In statistical mechanics, the finite size scaling method provides a systematic way to extrapolate information about criticality obtained from a finite system to the thermodynamic limit. For quantum systems, the finite size corresponds not to the spatial dimension but to the number of elements in a complete basis set used to expand the exact wave function of a given Hamiltonian. In this lecture I will discuss how finite size scaling works in quantum mechanics and how to calculate quantum critical parameters for stability of atomic, molecular and quantum dot systems.
Sabre Kais is a Professor of Chemistry and Computer Science (courtesy). He was a Postdoc in the Chemistry Department at Harvard University with Professor Dudley Herschbach (Nobel Laureate in Chemistry 1986), and joined the faculty of the Department of Chemistry at Purdue in 1994. He and his students and postdoctoral associates have published 117 papers in peer-reviewed journals. His research interests include: Electronic structure and dynamics of atoms, molecules and quantum dots; quantum information and computation; stability of matter in superintense laser fields. He received the National Science Foundation Career Award; Purdue University Faculty Scholar Award 2004-2009; 2005 Guggenheim Fellowship Award and was elected this year as Fellow of the American Physical Society and Fellow of the American Association for the Advancement of Science.