Quantenfeldtheorie wechselwirkender Vielteilchensysteme zur semiklassischen Beschreibung von kollektiver Bewegung mit großen Amplituden

Abstract

ZusammenfassungUnter Bcnutzung von Funktionalintegralmethoden wird eine kollektive Quantenfeldtheorie wcchselwirkender Vielteilchensysteme abgeleitet, deren klassischer Grenzfall durch die zeitabhangige Mean-Field-Approximation gegeben ist. Auf diese Weise wird die Mean-Field-Approximation in die volle Quantenmcchanik eingebettet und die Quantenkorrekturen zur ,,klassischen" Mean-Field-Approximation konnen systematisch berechnet werden. Unter EinschluB der dominierenden Quantenkorrekturen zur Mean-Field-Approximation wird eine semiklassische Theorie der kollektiven Bewegungen groeer Amplituden in Vielteilchensystemen, die eine stark nichtlinenre Dynamik besitzen und den konventionellen storungstheorctischen Methoden nicht zugangig sind, entwickelt. Die semiklassische Theorie wird explizit fur gebundene Zustkinde und Zerfallsprozesse ausgearbeitet. Fur gebundene Zustande fuhrt dies zur Quantisierung der nichtlinearen zeitabhangigen Hartree-Fock-Theoric, die a m Beispiel einer gleichformigen Kernrotation illustriert wird. AbstractBy using path integral methods a collective quantum field theory of interacting many-body systems is developed, the classical limit of whici is given by the time-dependent mean-field approximation. In this way the mean-field approximation is embeded into the full quantum mechanics and the quantum corzections to the "classical" mean-field approximation can be systematically evaluated. By including the dominant quantum corrections to the mean-field approximation a semiclassical theory of large amplitude collective motions in many-body-systems, which show a highly nonlinear dynamic andare not accessible to perturbation theoretical methods, is derived. Tho semiclassical theory is developed explicitly for boundstates and decay processes like nuclear fission. I n the case of bound states this leads to the quantization of the time-dependent Hartrec-Fock-Theory, which is demonstrated for a uniform nuclear rotation.

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

“…One set involves H. Reinhardt and collaborators (see the review in Ref. [227]), and comprises two papers on the application of PIM to simple solvable models [228,229], two formal papers deriving a theory of large amplitude collective motion [230] and a theory of fission [231], and finally, one paper [232] showing how to extract adiabatic TDHF by the path integral method. In the work of Levit, Negele, et al, we encounter a formal development [233,234], which then concentrates on the problem of fission [235], culminating in a method of solution that showed considerable promise [236,237].…”

Continuum singularities of a mean-field theory of collisions

“…Because of the nonlinear nature of Eqs. (3)(4) in single particle space, our claim is not obvious, and will be qualified in this paper.…”

“…It will be noticed here that, although the physical branch gives real values of D sy when z < 0 and complex values of the same when z > 0, there are always one real root and two complex conjugate roots on both sides in the vicinity of z = 0. This happens indeed because the corresponding discriminant, ∆ 3 = 256z 2 (27 + 16z) 3 /(2 + z) 4 , actually changes sign, not for z = 0, but rather for z = −27/16. This helps to understand the nature of the unphysical singularity occurring at z = −27/16.…”

“…A serious, conceptual problem arises from spurious cross channel correlations [2,3]: when projecting the TDHF Slater determinant for large times on an orthogonal set of channel wave functions, the expansion coefficients and the respective S-matrix vary in time ad infinitum. To overcome the shortcomings of TDHF, the time-dependent mean field (TDMF) approach [2,3,4] expands the density in two sets of (bi-orthogonal) single-particle wave functions and solves the equations of motion as boundary value problem in time, fixing initial and final densities. It has been proven that for TDMF an S-matrix can be defined which becomes asymptotically constant [2].…”

Mean field methods for atomic and nuclear reactions: The link between time–dependent and time–independent approaches

“…In mean field approximation one takes χ, χ ′ as Slater determinants, 4) and the variational functions Ψ, Ψ ′ are correspondingly restricted to Slater determinants as well,…”