Related papers: Dynamics of wave packets in the functional mechani…
In this note, we propose coordinate-invariant notions of incremental Lyapunov function and provide characterizations of incremental stability in terms of existence of the proposed Lyapunov functions.
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
We continue the semiclassical analysis, started in a previous paper, of the intertwiner sector of the flipped vertex spinfoam model. We use independently both a semi-analytical and a purely numerical approach, finding the correct behavior…
In this paper a new functional integral representation for classical dynamics is introduced. It is achieved by rewriting the Liouville picture in terms of bosonic creation-annihilation operators and utilizing the standard derivation of…
The model of laminated wave turbulence presented recently unites both types of turbulent wave systems - statistical wave turbulence (introduced by Kolmogorov and brought to the present form by numerous works of Zakharov and his scientific…
Geminal wavefunctions, introduced in the late 1950s, have long been recognized for their ability to compactly capture strong electron correlation. Despite their promise, they were historically overshadowed by more computationally efficient…
The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…
The idea that wave-function collapse is a physical process stems from a misunderstanding of probability and the role it plays in quantum mechanics.
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
We study phase contributions of wave functions that occur in the evolution of Gaussian surface gravity water wave packets with nonzero initial momenta propagating in the presence and absence of an effective external linear potential. Our…
In this work we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on shell approach for the scattering matrix, commonly…
A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…
After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
This note is a complement to Pusz--Woronowicz's works on functional calculus for two positive forms from the viewpoint of operator theory. Based on an elementary, self-contained and purely Hilbert space operator explanation of their…
Under the framework of V. Yakhot [Phys.Rev.E, {\bf57}, 1737 (1998)] modelling of intermittent structure functions in fully developed turbulence and based on the experimentally supported Markovian nature of turbulence cascades [R.Friedrich…