Finite Size Scaling for Quantum Critical Phenomena


Professor Sabre Kais, Department of Chemistry, Purdue University


Abstract.  The finite size scaling ansatz is combined with the
variational method to extract information about critical behavior of
quantum Hamiltonians. This approach is based on taking the number of
elements in a complete basis set as the size of the system.  As in
statistical mechanics, the finite size scaling can then be used
directly to the Schrodinger equation.  This approach is general and
gives very accurate results for the critical parameters, for which the
bound state energy becomes absorbed or degenerate with a continuum.
To illustrate the applications in quantum calculations, we present
detailed calculations for stability of atomic and molecular systems
and size effects in the electronic properties of quantum dots.