Atomic shell structure from an orbital-free-related density-functional-theory Pauli potential

• URL: http://arxiv.org/abs/2211.15764v1
• Date: Mon, 28 Nov 2022 20:49:40 GMT
• Title: Atomic shell structure from an orbital-free-related density-functional-theory Pauli potential
• Authors: Russell B. Thompson
• Abstract summary: Polymer self-consistent field theory techniques are used to find radial electron densities and total binding energies for isolated atoms. Quantum particles are modelled as Gaussian threads with ring-polymer architecture in a four dimensional thermal-space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Polymer self-consistent field theory techniques are used to find radial electron densities and total binding energies for isolated atoms. Quantum particles are modelled as Gaussian threads with ring-polymer architecture in a four dimensional thermal-space, and a Pauli potential is postulated based on classical excluded volume implemented in the thermal-space using Edwards/Flory-Huggins interactions in a mean-field approximation. Other approximations include a Fermi-Amaldi correction for electron-electron self-interactions, a spherical averaging approximation to reduce the dimensionality of the problem, and the neglect of correlations. Polymer scaling theory is used to show that the excluded volume form of Pauli potential reduces to the known Thomas-Fermi energy density in the uniform limit. Self-consistent equations are solved using a bilinear Fourier expansion, with radial basis functions, for the first eighteen elements of the periodic table. Radial electron densities show correct shell structure, and the errors on the total binding energies compared to known binding energies are less than 9% for the lightest elements and drop to 3% or less for atoms heavier than nitrogen. More generally, it is suggested that only two postulates are needed within classical statistical mechanics to achieve equivalency of predictions with static, non-relativistic quantum mechanics: First, quantum particles are modelled as Gaussian threads in four dimensional thermal-space and, second, pairs of threads (allowing for spin) are subject to classical excluded volume in the thermal-space. It is shown that these two postulates in thermal-space become the same as the Heisenberg uncertainty principle and the Pauli exclusion principle in three dimensional space.

Related papers

• Energetics of the dissipative quantum oscillator [22.76327908349951]
  We discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap. Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy. We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator.
  arXiv  Detail & Related papers  (2023-10-05T15:18:56Z)
• Independent-oscillator model and the quantum Langevin equation for an oscillator: A review [19.372542786476803]
  A derivation of the quantum Langevin equation is outlined based on the microscopic model of the heat bath. In the steady state, we analyze the quantum counterpart of energy equipartition theorem. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion.
  arXiv  Detail & Related papers  (2023-06-05T07:59:35Z)
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
  A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field. We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
  arXiv  Detail & Related papers  (2023-05-10T12:59:07Z)
• An alternative derivation of orbital-free density functional theory [0.0]
  Polymer self-consistent field theory techniques are used to derive quantum density functional theory. The equations are shown to be equivalent to Kohn-Sham density functional theory.
  arXiv  Detail & Related papers  (2022-11-20T22:16:08Z)
• On the Origins of Spontaneous Spherical Symmetry-Breaking in Open-Shell Atoms Through Polymer Self-Consistent Field Theory [0.0]
  An alternative approach to density functional theory is applied to neutral atoms hydrogen to neon in their ground states. The spontaneous emergence of atomic shell structure and spherical symmetry-breaking of the total electron density is predicted by the model. The model shows excellent agreement with Hartree-Fock theory for the atomic binding energies and density profiles of the first six elements.
  arXiv  Detail & Related papers  (2022-09-29T01:54:26Z)
• Gaussian Basis Functions for a Polymer Self-Consistent Field Theory of Atoms [0.0]
  A representation of polymer self-consistent field theory is given in terms of non-orthogonal basis sets. The binding energies and radial electron densities of neutral atoms hydrogen through krypton are calculated. An exact electron self-interaction correction is adopted and the Pauli-exclusion principle is enforced.
  arXiv  Detail & Related papers  (2022-08-18T22:02:24Z)
• An Interpretation of Quantum Foundations Based on Density Functional Theory and Polymer Self-Consistent Field Theory [0.0]
  Feynman quantum-classical isomorphism is used to connect classical polymer self-consistent field theory with quantum time-dependent density functional theory. One dynamic postulate is added to two static postulates which allows for a complete description of quantum physics from a 5 dimensional thermal-space perspective.
  arXiv  Detail & Related papers  (2021-11-28T20:46:45Z)
• Relativistic aspects of orbital and magnetic anisotropies in the chemical bonding and structure of lanthanide molecules [60.17174832243075]
  We study the electronic and ro-vibrational states of heavy homonuclear lanthanide Er2 and Tm2 molecules by applying state-of-the-art relativistic methods. We were able to obtain reliable spin-orbit and correlation-induced splittings between the 91 Er2 and 36 Tm2 electronic potentials dissociating to two ground-state atoms.
  arXiv  Detail & Related papers  (2021-07-06T15:34:00Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Light-matter hybrid-orbital-based first-principles methods: the influence of the polariton statistics [0.0]
  We show the importance of the resulting hybrid Fermi-Bose statistics of the polaritons. We also present a general prescription how to extend a given first-principles approach to polaritons. We find that the more delocalized the bound-state wave function of the particles is, the stronger it reacts to photons.
  arXiv  Detail & Related papers  (2020-05-05T09:01:28Z)
• Quantum decoherence by Coulomb interaction [58.720142291102135]
  We present an experimental study of the Coulomb-induced decoherence of free electrons in a superposition state in a biprism electron interferometer close to a semiconducting and metallic surface. The results will enable the determination and minimization of specific decoherence channels in the design of novel quantum instruments.
  arXiv  Detail & Related papers  (2020-01-17T04:11:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.