scholarly journals DENSITY FUNCTIONAL FOR PAIRING WITH PARTICLE NUMBER CONSERVATION

2010 ◽  
Vol 25 (21n23) ◽  
pp. 1854-1857
Author(s):  
DENIS LACROIX ◽  
GUILLAUME HUPIN
Keyword(s):  
Density Functional ◽  
Particle Number ◽  
Many Body ◽  
New Approach ◽  
Occupation Numbers ◽  
Particle Number Conservation ◽  
Coupling Strengths ◽  
Pairing Correlations ◽  
Many Body Systems ◽  
Good Agreement

In this work, a new functional is introduced to treat pairing correlations in finite many-body systems. Guided by the projected BCS framework, the energy is written as a functional of occupation numbers. It is shown to generalize the BCS approach and to provide an alternative to Variation After Projection framework. Illustrations of the new approach are given for the pairing Hamiltonian for various particle numbers and coupling strengths. In all case, a very good agreement with the exact solution is found.

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.

scholarly journals KEY CONCEPTS IN TIME-DEPENDENT DENSITY-FUNCTIONAL THEORY

2001 ◽  
Vol 15 (14) ◽  
pp. 1969-2023 ◽  
Author(s):  
ROBERT VAN LEEUWEN
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Time Dependent ◽  
Response Functions ◽  
Many Body ◽  
Functional Theory ◽  
Key Concepts ◽  
Initial States ◽  
Many Body Systems ◽  
Dependent Density

We give an overview of the underlying concepts of time-dependent density-functional theory. The basic relations between densities, potentials and initial states, for time-dependent many-body systems are discussed. We obtain some new results concerning the invertability of response functions. Some fundamental difficulties associated with the time-dependent action principle are discussed and we show how these difficulties can be resolved by means of the Keldysh formalism.

scholarly journals Covariant density functional theory for rare isotopes

2019 ◽  
Vol 14 ◽  
pp. 25
Author(s):  
P. Ring
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Open Shell ◽  
Effective Field ◽  
Many Body ◽  
Functional Theory ◽  
System Use ◽  
Pairing Correlations ◽  
Rare Isotopes ◽  
Covariant Density

Modern methods for the description of the nuclear many-body system use the concepts of density functional theory (DFT) and of effective field theory (EFT). The covariant version of this theory is based on a density functional which takes into account Lorentz symmetry in a self-consistent way. Pairing correlations play an important role in all open-shell configurations. They are included in relativistic Hartree Bogoliubov (RHB) theory by an effective residual interaction of finite range. With a minimal number of phenomenological parameters this theory allows a very successful phenomenological description of ground state properties of nuclei all over the periodic table. Recently this method has also been extended for the investigations of excited states, such as collective vibrations and rotations.

scholarly journals Lattice Dynamics of the High Tc Superconductor ErBa2Cu3O7

1994 ◽  
Vol 47 (1) ◽  
pp. 103 ◽  
Author(s):  
S Mohan ◽  
R Kannan
Keyword(s):  
Lattice Dynamics ◽  
Many Body ◽  
New Approach ◽  
High Tc ◽  
High Tc Superconductor ◽  
Zone Centre ◽  
Three Body ◽  
Many Body Interactions ◽  
Good Agreement ◽  
Infrared Data

The lattice dynamics of the high Tc superconductor ErBa2Cu307 have been investigated in detail with a modified three-body force shell model. The model accounts for the effect of many-body interactions in the lattice potential. The aim of the present work is to treat the various interactions between the ions in generalised way without making them numerically equal. The values of the phonon frequencies calculated at the zone centre by this new approach are in good agreement with the available Raman and infrared data.

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 SURPRISING PHENOMENON OF LEVEL MERGING IN FINITE FERMI SYSTEMS

2008 ◽  
Vol 22 (25n26) ◽  
pp. 4452-4463
Author(s):  
JOHN W. CLARK ◽  
VICTOR A. KHODEL ◽  
HAOCHEN LI ◽  
MIKHAIL V. ZVEREV
Keyword(s):  
Single Particle ◽  
Energy Levels ◽  
Fermi System ◽  
Particle Energy ◽  
Particle Spectrum ◽  
Many Body ◽  
Occupation Numbers ◽  
Inherent Feature ◽  
Wide Range ◽  
Many Body Systems

When applied to a finite Fermi system having a degenerate single-particle spectrum, the Landau-Migdal Fermi-liquid approach leaves room for the possibility that different single-particle energy levels merge with one another. It will be argued that the opportunity for this behavior exists over a wide range of strongly interacting quantum many-body systems. An inherent feature of the mergence phenomenon is the presence of nonintegral quasiparticle occupation numbers, which implies a radical modification of the standard quasiparticle picture. Consequences of this alteration are surveyed for nuclear, atomic, and solid-state systems.

