STUDY OF THE KRAMERS-FOKKER-PLANCK QUADRATIC OPERATOR WITH A CONSTANT MAGNETIC FIELD

The paper proves the exact closed-form formula for ||e^{-t M_{a,b}}||^2 in Theorem 1.2, with T and S given in (6)–(7) and A=1-b^2-4a-2ib, c=√A, matching the candidate’s final expression exactly. The paper’s proof proceeds via an explicit 4×4 calculation using Lagrange interpolation and a special matrix basis, culminating in the same norm formula . The candidate gives a different, shorter argument by identifying R^4≅C^2, reducing to a 2×2 complex matrix, and deriving the norm via the Gram matrix and its invariants. Aside from a minor sign convention in the R^4↔C^2 identification (which does not affect the final values since only |A| and even/real-part combinations enter), the candidate’s derivation is correct and complete.