Related papers: Force-Field Functor Theory: Classical Force-Fields…
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
Given an arbitrary Lagrangian function on \RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…
We derive a version of the so-called "best Fokker-Planck approximation" (BFPA) to describe the spatial properties of interacting active Ornstein-Uhlenbeck particles (AOUPs) in arbitrary spatial dimensions. In doing so, we also take into…
We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action…
A generalization of the action principle of classical mechanics, motivated by the Closed Time Path (CTP) scheme of quantum field theory, is presented to deal with initial condition problems and dissipative forces. The similarities of the…
It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion…
An approach to approximate evaluation of the continuum Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are…
The effective potential theory is a physically motivated method for extending traditional plasma transport theories to stronger coupling. It is practical in the sense that it is easily incorporated within the framework of the Chapman-Enskog…
Given a vector space of microscopic quantum observables, density functional theory is formulated on its dual space. A generalized Hohenberg-Kohn theorem and the existence of the universal energy functional in the dual space are proven. In…
We show that the Franck-Condon Factor (FCF) associated to a transition between initial and final vibrational states in two different potential energy surfaces, having $N$ and $M$ vibrational quanta, respectively, is equivalent to…
A flat Fiedmann-Robertson-Walker (FRW) multi-scalar field cosmology is studied with a particular potential of the form $ \rm V(\phi,\sigma)=V_0 e^{-\lambda_1 \phi-\lambda_2 \sigma}$, which emerges as a relation between the time derivatives…
In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…
The concept of effective particles is introduced in the Minkowski space-time Hamiltonians in quantum field theory using a new kind of the relativistic renormalization group procedure that does not integrate out high-energy modes but instead…
We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…
We derive an equation for the current of particles in energy space; particles are subject to a mean field effective potential that may represent quantum effects. From the assumption that non-interacting particles imply a free diffusion…
We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…
Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between…