expect the project to have a significant numerical aspect to it (some programming skills will be required).

Intern application deadline is 29th of May.

Interns will get 1000 Eur monthly stipend. Plus, for students coming from other countries or cities to Vilnius there is possibility to get support for accommodation. Based on this call's rules I will have to give priority to students outside Vilnius University.

More details about this call is available on RCL's website: https://lmt.lrv.lt/en/research-funding/career-development-mobility-and-networking-opportunities/funding-for-students-research-projects-summer-schollarships/.

When presenting heterogeneous detrapping process at the DPG conference I got a question (or a suggestion to check) what would happen if instead of heterogeneous traps we would require multiple successes for the charge carrier to escape? In the previous post we have seen that this change makes relatively little difference when the detrapping times are exponential. But what if they are power-law? What if we require \( N_{success} \) successes within the heterogeneous detrapping process?

We previously delved into the statistical physics of birds on a wire, where the avian subjects, though sober, exhibited remarkably short tempers. Now, consider the following: which journey is more likely to be completed, that of a drunkard finding their way home or a tipsy bird navigating its flight path homeward? It's an intriguing question posed by Mathemaniac in a video that explores the theoretical disparities between Brownian motion in 2D and 3D realms, all without any harm to our feathered or human friends.