Related papers: Foundation q-rules
Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the…
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
The scattering of electromagnetic waves by resonant systems is determined by the excitation of quasinormal modes (QNMs), i.e., the eigenmodes of the system. This Review addresses three fundamental concepts in relation with the…
The Schr\"odinger-Lohe model consists of wave functions interacting with each other, according to a system of Schr\"odinger equations with a specific coupling such that all wave functions evolve on the $L^2$ unit ball. This model has been…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
The propagation of nonrelativistic excitations in material media with topological defects can be modeled in terms of an external torsion field modifying the Schroedinger equation. Through a perturbative approach, we find a solution for the…
Consider the cubic nonlinear Schr\"odinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, on average, the evolution of the moduli of the…
Quantum systems are dynamic systems restricted by the principles of quantum mechanics (linearity of dynamic equations, linear transformation of the wave function etc.). One suggests to investigate the quantum systems simply as dynamic…
Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…
The basic principles of the quantum mechanics in the K-field formalism are stated in the paper. The basic distinction of this theory arises from that the quantum theory equations (including well-known Schrodinger, Klein-Gordon and quadratic…
Special relativity combined with the stochastic vacuum flux impact model lead to an explicit interpretation of many of the phenomena of elementary quantum mechanics. We examine characteristics of a repetitively impacted submicroscopic…
A concise review of the derivation of the Born rule and Schr\"odinger equation from first principles is provided. The starting point is a formalization of fundamental notions of measurement and composition, leading to a general framework…
Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schr\"odinger equation with a quintic nonlinearity. These patterns include bright pulses, fronts and dark solitons. The evolution of the wave…
The change with time of the system consisting of the quantum object and the macroscopic measuring instrument is described on the base of the uniform dynamic law, which is suitable both evolution and reduction processes description. It is…
Proofs are given that the quantum-mechanical description of the LC-circuit with a time dependent external source can be readily established by starting from a general discretization rule of the electric charge. For this purpose one resorts…
Linearised relativistic elasticity equations of motion are considered for a rod and a spinning ring encountering a gravitational wave. In the case of the rod, the equations reduce to a wave equation with appropriate boundary conditions.…
We seek an extension to Schrodinger's equation that incorporates the macroscopic measurement-induced wavefunction collapse phenomenon. We find that a suitable hybrid between two leading approaches, the Bohm-de Broglie pilot-wave and…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
A series of successive quantizations is considered, starting with the quantization of a non relativistic or relativistic point particle: 1) quantization of a particle's position, 2) quantization of wave function, 3) quantization of wave…
We consider the Schr\"odinger equation with nonlinear derivative term on $[0,+\infty)$ under Robin boundary condition at $0$. Using a virial argument, we obtain the existence of blowing up solutions and using variational techniques, we…