- Apr 11, 2025
Several features of the eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition are discussed. The distribution of the eigenvalues is discussed in detail, making use of a phase angle function called θ. The limiting cases of a disk and a circle are discussed.
- Mar 3, 2025
Indistinguishability plays an important role in enumerative problems in combinatorics. This article explains the concept and significance of particle indistinguishability in statistical mechanics.
- Dec 22, 2023
The conformal map w(z) transforms the trajectory with energy −B in potential U(z):=A∣dw/dz∣2 into the trajectory with energy −A in potential V(w):=B∣dz/dw∣2. I will prove this beautiful result and show some implications of it.
- Nov 9, 2023
For a plane lattice, there is only a finite number of different rotational symmetries that are compatible with the discrete translational symmetry. For example, the 5-fold rotational symmetry is not one of them. Why is that? It turns out that whether an m-fold symmetry is compatible with translational symmetry is the same as whether φ(m)≤2.
- May 1, 2023
For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.
- Mar 30, 2023
For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.