Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1608.05268 · Journal of Statistical Physics

Mean Field Evolution of Fermions with Coulomb Interaction

Marcello Porta, Simone Rademacher, Chiara Saffirio, Benjamin Schlein

Published Jan 30, 2017• 51 citations
arXivHTMLPDF
DOI
10.1007/s10955-017-1725-y

Related papers

Mean-Field Evolution of Fermions with Singular Interaction

Chiara Saffirio

arXiv:1801.02883•Springer proceedings in mathematics & statistics•Jan 1, 2018•19 citations

Hartree corrections in a mean-field limit for fermions with Coulomb interaction*

Sören Petrat

Abstract We consider the many-body dynamics of fermions with Coulomb interaction in a mean-field scaling limit where the kinetic and potential energy are of the same order for large particle numbers. In the considered limit the spatial variation of the mean-field is small. We prove two results about this scaling limit. First, due to the small variation, i.e., small forces, we show that the many-body dynamics can be approximated by the free dynamics with an appropriate phase factor with the conjectured optimal error term. Second, we show that the Hartree dynamics gives a better approximation with a smaller error term. In this sense, assuming that the error term in the first result is optimal, we derive the Hartree equations from the many-body dynamics with Coulomb interaction in a mean-field scaling limit.

arXiv:1609.04754•Journal of Physics A Mathematical and Theoretical•Apr 20, 2017•20 citations

Mean–Field Evolution of Fermionic Systems

Niels Benedikter, Marcello Porta, Benjamin Schlein

arXiv:1305.2768•Communications in Mathematical Physics•Apr 22, 2014•96 citations

Random Phase Approximation (RPA)

Lukong Cornelius Fai

This chapter examines different problems that apply the field theory in condensed matter physics. It considers bosonic as well as fermionic systems and applies the techniques of the quantum field theory. The chapter provides a model describing electrons in a metal known as the electron gas model that considers a system of electrons interacting with each other via the instantaneous Coulomb force e2r. The electron gas model provides a framework from which introduces standard many-body approaches such as the Gell-Mann-Bruckner theory or random phase approximation and show how they are formulated within diagrammatic or functional integral techniques. The chapter also considers a quantum three-dimensional coulomb gas and apply the field-theoretic techniques to systems of interacting electrons. The terminology of the order parameter for the field ϕ is to indicate the treatment of the Coulomb interaction within a mean-field theory with the inclusion of Gaussian fluctuations around the mean-field value of the order parameter.

CRC Press eBooks•Jun 20, 2019•0 citations

Gutzwiller variational method for intersite Coulomb interactions: The spinless fermion model in one dimension

Mohammad Sherafati, S. Satpathy, Dix H. Pettey

We study the Gutzwiller method for the spinless fermion model in one dimension, which is one of the simplest models that incorporates the intersite Coulomb interaction. The Gutzwiller solution of this model has been studied in the literature but with differing results. We obtain the Gutzwiller solution of the problem by a careful enumeration of the many-particle configurations and explain the origin of the discrepancy in the literature to be due to the neglect of the correlation between the neighboring bond occupancies. The correct implementation of the Gutzwiller approach yields results different from the slave-boson mean-field theory, unlike for the Hubbard model with on-site interaction, where both methods are known to be equivalent. The slave-boson and the Gutzwiller results are compared to the exact solution, available for the half-filled case, and to the numerical exact diagonalization results for the case of general filling.

arXiv:1302.2108•Physical Review B•Jul 11, 2013•3 citations

Mean field dynamics of fermions and the time-dependent Hartree–Fock equation

Claude Bardos, François Golse, Alex D. Gottlieb +1 more

arXiv:math-ph/0204009•Journal de Mathématiques Pures et Appliquées•Jun 1, 2003•114 citations
Abstract We consider the many-body dynamics of fermions with Coulomb interaction in a mean-field scaling limit where the kinetic and potential energy are of the same order for large particle numbers. In the considered limit the spatial variation of the mean-field is small. We prove two results about this scaling limit. First, due to the small variation, i.e., small forces, we show that the many-body dynamics can be approximated by the free dynamics with an appropriate phase factor with the conjectured optimal error term. Second, we show that the Hartree dynamics gives a better approximation with a smaller error term. In this sense, assuming that the error term in the first result is optimal, we derive the Hartree equations from the many-body dynamics with Coulomb interaction in a mean-field scaling limit.
This chapter examines different problems that apply the field theory in condensed matter physics. It considers bosonic as well as fermionic systems and applies the techniques of the quantum field theory. The chapter provides a model describing electrons in a metal known as the electron gas model that considers a system of electrons interacting with each other via the instantaneous Coulomb force e2r. The electron gas model provides a framework from which introduces standard many-body approaches such as the Gell-Mann-Bruckner theory or random phase approximation and show how they are formulated within diagrammatic or functional integral techniques. The chapter also considers a quantum three-dimensional coulomb gas and apply the field-theoretic techniques to systems of interacting electrons. The terminology of the order parameter for the field ϕ is to indicate the treatment of the Coulomb interaction within a mean-field theory with the inclusion of Gaussian fluctuations around the mean-field value of the order parameter.
We study the Gutzwiller method for the spinless fermion model in one dimension, which is one of the simplest models that incorporates the intersite Coulomb interaction. The Gutzwiller solution of this model has been studied in the literature but with differing results. We obtain the Gutzwiller solution of the problem by a careful enumeration of the many-particle configurations and explain the origin of the discrepancy in the literature to be due to the neglect of the correlation between the neighboring bond occupancies. The correct implementation of the Gutzwiller approach yields results different from the slave-boson mean-field theory, unlike for the Hubbard model with on-site interaction, where both methods are known to be equivalent. The slave-boson and the Gutzwiller results are compared to the exact solution, available for the half-filled case, and to the numerical exact diagonalization results for the case of general filling.