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1. Landau ordering phase transitions beyond the Landau paradigm

   https://doi.org/10.1103/PhysRevResearch.2.023031  

   Bi, Zhen; Lake, Ethan; Senthil, T. (April 2020, Physical Review Research)
2. Kinetic shock profiles for the Landau equation

   https://doi.org/10.15781/5z5b3583  

   Albritton, Dallas; Bedrossian, Jacob; Novack, Matthew (January 2026, Ars inveniendi analytica)

   The physical quantities in a gas should vary continuously across a shock. However, the physics inherent in the compressible Euler equations is insufficient to describe the width or structure of the shock. We demonstrate the existence of weak shock profiles to the kinetic Landau equation, that is, traveling wave solutions with Maxwellian asymptotic states whose hydrodynamic quantities satisfy the Rankine-Hugoniot conditions. These solutions serve to capture the structure of weak shocks at the kinetic level. Previous works considered only the Boltzmann equation with hard sphere and angular cut-off potentials. 

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3. Interaction-mitigated Landau damping

   https://doi.org/10.1103/PhysRevB.109.L121102  

   Wang, Xuepeng; Moessner, Roderich; Chowdhury, Debanjan (March 2024, Physical Review B)
4. A particle method for the homogeneous Landau equation

   https://doi.org/10.1016/j.jcpx.2020.100066  

   Carrillo, Jose A; Hu, Jingwei; Wang, Li; Wu, Jeremy (June 2020, Journal of Computational Physics: X)
5. Landau levels for charged particles with anisotropic mass

   https://doi.org/10.1119/5.0123039  

   Ciftja, Orion (August 2024, American Journal of Physics)

   The problem of the two-dimensional motion of a charged particle with constant mass in the presence of a uniform constant perpendicular magnetic field features in several undergraduate and graduate quantum physics textbooks. This problem is very important to studies of two-dimensional materials that manifest quantum Hall behavior, as evidenced by several major discoveries over the last few years. Many real experimental samples are more complicated due to the anisotropic mass of the electrons. In this work, we provide the exact solution to this problem by means of a clever scaling of coordinates. Calculations are done for a symmetric gauge of the magnetic field. This study allows a broad audience of students and teachers to understand the mathematical techniques that lead to the solution of this quantum problem. 

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