Related papers: Dynamics of wave packets in the functional mechani…
This is an idiosyncratic survey of statistical fluid mechanics centering on the Hopf functional differential equation. Using the Burgers equation for illustration we review several functional integration approaches to theory of turbulence.…
A novel geometric interpretation of the solutions of the WDVV equations formerly found by A.P. Veselov is suggested.
Particles moving inside a fluid near, and interacting with, invariant manifolds is a common phenomenon in a wide variety of applications. One elementary question is whether we can determine once a particle has entered a neighbourhood of an…
We develop an elementary formalism of functional calculus for entire holomorphic functions in the setting of Clausen and Scholze's $p$-liquid vector spaces.
A modified form of quantum mechanics which includes a new mechanism for wavefunction collapse is proposed. The collapse provides a solution to the quantum measurement problem. This modified quantum mechanics is shown to arise naturally from…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a stationary Markov process satisfying certain technical criteria, we show that the square amplitude of…
We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…
In the present paper a description of a problem of point vortices on a plane and a sphere in the "internal" variables is discussed. The hamiltonian equations of motion of vortices on a plane are built on the Lie-Poisson algebras, and in the…
It is shown that von Neumann-Landau equation for wave functions can present a mathematical formalism of motion of quantum mechanics. The wave functions of von Neumann-Landau equation for a single particle are `bipartite', in which the…
The time-independent Schroedinger and Klein-Gordon equations - as well as any other Helmholtz-like equation - were recently shown to be associated with exact sets of ray-trajectories (coupled by a "Wave Potential" function encoded in their…
In this paper we continue the study, started in [1], of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the Thirties. In particular we show that the introduction of the KvN Hilbert space of…
The fluctuations of dynamical functionals such as the empirical density and current as well as heat, work and generalized currents in stochastic thermodynamics are usually studied within the Feynman-Kac tilting formalism, which in the…
We expand on a previous study, offering a generalized wave function associated with the parabolic cylinder function and a connection with a two-particle position-space wave function. We also provide an explicit formula for a wave function…
We investigate the meaning of the wave function by analyzing the mass and charge density distribution of a quantum system. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus…
We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…
We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…
We summarize the theoretical description of wave packets on molecular energy levels. We review the various quantum mechanical effects which can be studied and the models that can be verified on this system. This justifies our claim that the…
Following the spirit of de Broglie and Einstein, we think the concepts of matter and radiation can be unified. We know a particle propagates like a wave; its motion is described by certain wave equations. At this point, it is not clear what…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…