Based on a NATO Advanced Summer Institute, this volume discusses physical models, mathematical formalisms, experimental techniques, and applications for ultrafast dynamics of quantum systems. These sy
These proceedings contain lectures given at the N.A.T.O. Advanced Study Institute entitled Scattering Theory in Mathematics and Physics held in Denver, Colorado, June 11-29, 1973. We have assembled the main series of lectures and some presented by other participants that seemed naturally to complement them. Unfortunately the size of this volume does not allow for a full account of all the contributions made at the Conference; however, all present were pleased by the number and breadth of those topics covered in the informal afternoon sessions. The purpose of the meeting, as reflected in its title, was to examine the single topic of scattering theory in as many of its manifestations as possible, i.e. as a hub of concepts and techniques from both mathematics and physics. The format of all the topics presented here is mathematical. The physical content embraces classical and quantum mechanical scattering, N-body systems and quantum field theoretical models. Left out are such subjects as the so-called analytic S-matrix theory and phenomeno logical models for high energy scattering. We would like to thank the main lecturers for their excellent presentations and written summaries. They provided a focus for the exceptionally strong interaction among the participants and we hope that some of the coherence achieved is reflected in these published notes. We have made no attempt to unify notation.
Excited-state dynamics in condensed matter systems plays a crucial role in determining their properties. Understanding and controlling ultrafast dynamics across multiple dimensions—such as time, space, energy, momentum, and spin—has become a key emerging direction in modern condensed matter physics. In recent decades, time-resolved ultrafast laser technology based on pump-probe techniques has advanced significantly. This technology has been integrated with various experimental methods, leading to developments in ultrafast spectroscopy, time- and angle-resolved photoemission spectroscopy (TR-ARPES), ultrafast scanning tunneling microscopy (STM), ultrafast electron diffraction (UED), and ultrafast X-ray techniques, enabling the study of lattice, electron, and spin dynamics. Meanwhile, to provide a clearer physical picture of ultrafast dynamics, real-time first-principles methods have been developed by combining electronic structure methods with dynamic approaches, allowing the study of multidimensional lattice, electron, and spin behaviors. This article reviews recent progress in the field and discusses its future challenges and opportunities.