scholarly journals Many-body and temperature effects in two-dimensional quantum droplets in Bose–Bose mixtures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Abdelâali Boudjemâa
Keyword(s):  
Finite Temperature ◽  
Temperature Effects ◽  
Local Density ◽  
Finite Size ◽  
Pitaevskii Equation ◽  
Two Dimensional ◽  
Interspecies Interactions ◽  
Many Body ◽  
Monte Carlo Data ◽  
Hartree Fock

AbstractWe study the equilibrium properties of self-bound droplets in two-dimensional Bose mixtures employing the time-dependent Hartree–Fock–Bogoliubov theory. This theory allows one to understand both the many-body and temperature effects beyond the Lee–Huang–Yang description. We calculate higher-order corrections to the excitations, the sound velocity, and the energy of the droplet. Our results for the ground-state energy are compared with the diffusion Monte Carlo data and good agreement is found. The behavior of the depletion and anomalous density of the droplet is also discussed. At finite temperature, we show that the droplet emerges at temperatures well below the Berezinskii–Kosterlitz–Thouless transition temperature. The critical temperature strongly depends on the interspecies interactions. Our study is extended to the finite size droplet by numerically solving the generalized finite-temperature Gross-Pitaevskii equation which is obtained self-consistently from our formalism in the framework of the local density approximation.

Interacting fermions in a two-dimensional trap and fractional exclusion statistics

2000 ◽  
Vol 78 (1) ◽  
pp. 9-19 ◽  
Author(s):  
M K Srivastava ◽  
R K Bhaduri ◽  
J Law ◽  
M.V.N. Murthy
Keyword(s):  
Excited States ◽  
State Energy ◽  
Local Density ◽  
Two Dimensional ◽  
Body System ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Thomas Fermi ◽  
Hartree Fock ◽  
Number Of Particles

We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a self-consistent Hartree-Fock calculation. The two results are shown to agree even for a small number of particles. We next use the finite-temperature Thomas-Fermi method to demonstrate that in the local density approximation, these interacting fermions are equivalent to a system of noninteracting particles obeying the Haldane-Wu fractional exclusion statistics. It is also shown that mapping onto a system of N noninteracting quasiparticles enables us to predict the energies of the ground and excited states of the N-body system. PACS Nos.: 05.30-d, 73.20Dx

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.

SHELLS AND SUPERSHELLS IN METAL CLUSTERS

1993 ◽  
Vol 07 (04) ◽  
pp. 197-216 ◽  
Author(s):  
O. GENZKEN
Keyword(s):  
Temperature Effects ◽  
Body Problem ◽  
Metal Clusters ◽  
Local Density ◽  
Density Approximation ◽  
Jellium Model ◽  
Many Body ◽  
Influence Of Temperature ◽  
Valence Electrons ◽  
The Many

We analyze the shell and supershell structure of valence electrons in large metal clusters. For this purpose we use the spherical jellium model for the ions, treat the many-body problem of the interacting valence electrons selfconsistently in local-density approximation and solve numerically the Kohn-Sham equations for up to N ~ 6000 electrons. We investigate the influence of temperature effects on the shell structure and compare our results to experimental data and other calculations performed with phenomenological Woods–Saxon potentials.

Hartree-Fock calculation for trapped, two-dimensional interacting Bose gases of finite size

2000 ◽  
Vol 33 (13) ◽  
pp. 2559-2569 ◽  
Author(s):  
Jae Gil Kim ◽  
Kab Seok Kang ◽  
Bong Soo Kim ◽  
Eok Kyun Lee
Keyword(s):  
Finite Size ◽  
Two Dimensional ◽  
Bose Gases ◽  
Hartree Fock

scholarly journals HYPERFINE STRUCTURE PARAMETERS FOR COMPLEX ATOMS WITHIN RELATIVISTIC MANY-BODY PERTURBATION THEORY

2021 ◽  
pp. 52-59
Author(s):  
M. Makushkina ◽  
O. Antoshkina ◽  
O. Khetselius
Keyword(s):  
Perturbation Theory ◽  
Hyperfine Structure ◽  
Finite Size ◽  
Structure Parameters ◽  
Radiative Corrections ◽  
Correlation Effects ◽  
Many Body ◽  
Radium Isotope ◽  
Hartree Fock ◽  
Many Body Perturbation Theory

The calculational results for the hyperfine structure (HFS) parameters for the Mn atom (levels of the configuration 3d64s) and  the results of advanced calculating the HFS constants and nuclear quadrupole moment for the radium isotope are obtained on the basis of computing within the relativistic many-body perturbation theory formalism with a correct and effective taking into account the exchange-correlation, relativistic, nuclear and radiative corrections. Analysis of the data shows that an account of the interelectron correlation effects is crucial in the calculation of the hyperfine structure parameters.  The fundamental reason of physically reasonable agreement between theory and experiment is connected with the correct taking into account the inter-electron correlation effects, nuclear (due to the finite size of a nucleus), relativistic and radiative corrections. The key difference between the results of the relativistic Hartree-Fock Dirac-Fock and many-body perturbation theory methods calculations is explained by using the different schemes of taking into account the inter-electron correlations as well as nuclear and radiative ones.

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