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369
Density functional theory of electronic structure
 J Phys Chem
, 1996
"... ReceiVed: March 5, 1996X Density functional theory (DFT) is a (in principle exact) theory of electronic structure, based on the electron density distribution n(r), instead of the manyelectron wave function Ψ(r1,r2,r3,...). Having been widely used for over 30 years by physicists working on the elect ..."
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Cited by 35 (0 self)
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ReceiVed: March 5, 1996X Density functional theory (DFT) is a (in principle exact) theory of electronic structure, based on the electron density distribution n(r), instead of the manyelectron wave function Ψ(r1,r2,r3,...). Having been widely used for over 30 years by physicists working on the electronic structure of solids, surfaces, defects, etc., it has more recently also become popular with theoretical and computational chemists. The present article is directed at the chemical community. It aims to convey the basic concepts and breadth of applications: the current status and trends of approximation methods (local density and generalized gradient approximations, hybrid methods) and the new light which DFT has been shedding on important concepts like electronegativity, hardness, and chemical reactivity index.
M.: The dielectric permittivity of crystals in the reduced HartreeFock approximation
, 2010
"... Abstract. In a recent article (Cancès, Deleurence and Lewin, Commun. Math. Phys. 281 (2008), pp. 129–177), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local d ..."
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Cited by 27 (9 self)
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Abstract. In a recent article (Cancès, Deleurence and Lewin, Commun. Math. Phys. 281 (2008), pp. 129–177), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this socalled reduced HartreeFock model, the ground state electronic density matrix is decomposed as γ = γ0 per + Qν,εF, where γ0 per is the ground state density matrix of the host crystal and Qν,ε F the modification of the electronic density matrix generated by a modification ν of the nuclear charge of the host crystal, the Fermi level εF being kept fixed. The purpose of the present article is twofold. First, we study more in details the mathematical properties of the density matrix Qν,ε F (which is known to be a selfadjoint HilbertSchmidt operator on L 2 (R 3)). We show in particular that if ´ R 3 ν ̸ = 0, Qν,ε F is not traceclass. Moreover, the associated density of charge is not in L 1 (R 3) if the crystal exhibits anisotropic dielectric properties. These results are obtained by analyzing, for a small defect ν, the linear and nonlinear terms of the resolvent expansion of Qν,ε F Second, we show that, after an appropriate rescaling, the potential generated by the microscopic total charge (nuclear plus electronic contributions) of the crystal in the presence of the defect, converges to a homogenized electrostatic potential solution to a Poisson equation involving the macroscopic dielectric permittivity of the crystal. This provides an alternative (and rigorous) derivation of the AdlerWiser formula. Contents
Long–time dynamics of the Schrödinger–Poisson–Slater system
, 2004
"... In this paper we analyze the asymptotic behaviour of solutions to the Schrödinger–Poisson–Slater (SPS) system in the frame of semiconductor modeling. Depending on the potential energy and on the physical constants associated with the model, the repulsive SPS system develops stationary or periodic so ..."
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Cited by 21 (1 self)
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In this paper we analyze the asymptotic behaviour of solutions to the Schrödinger–Poisson–Slater (SPS) system in the frame of semiconductor modeling. Depending on the potential energy and on the physical constants associated with the model, the repulsive SPS system develops stationary or periodic solutions. These solutions preserve the L p (R 3) norm or exhibit dispersion properties. In comparison with the Schrödinger–Poisson (SP) system, only the last kind of solutions appear. Keywords: Open quantum system, SchrödingerPoisson system, dispersion, X αapproach, asymptotic behaviour, stationary solutions.
On the timedependent Hartree–Fock equations coupled with a classical nuclear dynamics
 MATH. MODELS METHODS APPL. SCI. 9
, 1999
"... We prove a globalintime existence and uniqueness result for the Cauchy problem in the setting of some model of Quantum Molecular Chemistry. The model we are concerned with consists of a coupling between the timedependent HartreeFock equations (for the electrons) and the classical Newtonian dynam ..."
