Estimates on derivatives of Coulombic wave functions and their electron densities

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Søren Fournais ◽  
Thomas Østergaard Sørensen
Keyword(s):  
Ground State ◽  
A Priori ◽  
Wave Functions ◽  
Many Body ◽  
A Priori Bounds ◽  
Electron Densities ◽  
The Many ◽  
Body Potential ◽  
Derivatives Of

Abstract We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions ψ, involving negative powers of the distance to the singularities of the many-body potential. We use these to derive bounds for all derivatives of the corresponding one-electron densities ρ, involving negative powers of the distance from the nuclei. The results are both natural and optimal, as seen from the ground state of Hydrogen.

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

scholarly journals Study of Zero Temperature Ground State Properties of the Repulsive Bose-Einstein Condensate in an Anharmonic Trap

2021 ◽  
Vol 13 (3) ◽  
pp. 733-744
Author(s):  
P. K. DEBNATH
Keyword(s):  
Ground State ◽  
Expansion Method ◽  
Einstein Condensate ◽  
Zero Temperature ◽  
Many Body ◽  
Ground State Properties ◽  
Potential Harmonic ◽  
The Stability ◽  
Average Size ◽  
Body Potential

The zero-temperature ground state properties of experimental 87Rb condensate are studied in a harmonic plus quartic trap [ V(r) =  ½mω2r2 + λr4 ]. The anharmonic parameter (λ) is slowly tuned from harmonic to anharmonic. For each choice of λ, the many-particle Schrödinger equation is solved using the potential harmonic expansion method and determines the lowest effective many-body potential. We utilize the correlated two-body basis function, which keeps all possible two-body correlations. The use of van der Waals interaction gives realistic pictures. We calculate kinetic energy, trapping potential energy, interaction energy, and total ground state energy of the condensate in this confining potential, modelled experimentally. The motivation of the present study is to investigate the crucial dependency of the properties of an interacting quantum many-body system on λ. The average size of the condensate has also been calculated to observe how the stability of repulsive condensate depends on anharmonicity. In particular, our calculation presents a clear physical picture of the repulsive condensate in an anharmonic trap.

scholarly journals Non-Hermitian fractional quantum Hall states

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Tsuneya Yoshida ◽  
Koji Kudo ◽  
Yasuhiro Hatsugai
Keyword(s):  
Ground State ◽  
Cold Atoms ◽  
Quantum Hall ◽  
Quantum Zeno Effect ◽  
Many Body ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Zeno Effect ◽  
Quantum Hall States ◽  
The Many

AbstractWe demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian Hamiltonian is considered to be relevant to cold atoms with dissipation. We conclude the emergence of the non-Hermitian FQH state by the presence of the topological degeneracy and by the many-body Chern number for the ground state multiplet showing Ctot = 1. The robust topological degeneracy against non-Hermiticity arises from the manybody translational symmetry. Furthermore, we discover that the FQH state emerges without any repulsive interactions, which is attributed to a phenomenon reminiscent of the continuous quantum Zeno effect.

EFFECTS OF CORE POLARIZATION AND PAIRING CORRELATIONS ON SOME GROUND-STATE PROPERTIES OF DEFORMED ODD-MASS NUCLEI WITHIN THE HIGHER TAMM–DANCOFF APPROACH

2011 ◽  
Vol 20 (02) ◽  
pp. 252-258 ◽  
Author(s):  
LUDOVIC BONNEAU ◽  
JULIEN LE BLOAS ◽  
PHILIPPE QUENTIN ◽  
NIKOLAY MINKOV
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Energy Difference ◽  
Pair Type ◽  
Many Body ◽  
Hartree Fock ◽  
Ground State Properties ◽  
Pairing Correlations ◽  
The Many ◽  
The Impact

In self-consistent mean-field approaches, the description of odd-mass nuclei requires to break the time-reversal invariance of the underlying one-body hamiltonian. This induces a polarization of the even-even core to which the odd nucleon is added. To properly describe the pairing correlations (in T = 1 and T = 0 channels) in such nuclei, we implement the particle-number conserving Higher Tamm–Dancoff approximation with a residual δ interaction in each isospin channel by restricting the many-body basis to two-particle–two–hole excitations of pair type (nn, pp and np) on top of the Hartree–Fock solution. We apply this approach to the calculation of two ground-state properties of well-deformed nuclei |Tz| = 1 nuclei around 24 Mg and 48 Cr , namely the isovector odd-even binding-energy difference and the magnetic dipole moment, focusing on the impact of pairing correlations.

