Mathematicians sharpen quantum predictions, boost computational efficiency
Researchers have tightened fundamental mathematical bounds used in quantum physics and materials science, potentially reducing computation time for simulations in drug discovery, semiconductors, and energy storage. The improvement—applicable across dimensions and magnetic field conditions—refines tools that engineers rely on when modeling physical systems at the quantum scale.
Originaltitel: Improved semiclassical eigenvalue estimates for the Laplacian and the Landau Hamiltonian
The Berezin-Li-Yau and the Kroger inequalities show that Riesz means of order >= 1 of the eigenvalues of the Laplacian on a domain Q of finite measure are bounded in terms of their semiclassical limit expressions. We show that these inequalities can be improved by a ' multiplicative factor that depends only on the dimension and the product root Lambda|Q|(1/d), where A is the eigenvalue cut-off parameter in the definition of the Riesz mean. The same holds when |Q|( 1/d) is replaced by a generalized inradius of Omega. Finally, we show similar inequalities in two dimensions in the presence of a constant magnetic field.