Related papers: Variational Approximations in a Path-Integral Desc…
The use of variational method in functional integral approach is discussed for fermion and boson systems with Coulomb interaction. The formal general expression of thermodynamic potential is obtained by Feynman path integral technique and…
The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…
It is shown that a relativistic multiple scattering theory for hadron-nucleus scattering can be consistently formulated in four-dimensions in the context of meson exchange. We give a multiple scattering series for the optical potential and…
An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider a model for spin-orbital motion: orbital…
We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
In evaluating differential cross section of elastic scattering, different theories were applied to low-momentum and relativistic particles. For low-momentum motion, Lippmann-Schwinger scattering equation was applied, called fundamental…
I review the Feynman-Wiener path-integral formalism for diffusion with drift and jumps.
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the…
In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes…
We present a variational solution of the T-matrix integral equation within a local approximation. This solution provides a simple form for the T matrix similar to Hubbard models but with the local interaction depending on momentum and…
A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatio-temporal fractionality, and a variational solution is obtained with the help of the…
A rigorous theory of diffraction scattering from extended objects is proposed. The present theory is based on a multiple asymptotic expansion of an integral equation for the exact wave function in terms of the large parameters of the…
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…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
The elastic neutron-${}^3\mathrm{H}$ scattering at intermediate energies is studied using rigorous integral equations solved in the momentum-space partial-wave basis. The four-particle transition operators are expanded into…