scholarly journals Landau–Zener Effect in Superfluid Nuclear Systems

2003 ◽  
Vol 18 (26) ◽  
pp. 1809-1817 ◽  
Author(s):  
M. Mirea
Keyword(s):  
Equations Of Motion ◽  
Deformation Energy ◽  
Cluster Decay ◽  
Many Body ◽  
Spectroscopic Factors ◽  
Nuclear Systems ◽  
Particle Level ◽  
Many Body Systems ◽  
Experimental Ratio ◽  
Good Agreement

The Landau–Zener effect is generalized for many-body systems with pairing residual interactions. The microscopic equations of motion are obtained and the 14C decay of 223Ra spectroscopic factors are deduced. An asymmetric nuclear shape parametrization given by two intersected spheres is used. The single particle level scheme is determined in the frame of the superasymmetric two-center shell model. The deformation energy is computed in the microscopic–macroscopic approximation. The penetrabilities are obtained within the WKB approximation. The fine structure of the cluster decay analyzed in the frame of this formalism gives a very good agreement with the experimental ratio of partial half-lives for transition to the first excited state and to the ground state.

A NONEQUILIBRIUM STATISTICAL ENSEMBLE FORMALISM MaxEnt–NESOM: Basic Concepts, Construction, Application, Open Questions and Criticisms

2000 ◽  
Vol 14 (28) ◽  
pp. 3189-3264 ◽  
Author(s):  
ROBERTO LUZZI ◽  
ÁUREA R. VASCONCELLOS ◽  
J. GALVÃO RAMOS
Keyword(s):  
Function Theory ◽  
Operator Method ◽  
Statistical Thermodynamics ◽  
Statistical Ensemble ◽  
Many Body ◽  
Open Questions ◽  
Nonlinear Quantum ◽  
Many Body Systems ◽  
Ensemble Formalism ◽  
Good Agreement

We describe a particular approach for the construction of a nonequilibrium statistical ensemble formalism for the treatment of dissipative many-body systems. This is the so-called Nonequilibrium Statistical Operator Method, based on the seminal and fundamental ideas set forward by Boltzmann and Gibbs. The existing approaches can be unified under a unique variational principle, namely, MaxEnt, which we consider here. The main six basic steps that are at the foundations of the formalism are presented and the fundamental concepts are discussed. The associated nonlinear quantum kinetic theory and the accompanying Statistical Thermodynamics (the Informational Statistical Thermodynamics) are very briefly described. The corresponding response function theory for systems away from equilibrium allows to connected the theory with experiments, and some examples are summarized; there follows a good agreement between theory and experimental data in the cases in which the latter are presently available. We also present an overview of some conceptual questions and associated criticisms.

scholarly journals Terahertz spectroscopy of 2,4,6-trinitrotoluene molecular solids from first principles

2018 ◽  
Vol 14 ◽  
pp. 381-388 ◽  
Author(s):  
Ido Azuri ◽  
Anna Hirsch ◽  
Anthony M Reilly ◽  
Alexandre Tkatchenko ◽  
Shai Kendler ◽  
...  
Keyword(s):  
Density Functional ◽  
Terahertz Spectroscopy ◽  
Chemical Change ◽  
Molecular Solids ◽  
Dispersion Interactions ◽  
Many Body ◽  
Functional Theory ◽  
Terahertz Spectrum ◽  
Intramolecular Vibrations ◽  
Good Agreement

We present a computational analysis of the terahertz spectra of the monoclinic and the orthorhombic polymorphs of 2,4,6-trinitrotoluene. Very good agreement with experimental data is found when using density functional theory that includes Tkatchenko–Scheffler pair-wise dispersion interactions. Furthermore, we show that for these polymorphs the theoretical results are only weakly affected by many-body dispersion contributions. The absence of dispersion interactions, however, causes sizable shifts in vibrational frequencies and directly affects the spatial character of the vibrational modes. Mode assignment allows for a distinction between the contributions of the monoclinic and orthorhombic polymorphs and shows that modes in the range from 0 to ca. 3.3 THz comprise both inter- and intramolecular vibrations, with the former dominating below ca. 1.5 THz. We also find that intramolecular contributions primarily involve the nitro and methyl groups. Finally, we present a prediction for the terahertz spectrum of 1,3,5-trinitrobenzene, showing that a modest chemical change leads to a markedly different terahertz spectrum.

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