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Cited by 19 (0 self)
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We prove a globalintime existence and uniqueness result for the Cauchy problem in the setting of some model of Quantum Molecular Chemistry. The model we are concerned with consists of a coupling between the timedependent HartreeFock equations (for the electrons) and the classical Newtonian dynamics (for the nuclei). The proof combines semigroup techniques and the Schauder fixedpoint theorem. We also extend our result in order to treat the case of a molecule subjected to a timedependent electric field.
A bird’seye view of densityfunctional theory
, 2006
"... manybody theory, localdensity approximation This paper is the outgrowth of lectures the author gave at the ..."
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Cited by 15 (0 self)
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manybody theory, localdensity approximation This paper is the outgrowth of lectures the author gave at the
Recent progress in quantum hadrodynamics
 Int. J. Mod. Phys. E
, 1997
"... Quantum hadrodynamics (QHD) is a framework for describing the nuclear manybody problem as a relativistic system of baryons and mesons. Motivation is given for the utility of such an approach and for the importance of basing it on a local, Lorentzinvariant lagrangian density. Calculations of nuclea ..."
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Cited by 15 (0 self)
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Quantum hadrodynamics (QHD) is a framework for describing the nuclear manybody problem as a relativistic system of baryons and mesons. Motivation is given for the utility of such an approach and for the importance of basing it on a local, Lorentzinvariant lagrangian density. Calculations of nuclear matter and finite nuclei in both renormalizable and nonrenormalizable, effective QHD models are discussed. Connections are made between the effective and renormalizable models, as well as between relativistic meanfield theory and more sophisticated treatments. Recent work in QHD involving nuclear structure, electroweak interactions in nuclei, relativistic transport theory, nuclear matter under extreme conditions, and the evaluation of loop diagrams is reviewed.
Entanglement Theory and the Quantum Simulation Of Manybody Physics
, 2008
"... Quantum mechanics led us to reconsider the scope of physics and its building principles, such as the notions of realism and locality. More recently, quantum theory has changed in an equally dramatic manner our understanding of information processing and computation. On one hand, the fundamental prop ..."
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Cited by 12 (2 self)
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Quantum mechanics led us to reconsider the scope of physics and its building principles, such as the notions of realism and locality. More recently, quantum theory has changed in an equally dramatic manner our understanding of information processing and computation. On one hand, the fundamental properties of quantum systems can be harnessed to transmit, store, and manipulate information in a more efficient and secure way than possible in the realm of classical physics. On the other hand, the development of systematic procedures to manipulate systems of a large number of particles in the quantum regime, crucial to the implementation of quantumbased information processing, has triggered new possibilities in the exploration of quantum manybody physics and related areas. In this thesis, we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement, intrinsically quantum correlations, and the exploration of the use of controlled quantum systems to the computation and simulation of quantum manybody phenomena. In the first part we introduce a new approach to the study of entanglement
FMetal Physics
, 1977
"... We derive a m constrained by i characterized by exchange and by through changes o is tested in the an of bulk and single meanfield appro restrict the freedo It is shown that c and saturation, w induced by chang effective spin–orb ..."
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Cited by 11 (0 self)
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We derive a m constrained by i characterized by exchange and by through changes o is tested in the an of bulk and single meanfield appro restrict the freedo It is shown that c and saturation, w induced by chang effective spin–orb
Numerical analysis of the planewave discretization of some orbitalfree and KohnSham models. ESAIM: Mathematical Modelling and Numerical Analysis
, 2012
"... We provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic ThomasFermivon Weizsäcker (TFW) model and for the spectral discretization of the KohnSham model, within the local density approximation (LDA). These models allow ..."
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Cited by 10 (1 self)
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We provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic ThomasFermivon Weizsäcker (TFW) model and for the spectral discretization of the KohnSham model, within the local density approximation (LDA). These models allow to compute approximations of the ground state energy and density of molecular systems in the condensed phase. The TFW model is stricly convex with respect to the electronic density, and allows for a comprehensive analysis. This is not the case for the KohnSham LDA model, for which the uniqueness of the ground state electronic density is not guaranteed. Under a coercivity assumption on the second order optimality condition, we prove that for large enough energy cutoffs, the discretized KohnSham LDA problem has a minimizer in the vicinity of any KohnSham ground state, and that this minimizer is unique up to unitary transform. We then derive optimal a priori error estimates for the spectral discretization method. 1