scholarly journals The construction and application of the many-body potential for the Fe-Cr-V-Ni-Si-C system multi-component alloy

2008 ◽  
Vol 57 (1) ◽  
pp. 358
Author(s):  
Liu Yan-Xia ◽  
Wang Xun ◽  
Ma Yong-Qing ◽  
Zhang Cheng-Hua
Keyword(s):  
Many Body ◽  
The Many ◽  
Body Potential

Study of Unbound HePs Using Exact Diagonalization Technique

2012 ◽  
Vol 733 ◽  
pp. 38-42
Author(s):  
Asier Zubiaga ◽  
Filip Tuomisto ◽  
Martti Puska
Keyword(s):  
Variational Method ◽  
Interaction Potential ◽  
Exact Diagonalization ◽  
Wave Functions ◽  
Many Body ◽  
Strong Electron ◽  
Stochastic Variational Method ◽  
Explicitly Correlated ◽  
Pauli Repulsion ◽  
The Many

The many-body wavefunction of the unbound He-Ps system has been studied by the exact diagonalization of a explicitly correlated gaussians basis optimized by a stochastic variational method. The nucleus-positron distance has been varied by constraining the parameters of the nucleus-positron correlated gaussian term. The constraining technique allows to describe He and Ps interacting at different distances. The calculated wavefunction can be approximated as composed by weakly perturbed He and Ps atoms. The electron forming the Ps tends to be farther from the nucleus than the positron due to the strong electron-electron Pauli repulsion with the electrons of He. The described technique gives accurate energy and wave functions for Ps interacting with atoms that can be used to calculate the interaction potential of Ps with molecular matter.

Modeling of supersonic crowdion clusters in FCC lattice: Effect of the interatomic potential

2021 ◽  
pp. 2050019
Author(s):  
Igor A. Shelepev ◽  
Ayrat M. Bayazitov ◽  
Elena A. Korznikova
Keyword(s):  
Interatomic Potential ◽  
High Energy ◽  
Propagation Path ◽  
Interatomic Potentials ◽  
Energy Localization ◽  
Many Body ◽  
Embedded Atom ◽  
Fcc Lattice ◽  
The Many ◽  
Body Potential

Among a wide variety of point defects, crowdions can be distinguished by their high energy of formation and relatively low migration barriers, which makes them an important agent of mass transfer in lattices subjected to severe plastic deformation, irradiation, etc. It was previously shown that complexes and clusters of crowdions are even more mobile than single interstitials, which opened new mechanisms for the transfer of energy and mass in materials under intense external impacts. One of the most popular and convenient methods for analyzing crowdions is molecular dynamics, where the results can strongly depend on the interatomic potential used in the study. In this work, we compare the characteristics of a crowdion in an fcc lattice obtained using two different interatomic potentials — the pairwise Morse potential and the many-body potential for Al developed by the embedded atom method. It was found that the use of the many-body potential significantly affects the dynamics of crowdion propagation, including the features of atomic collisions, the evolution of energy localization and the propagation path.

Singularly Perturbed Convection — Diffusion Problems in One Dimension: Bounds on Derivatives

2009 ◽  
Vol 9 (3) ◽  
pp. 281-291
Author(s):  
A. Naughton ◽  
M. Stynes
Keyword(s):  
Numerical Analysis ◽  
A Priori ◽  
Singularly Perturbed ◽  
One Dimension ◽  
Point Boundary ◽  
A Priori Bounds ◽  
Convection Diffusion ◽  
Convection Dominated ◽  
Derivatives Of ◽  
Diffusion Problems

AbstractA convection-dominated singularly perturbed two-point boundary problem is considered. For the numerical analysis of such problems, it is necessary to prove certain a priori bounds on the derivatives of its solution. This paper provides a survey of the ways in which such bounds can be proved, while assessing the feasibility of extending such proofs to convection-dominated partial differential equations, and also introduces a new proof based on a classical finite-difference argument of Brandt.

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