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We propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory. We consider the following essential and related problems : i) how to find the correct…
We present an effective potential that allows quantum thermal expectation values of a position-dependent observable to be estimated as a classical ensemble average of the corresponding function. We follow the approach of Feynman and Hibbs,…
New physical insight into the correspondence between path integral concepts and the Schr\"odinger formulation is gained by the analysis of the effective classical potential, that is defined within the Feynman path integral formulation of…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
Modeling nuclear quantum effects is required for accurate molecular dynamics (MD) simulations of molecules. The community has paid special attention to water and other biomolecules that show hydrogen bonding. Standard methods of modeling…
A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
Force fields are usually formulated directly in nuclear configuration space, whereas density functional theory is naturally formulated in terms of external potentials, densities, and variational duality. We show that exact force fields are…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
A canonical formulation of effective equations describes quantum corrections by the back-reaction of moments on the dynamics of expectation values of a state. As a first step toward an extension to quantum-field theory, these methods are…
The Hohenberg-Kohn (HK) theorem -- the bedrock of density functional theory (DFT) -- establishes a universal map from the external potential to the energy. It also relates the electron density and atomic forces to the variation of the…
We propose a method to construct a classical analog of an open quantum system, namely a single quantum particle confined in a potential well and immersed in a thermal bath. The classical analog is made out of a collection of identical wells…
We derive expressions for the expectation values of the local energy and the local power transferred by an external electrical field to a many-particle system of interacting spinless electrons. In analogy with the definition of the (local)…
We examine the equilibrium properties of hot, dilute, non-relativistic plasmas. The partition function and density correlation functions of a classical plasma with several species are expressed in terms of a functional integral over…
Using techniques of effective field theory, we consider the thermodynamical properties of a dilute two-dimensional plasma interacting via a $1/r$ potential. The first one-loop correction to the partition function is already logarithmically…
Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of…
We construct a space of ideal elements (particles and their paths) to analyze certain aspects of quantum physics. The particles are taken from a model of particle interaction first described by David Deutsch (based on a different but…
This article reports an explicit function form for confining classical Yang-Mills vector potentials and quantum fluctuations around the classical field. The classical vector potential, which is composed of a confining localized function and…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer,…