Related papers: Another derivation of generalized Langevin equatio…

Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role,…

A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…

General equations are derived for slow viscous thin fluid film flows on curved surfaces through an extension of Leal's pedagogical approach, which leaves the characteristic velocity scale unspecified and employs a direct through-thickness…

This work is devoted to the derivation and the matematical study of a new model for water-soluble polymers and metal ions interactions, which are used in chemistry for their wide range of applications. First, we motivate and derive a model…

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum…

The evolution of finitely many particles obeying Langevin dynamics is described by Dean-Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised…

We show that all results of Yasar and Ozer [Comput. Math. Appl. 59 (2010), 3203-3210] on symmetries and conservation laws of a "nonconservative Fokker-Planck equation" can be easily derived from results existing in the literature by means…

As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide neural networks in the mean field regime, and hence the…

We use the light front ``machinery'' to study the behavior of a relativistic free particle and obtain the quantum commutation relations from the classical Poisson brackets. We argue that their usual projection onto the light-front…

We show that the Fokker Planck equation can be derived from a Hypergeometric differential equation. The same applies to a non linear generalization of such equation.

We investigate whether the stationary solution of the Fokker-Planck equation of the complex Langevin algorithm reproduces the correct expectation values. When the complex Langevin algorithm for an action $S(x)$ is convergent, it produces an…

In literature one can find many generalizations of the usual Leibniz derivative, such as Jackson derivative, Tsallis derivative and Hausdorff derivative. In this article we present a connection between Jackson derivative and recently…

As it is well-known, Poisson brackets play a fundamental role both in mechanics and in classical field theories. In this paper we develop a theory of extensions of graded Poisson brackets in graded Dirac manifolds. We then show how these…

The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…

We emphasize the usefulness of the Lie brackets in the context of classical and quantum mechanics. By way of examples we show that many dynamical systems, especially the ones with (gauge) constraints, can equally be treated in their time…

This paper shows how the forms of gauge theory, Hamiltonian mechanics and quantum mechanics arise from a non-commutative framework for calculus and differential geometry. Discrete calculus is seen to fit into this pattern by reformulating…

As an alternative to the covariant Ostrogradski method, we show that higher-derivative relativistic Lagrangian field theories can be reduced to second differential-order by writing them directly as covariant two-derivative theories…

Starting with the relativistic Boltzmann equation where the collision term was generalized to include gradients of the phase-space distribution function, we recently presented a new derivation of the equations for the relativistic…

Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…

In this paper we discuss the connections between a Vlasov-Fokker-Planck equation and an underlying microscopic particle system, and we interpret those connections in the context of the GENERIC framework (\"Ottinger 2005). This…