© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Birkhäuser Boston eBooks

A Few Methods for the Theory of Collective Motions and Collisions

BERTRAND G. GIRAUD

Published Jan 1, 1985• 0 citations

Abstract

The title originally planned for this series of lectures was “Time-dependent Hartree Fock Theory of Nuclear Motions and Collisions”. In fact, in what follows, the TDHF method will be considered for collective motion only. This is because a new, more practical theory of collisions has recently emerged. These lectures thus contain two main and distinct chapters, the first dedicated to this new theory of collisions and the second to collective motion. As a distraction to the reader, a last and small chapter recalls elementary ideas about some conjectured mechanisms for the dynamics of a very special system with collective motions, namely a living organ in the nervous system. This Summer School being dedicated to the subject of order and chaos, it is hoped that the considerations which follow never go too far from that fascinating subject indeed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI: 10.1007/978-1-4899-6650-6_9

Related papers

Sketch of the Formalism

Simon Friederich

This chapter reviews the quantum theoretical formalism and sketches its foundational problems. The main function of this chapter is to establish common ground for the interpretive discussions which follow, not to provide a comprehensive introduction to quantum theory. 6 Its first section recapitulates the essential aspects of the Hilbert space formalism of quantum mechanics, the second section covers the textbook account of measurement and measurement collapse, and the third and final section outlines the quantum theoretical treatment of many-component systems and explains the concept of quantum entanglement. Further introductory material is provided in the Appendices A, B, and C, all of which cover important no-go theorems for the interpretation of the theory. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Palgrave Macmillan UK eBooks•Jan 1, 2015•0 citations

Theory of Collective Motion in Many-Body Systems with Special Application to the Calculation of Rotational Parameters of Deformed Nuclei.

S.K.M. Wong

•Jan 1, 1968•0 citations

The time-dependent Hartree–Fock method and chaos in nuclear dynamics

Michael R. Strayer

The long‐time classical behavior of many‐body systems is examined using time‐dependent Hartree–Fock (TDHF) theory. Detailed computer simulations for the formation of a nuclear molecule in low‐energy 12C+12C collisions are discussed at length. The representation of effective classical coordinates, and their correspondence to physical observable for systems which undergo large‐amplitude quasi‐periodic and chaotic motion is briefly summarized. The relationship between these calculations and new methods, which allow the calculation of quasiperiodic solutions to the TDHF equations under more general circumstances, is summarized.

AIP conference proceedings•Jan 1, 1987•0 citations

An adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems

Michel Baranger, M. Vénéroni

Annals of Physics•Sep 1, 1978•264 citations

Quantum Mechanics

Yorick Hardy, Willi-Hans Steeb

In this chapter we introduce the Hilbert space which plays the central role in quantum mechanics. For a more detailed discussion of this subject we refer to the books of Balakrishnan [5], Richtmyer [137], Sewell [146], Stakgold [152], Steeb [163], Weidmann [181], Yosida [185]. Moreover the proofs of the theorems given in this chapter can be found in these books. We assume that the reader is familiar with the notation of a linear space. First we introduce the pre-Hilbert space. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Birkhäuser Basel eBooks•Jan 1, 2001•6 citations

Time-Dependent Problems and Equations of Motion

Gianluca Stefanucci, Robert van Leeuwen

The Green’s function method is among the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. With entirely new chapters and updated example problems, the second edition of this popular text continues to provide an ideal introduction to nonequilibrium many-body quantum systems and ultrafast phenomena in modern science. Retaining the unique and self-contained style of the original, this new edition has been thoroughly revised to address interacting systems of fermions and bosons, simplified many-body approaches like the GKBA, the Bloch equations, and the Boltzmann equations, and the connection between Green’s functions and newly developed time-resolved spectroscopy techniques. Small gaps in the theory have been filled, and frequently overlooked subtleties have been systematically highlighted and clarified. With an abundance of illustrative examples, insightful discussions, and modern applications, this book remains the definitive guide for students and researchers alike.

Cambridge University Press eBooks•Jan 2, 2025•0 citations

The title originally planned for this series of lectures was “Time-dependent Hartree Fock Theory of Nuclear Motions and Collisions”. In fact, in what follows, the TDHF method will be considered for collective motion only. This is because a new, more practical theory of collisions has recently emerged. These lectures thus contain two main and distinct chapters, the first dedicated to this new theory of collisions and the second to collective motion. As a distraction to the reader, a last and small chapter recalls elementary ideas about some conjectured mechanisms for the dynamics of a very special system with collective motions, namely a living organ in the nervous system. This Summer School being dedicated to the subject of order and chaos, it is hoped that the considerations which follow never go too far from that fascinating subject indeed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This chapter reviews the quantum theoretical formalism and sketches its foundational problems. The main function of this chapter is to establish common ground for the interpretive discussions which follow, not to provide a comprehensive introduction to quantum theory. 6 Its first section recapitulates the essential aspects of the Hilbert space formalism of quantum mechanics, the second section covers the textbook account of measurement and measurement collapse, and the third and final section outlines the quantum theoretical treatment of many-component systems and explains the concept of quantum entanglement. Further introductory material is provided in the Appendices A, B, and C, all of which cover important no-go theorems for the interpretation of the theory. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The long‐time classical behavior of many‐body systems is examined using time‐dependent Hartree–Fock (TDHF) theory. Detailed computer simulations for the formation of a nuclear molecule in low‐energy 12C+12C collisions are discussed at length. The representation of effective classical coordinates, and their correspondence to physical observable for systems which undergo large‐amplitude quasi‐periodic and chaotic motion is briefly summarized. The relationship between these calculations and new methods, which allow the calculation of quasiperiodic solutions to the TDHF equations under more general circumstances, is summarized.

In this chapter we introduce the Hilbert space which plays the central role in quantum mechanics. For a more detailed discussion of this subject we refer to the books of Balakrishnan [5], Richtmyer [137], Sewell [146], Stakgold [152], Steeb [163], Weidmann [181], Yosida [185]. Moreover the proofs of the theorems given in this chapter can be found in these books. We assume that the reader is familiar with the notation of a linear space. First we introduce the pre-Hilbert space. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The Green’s function method is among the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. With entirely new chapters and updated example problems, the second edition of this popular text continues to provide an ideal introduction to nonequilibrium many-body quantum systems and ultrafast phenomena in modern science. Retaining the unique and self-contained style of the original, this new edition has been thoroughly revised to address interacting systems of fermions and bosons, simplified many-body approaches like the GKBA, the Bloch equations, and the Boltzmann equations, and the connection between Green’s functions and newly developed time-resolved spectroscopy techniques. Small gaps in the theory have been filled, and frequently overlooked subtleties have been systematically highlighted and clarified. With an abundance of illustrative examples, insightful discussions, and modern applications, this book remains the definitive guide for students and researchers alike.