Exponent (United States)

Total-energy-assisted Tight-binding Method Based on Density Functional Theory — Design Principles Toward Transferability and Extrapolation

The previously proposed tight-binding (TB) method derived from the total energy has been extended within the local density approximation [TE-TB method; J. Phys. Soc. Jpn. 87, 064802 (2018) ]. Unlike the earlier two-parameter formulation, the present method introduces three parame...

Weil's Rosetta Stone as a correspondence of clocks, not of spaces

Weil's "trilingual text" — number fields, curves over finite fields, Riemann surfaces — is usually read as a dictionary between objects: primes ↔ points, Galois groups ↔ fundamental groups, and in Mazur's 3-dimensional refinement, primes ↔ knots, Legendre symbol ↔ linking number...