Related papers: Variational Approximations in a Path-Integral Desc…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
In the framework of functional integration the non-leading terms to leading eikonal behavior of the Planckian-energy scattering amplitude are calculated by the straight-line path approximation. We show that the allowance for the first-order…
We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…
A quantum model based on a Euler-Lagrange variational approach is proposed. In analogy with the classical transport, our approach maintain the description of the particle motion in terms of trajectories in a configuration space. Our method…
On the basis of the eikonal approximation of quantum scattering theory, the problem of fast charged particles scattering in a thin crystal when particles fall along one its plane of atoms and in a thin layer of amorphous matter is…
Motivated by recently developed techniques making it possible to compute Casimir energies for any object whose scattering S-matrix (or, equivalently, T-matrix) is available, we develop a variable phase method to compute the S-matrix for…
We use the Feynman path integral approach to nonrelativistic quantum mechanics twofold. First, we derive the lagrangian for a spinless particle moving in a uniformly but not necessarily constantly accelerated reference frame; then, applying…
We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest.…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
This article provides a new theory for the analysis of forward and backward particle approximations of Feynman-Kac models. Such formulae are found in a wide variety of applications and their numerical (particle) approximation are required…
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…
We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem…
Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasi-potential…
A local and distributive algorithm is proposed to find an optimal trial wave-function minimizing the Hamiltonian expectation in a quantum system. To this end, the quantum state of the system is connected to the Gibbs state of a classical…
A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and…
The method of regions, which provides a systematic approach for computing Feynman integrals involving multiple kinematic scales, proposes that a Feynman integral can be approximated and even reproduced by summing over integrals expanded in…
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…
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…