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International Journal of Modern Physics B

MEMORIAL TRIBUTE TO MANFRED L. RISTIG (1935–2011)

J. W. Clark

Published Jun 4, 2013• 0 citations
Publisher

Abstract

Manfred Ristig was a leading contributor to the advancement of microscopic theory of strongly interacting quantum many-body systems for over four decades. This retrospective on his life and scientific career pays tribute to his pivotal role in the development of correlated wavefunction approaches to quantitative ab initio description of quantum fluids, nuclear systems and condensed matter more generally. Highlights include his contributions to the formulation of Fermi hypernetted chain theory and correlated density matrix theory. Special attention is given to Ristig's seminal work of recent years, which has yielded rich insights into the interplay of exchange effects (arising from quantum statistics) and the strong interactions between constituent bosons or fermions.

DOI
10.1142/s0217979213470036

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Manfred Ristig was a leading contributor to the advancement of microscopic theory of strongly interacting quantum many-body systems for over four decades. This retrospective on his life and scientific career pays tribute to his pivotal role in the development of correlated wavefunction approaches to quantitative ab initio description of quantum fluids, nuclear systems and condensed matter more generally. Highlights include his contributions to the formulation of Fermi hypernetted chain theory and correlated density matrix theory. Special attention is given to Ristig's seminal work of recent years, which has yielded rich insights into the interplay of exchange effects (arising from quantum statistics) and the strong interactions between constituent bosons or fermions.
In July 2000 a conference was held to honour the 65th birthdays of four of the leading international figures in the field of quantum many-body theory. The joint research careers of John Clark, Alpo Kallio, Manfred Ristig and Sergio Rosati total some 150 years, and this festschrift celebrated their achievements. These cover a remarkably wide spectrum. The topics in this book reflect that diversity, ranging from formal aspects to real systems, including nuclear and subnuclear systems, quantum fluids and solids, quantum spin systems and strongly correlated electron systems. The book collects more than 30 invited contributions from eminent scientists, chosen both from among the participants at the conference and from colleagues who were unable to attend but nevertheless wished to contribute. To match the high standing of the honourees, the articles are of an exceptionally high quality. Together they provide a vivid overview of current work across the spectrum of quantum many-body theory.
In July 2000 a conference was held to honour the 65th birthdays of four of the leading international figures in the field of quantum many-body theory. The joint research careers of John Clark, Alpo Kallio, Manfred Ristig and Sergio Rosati total some 150 years, and this festschrift celebrated their achievements. These cover a remarkably wide spectrum. The topics in this book reflect that diversity, ranging from formal aspects to real systems, including nuclear and subnuclear systems, quantum fluids and solids, quantum spin systems and strongly correlated electron systems. The book collects more than 30 invited contributions from eminent scientists, chosen both from among the participants at the conference and from colleagues who were unable to attend but nevertheless wished to contribute. To match the high standing of the honourees, the articles are of an exceptionally high quality. Together they provide a vivid overview of current work across the spectrum of quantum many-body theory.
Density functional theory provides the basis for uncounted studies of ground-state properties of many-body systems. However, the connection between the energy density functional and the underlying microscopic interactions of a given theory is not fully understood. In this thesis we use renormalization-group techniques in combination with density functional theory to study many-body systems from microscopic interactions. We apply our formalism to different one-dimensional systems. We start with systems of identical fermions interacting via a short-range repulsive and long-range attractive interaction which serves as a simple one-dimensional toy model for nuclei. After that we study systems of spin-1/2 fermions, where we assume interactions only between fermions with different spins and consider both a non-local interaction as in the previous case and a contact interaction. In particular, the contact interaction plays a prominent role for ultracold Fermi gases. We calculate ground-state properties such as the energy, density, intrinsic density and density correlation functions and compare our results to values obtained from other approaches. Moreover, we show how energies of excited states and the absolute square of the ground-state wavefunction can be extracted from the density-density correlation function. The relation between our formalism and conventional density functional theory as well as many-body perturbation theory is discussed which may help to guide the development of ab initio functionals for quantitative studies of nuclei in the future.
Quantum many-body theory as a discipline in its own right dates largely from the 1950's. It has developed since then to its current position as one of the cornerstones of modern theoretical physics. The field remains vibrant and active, vigorous and exciting. Indeed, its successes and importance were vividly illustrated prior to the conference by the sharing of the 1998 Nobel Prizes in both Physics and Chemistry by three many-body theorists. Two of those Nobel laureates, Walter Kohn and Bob Laughlin, delivered invited lectures at this meeting, the tenth in the series of International Conferences on Recent Progress in Many-Body Theories. This series is universally recognized as being the premier series of meetings on this subject, and its proceedings have always summarized the current state of the art through the lectures of its leading practitioners. The present volume is no exception. A major aim of this conference series has been to foster the exchange of ideas between physicists working in all the diverse fields of application of quantum many-body theory. These include nuclear and subnuclear physics, quantum fluids, strongly correlated electronic systems, and low-dimensional condensed-matter systems and materials. All of these fields and others are represented in the present volume. Other topical themes covered include density functional theory and its applications to nuclear and electronic systems, quantum dots and chaos, and trapped Bose?Einstein condensates. Through this breadth of applications the reader will get a clear illustration of the power of the tools of modern microscopic quantum many-body theory, and their usefulness both in achieving a commonality of approach and understanding, and in transferring powerful ideas from one field to another.