In this series, methods that have become fundamental tools in computational physics and chemistry will be presented by their originators at a level appropriate for master and graduate students. The lectures will be followed by an interview with the presenters: we’ll ask them to recall for us the period, problems, people and circumstances that accompanied the creation of milestone methods and algorithms that we now routinely use.
We hope that you will be able to join us and share with us this unusual and interesting opportunity to learn first hand from pioneers who have contributed significantly to our field and to get to know better the history and anecdotes behind work that is now recorded in books.
15:00 – Introduction
15:10 – Conceptual Aspects of the Theory of Electric Polarization and Orbital Magnetization (D. Vanderbilt)
16:00 – Break
16:10 – Electric Polarization, Orbital Magnetization, and Other Geometrical Observables (R. Resta)
17:00 – Interview and recollections
17:45 – End
Conceptual Aspects of the Theory of Electric Polarization and
David Vanderbilt, Rutgers University
In this talk I will take a conceptual approach, rather than a
historical or mathematical one, to the "modern theory" of electric
polarization and orbital magnetization. In particular, I will
present a series of physical arguments that severely constrain the
form of any such theory. For example, I will explain why we expect electric polarization to be well defined only up to a quantum, and discuss the theorem relating bulk polarization to surface charge in general terms. As for orbital magnetization, I will explain why this quantity is not subject to the same kind of quantum of indeterminacy that was found for the electric polarization. Only then will I introduce the mathematical concepts of Berry phase and Berry curvature, and briefly point the way to their utilization as the basis for the by-now well-established theories of electric polarization and orbital magnetization.
Electric Polarization, Orbital Magnetization, and Other Geometrical Observables
Raffaele Resta (IOM-CNR Democritos, Trieste)
Electric polarization and orbital magnetization have a very similar definition at the textbook level; yet within quantum mechanics they are intensive geometrical observables of a very different nature. At the fundamental level polarization is essentially a one-dimensional quantity and orbital magnetization a two-dimensional one: the difference between them can be traced back to basic features of algebraic geometry in odd vs. even dimensions. One- and three-dimensional observables make sense in insulators only and are well defined only up to a quantum: the former case is polarization, the latter case occurs in magnetoelectric coupling. When a bounded sample is addressed, the quantum indeterminacy is fixed by the chosen termination. Two-dimensional observables exist in metals as well and are exempt from the quantum indeterminacy; their value does not depend on sample termination. Besides magnetization, I will discuss anomalous Hall conductivity in insulators and metals.
About the speakers
David Vanderbilt received his BA in Physics from Swarthmore College in 1976 and his PhD in Physics from the Massachusetts Institute of Technology in 1981. He spent three years as a Miller Postdoctoral Fellow at the University of California at Berkeley before joining the faculty of the Physics Department at Harvard University in 1984, first as an Assistant and then as an Associate Professor. He has been a Professor in the Department of Physics and Astronomy at Rutgers University since 1991, and was named Board of Governors Professor of Physics in 2009. Dr. Vanderbilt is an expert in the development of methods for electronic structure calculations and the application of such methods for computational materials theory. Dr. Vanderbilt has published over 325 articles in scientific journals and has a Web of Science h-index of 96. He became a Fellow of the American Physical Society (APS) in 1995, is a winner of the 2006 Rahman Prize in Computational Physics awarded by the APS, and served as Chair of the Division of Materials Physics of the APS in 2006. He was awarded a Simons Fellowship in Theoretical Physics in 2014. He was elected to the National Academy of Sciences in 2013, and to the National Academy of Arts and Sciences in 2019.
Raffaele Resta has been a student at Scuola Normale Superiore (Pisa) from 1965 to 1969. Immediately after the degree (Laurea) he got a tenure-track position at the Pisa University, where he was tenured in 1971, aged 24, as "Assistente Ordinario". Until 1976 he practiced semi-professional sailing at the international level, also writing a few physics papers. He has been teaching under different roles at Pisa University and (since 1981) at SISSA in Trieste; he became full professor at Trieste University in 1994; he suffered mandatory retirement in 2017. He is now Senior Research Associate with the National Research Council, and "Professore a Contratto" at Trieste University. He has spent several periods at EPFL under visiting positions, where he also delivered cycles of Lectures: "Troisieme Cycle de la Physique en Suisse Romande" in 1990, 1995, 1999. Since the beginning of professional life his main interest has been in the theory of materials, using a variety of approaches, from analytical theories and models to first–principle computations. Since the birthdate (about 1980) of the modern computational theory of materials, his mainstream research activity has been in this area, working both at the development of new methods and at actual computations; the recent years were mostly devoted to computational physics "light": simple simulations on a laptop which lead to the discovery and validation of new "theorems". He has made crucial advances in the understanding of piezoelectricity, macroscopic polarization, orbital magnetization, magnetoelectric couplings, anomalous Hall conductivity, and the nature of the insulating state. He is the author of 200 publications (articles, book chapters, conference proceedings), about one third of them single-authored. He is a fellow of the American Physical Society, and a former (2002-08) Divisional Associate Editor for Physical Review Letters.
Previous CECAM and MARVEL lectures can be found at:
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