Related papers: Translation-invariant relativistic Langevin equati…
Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for…
It is shown that the solution of generalized Langevin equation can be obtained on the basis of simple comparison of the time scale for the velocity autocorrelation function of a particle (atom, molecule) and of the time scale for the…
Dynamical random walk of classical particle in thermodynamically equilibrium fluctuating medium, - Gaussian random potential field, - is considered in the framework of explicit stochastic representation of deterministic interactions. We…
The formal derivation of Langevin equations (and, equivalently Fokker-Planck equations) with projection operator techniques of Mori, Zwanzig, Kawasaki and others apparently not has widely found its way into textbooks. It has been reproduced…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
A colloidal particle is a prominent example of a stochastic system, and, if suspended in a simple viscous liquid, very closely resembles the case of an ideal random walker. A variety of new phenomena have been observed when such colloid is…
We study a minimal non-Markovian model of superdiffusion which originates from long-range velocity correlations within the generalized Langevin equation (GLE) approach. The model allows for a three-dimensional Markovian embedding. The…
Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative…
Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and…
This paper derives and analyzes exact, nonlocal Langevin equations appropriate in a cosmological setting to describe the interaction of some collective degree of freedom with a surrounding ``environment.'' Formally, these equations are much…
Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…
We formulate a perturbative approximation to gravitational instability, based on Lagrangian hydrodynamics in Newtonian cosmology. We take account of `pressure' effect of fluid, which is kinematically caused by velocity dispersion, to aim…
Renormalization group method is applied to the study of vibrational energy transfer in protein molecule. An effective Lagrangian and associated equations of motion to describe the resonant energy transfer are analyzed in terms of the…
A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion,…
The task of finding a consistent relationship between a quantum Hamiltonian and a classical Lagrangian is of utmost importance for basic, but ubiquitous techniques like canonical quantization and path integrals. Nonconvex kinetic energies…
We formulate a class of stochastic partial differential equations based on Kelvin's circulation theorem for ideal fluids. In these models, the velocity field is randomly transported by white-noise vector fields, as well as by its own…
The forward--backward path integral describing a charged particle moving in a thermal bath of photons is expressed in terms of the solution of a Langevin-type of equation. Approximate methods for solving this equation are discussed.
We consider the problem of building a continuous stochastic model, i.e. a Langevin or Fokker-Planck equation, through a well-controlled coarse-graining procedure. Such a method usually involves the elimination of the fast degrees of freedom…
We analyze the non-linear generalized Langevin equation which contains a thermodynamic force. We show that even for systems in thermal equilibrium the presence of the thermodynamic force implies that the auto-correlation function of the…
We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the…