Erweiterung der Neuen Tamm-Dancoff-Methode auf Phasen- übergänge in Vielteilchensystemen / Extension of the New Tamm-Dancoff Method to Phase Transitions in Many-Body Systems

1975 ◽  
Vol 30 (2) ◽  
pp. 142-157
Author(s):  
A. Friederich ◽  
W. Gerling ◽  
K. Bleuler
Keyword(s):  
Function Method ◽  
Many Body ◽  
Quasi Particle ◽  
First Order ◽  
Hartree Fock ◽  
Bogoliubov Theory ◽  
Lipkin Model ◽  
Exactly Solvable ◽  
Intermediate States ◽  
Many Body Systems

Abstract We extend the New Tamm-Dancoff method by introducing intermediate states. In this way we are able to treat with the Green's function method the effect of nearby levels in many-body systems. We formulate the η-and the ζ-function method with intermediate states. Aldready in first order, the ζ-function method yields a whole series of new approximations in addition to known theories such as the Hartree-Fock theory and the Hartree-Bogoliubov theory. As an example we study intensively "the Hartree-Fock theory with intermediate states". The ζ-function method which is based on the η-function method yields in first order in addition to RPA, quasi-particle RPA and other approximations "RPA with intermediate states". We apply the Hartree-Fock theory with intermediate states and RPA with intermediate states to the exactly solvable Lipkin model.

EVOLUTION OF DEFORMATIONS IN SD AND PF SHELL NUCLEI

2006 ◽  
Vol 15 (08) ◽  
pp. 1779-1788
Author(s):  
XIAN-RONG ZHOU ◽  
H. SAGAWA ◽  
XI-ZHEN ZHANG
Keyword(s):  
Mass Number ◽  
Nuclear Deformation ◽  
Quadrupole Moments ◽  
Many Body ◽  
Hartree Fock ◽  
Pairing Correlations ◽  
Many Body Systems ◽  
Pf Shell ◽  
Vibration Coupling ◽  
Hf Calculations

In the frame of deformed Skyrme Hartree-Fock (HF) model with pairing correlations, the strong mass number dependence of quadrupole deformations in sd and pf shell nuclei with mass A =(16 ~ 56) is studied as a clear manifestation of the evolution of nuclear deformation in nuclear many-body systems. The competition between the deformation driving particle-vibration coupling and the shell structure is shown by a systematic study on the ratios of the protons to neutrons quadrupole moments in nuclei with T =| T z|=1. The mass number dependence of deformations obtained by deformed HF calculations is compared with the results of shell model and experimental data.

Wick-Regeln mit Zwischenzuständen und die Neue Tamm-Dancoff-Methode mit Zwischenzuständen / On Wick Rules with Intermediate States and the New Tamm-Dancoff Method with Intermediate States

1976 ◽  
Vol 31 (8) ◽  
pp. 872-886 ◽  
Author(s):  
A. Friederich ◽  
W. Gerling
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Equations Of Motion ◽  
Random Phase ◽  
Dimensional Subspace ◽  
Finite Dimensional Subspace ◽  
Great Success ◽  
Hartree Fock ◽  
Intermediate States ◽  
Many Body Systems

AbstractInstead of emphasizing the ground state as is done in Green's function method, we take a finite-dimensional subspace of the Hilbert space: the space of the "intermediate states". A systematic introduction of intermediate states is effected by an extension of the method of generating functionals: we combine the generating functionals of the n-point Green's functions to a "matrix functional" T, and form new matrix functionals, which are matrix functions of T. The aim of this paper is to develop the functional calculus in such a way that the transition from scalar functionals to matrix functionals is straightforward, and the method of obtaining further results becomes clear. Following the lines of Dürr and Wagner we get u η-and ζ-rules with intermediate states". Using them we define a truncation procedure for the equations of motion of the n-point Green's functions, the "New Tamm-Dancoff method with intermediate states". This extension makes it possible to treat the effect of nearby levels in many body systems with Green's functions. In ad-dition to well-known approximations, such as the Hartree-Fock and the Hartree-Bogoliubov theory, the RPA and the quasiparticle RPA, we obtain a series of new approximations. Among these are the "Hartree-Fock theory with intermediate states" and the "random-phase approximation with intermediate states", which we already applied with great success to some exactly soluble models.

Quantum mechanics II–many body systems

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Local Density Approximation ◽  
Density Functional ◽  
Local Density ◽  
Slater Determinant ◽  
Density Approximation ◽  
Many Body ◽  
Hartree Fock ◽  
Separation Of Scales ◽  
Many Body Systems ◽  
Molecular Computations

Chapter 23 develops formalism relevant to atomic and molecular electronic structure. A review of the product Ansatz, the Slater determinant, and atomic configurations is followed by applications to small atoms. Then the self-consistent Hartree-Fock method is introduced and applied to larger atoms. Molecular structure is addressed by introducing an adiabatic separation of scales and the construction of molecular orbitals. The use of specialized bases for molecular computations is also discussed. Density functional theory and its application to complicated molecules is introduced and the local density approximation and the Kohn-Sham procedure for solving the functional equations are explained. Techniques for moving beyond the local density approximation are briefly reviewed.

The Scattering Equations for Charged Particles Colliding with Many Body Systems

1975 ◽  
Vol 53 (17) ◽  
pp. 1615-1623 ◽  
Author(s):  
T. D. Bui ◽  
A. D. Stauffer
Keyword(s):  
Cross Sections ◽  
Adiabatic Approximation ◽  
Perturbation Technique ◽  
Sodium Atom ◽  
Orbital Method ◽  
Many Body ◽  
First Order ◽  
Atom Scattering ◽  
Alkali Atoms ◽  
Many Body Systems

We have derived the total wave function of a many body system scattering by a charged particle by using a first order perturbation technique (the polarized orbital method). The derivation is based on an adiabatic approximation for the incoming particle. Particular cases of electrons colliding with the alkali atoms are shown. S, P, and D wave phase shifts and the total elastic cross sections for electron–sodium atom scattering are calculated using this method for the energy range 0 to 4 eV.

scholarly journals Page curve from non-Markovianity

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Kaixiang Su ◽  
Pengfei Zhang ◽  
Hui Zhai
Keyword(s):  
Many Body ◽  
Thermal Entropy ◽  
Initial Stage ◽  
Environment Temperature ◽  
Exactly Solvable ◽  
Long Time ◽  
Kitaev Model ◽  
Many Body Systems ◽  
Near Future ◽  
System Entropy

Abstract In this paper, we use the exactly solvable Sachdev-Ye-Kitaev model to address the issue of entropy dynamics when an interacting quantum system is coupled to a non-Markovian environment. We find that at the initial stage, the entropy always increases linearly matching the Markovian result. When the system thermalizes with the environment at a sufficiently long time, if the environment temperature is low and the coupling between system and environment is weak, then the total thermal entropy is low and the entanglement between system and environment is also weak, which yields a small system entropy in the long-time steady state. This manifestation of non-Markovian effects of the environment forces the entropy to decrease in the later stage, which yields the Page curve for the entropy dynamics. We argue that this physical scenario revealed by the exact solution of the Sachdev-Ye-Kitaev model is universally applicable for general chaotic quantum many-body systems and can be verified experimentally in near future.

Sign in / Sign up

Export Citation Format

Share Document