Related papers: A discrete model of energy-conserved wavefunction …
Four problematic circumstances are considered, involving models which describe dynamical wavefunction collapse toward energy eigenstates, for which it is shown that wavefunction collapse of macroscopic objects does not work properly. In one…
Almost a century after the development of quantum mechanics, we still do not have a consensus on the process of collapse of wavefunctions. Some theories require the intervention of a conscious observer while some see it as a stochastic…
A typical feature of spontaneous collapse models which aim at localizing wavefunctions in space is the violation of the principle of energy conservation. In the models proposed in the literature the stochastic field which is responsible for…
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…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
The basic strategy underlying models of spontaneous wave function collapse (collapse models) is to modify the Schroedinger equation by including nonlinear stochastic terms, which tend to localize wave functions in space in a dynamical…
Non-interferometric experiments have been successfully employed to constrain models of spontaneous wave function collapse, which predict a violation of the quantum superposition principle for large systems. These experiments are grounded on…
Dynamical wave function collapse models entail the continuous liberation of a specified rate of energy arising from the interaction of a fluctuating scalar field with the matter wave function. We consider the wave function collapse process…
A model of spontaneous wavefunction collapse, which is explicitly local and Lorentz-invariant, is defined. Some of the predictions of the model for specific experimental situations are derived. It is shown that, although incompatible…
We study a model of spontaneous wavefunction collapse for a free quantum particle. We analyze in detail the time evolution of the single-Gaussian solution and the double-Gaussian solution, showing how the reduction mechanism induces the…
In this paper we consider a wave model with non-effective mass and dissipation terms and provide asymptotic descriptions of its representation of solutions. In particular we conclude sharp estimates for a corresponding energy and estimates…
The assumption that wave function collapse is induced by correlating interactions of the kind that constitute measurements leads to a stochastic collapse equation that does not require the introduction of any new physical constants and that…
We introduce an energy-based model, which seems especially suited for constrained systems. The proposed model provides an alternative to the popular port-Hamiltonian framework and exhibits similar properties such as energy dissipation as…
In this article, a numerical analysis of the asymptotic behavior of the discrete energy associated to a dissipative coupled wave system is conducted. The numerical approximation of the system is constructed using the P1 finite element…
We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is…
An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or…
Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. Recent developments in neural networks have enabled the…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
Using the method of a priori energy estimates, energy dissipation is proved for the class of hereditary fractional wave equations, obtained through the system of equations consisting of equation of motion, strain, and fractional order…
In this paper, we pursue our series of papers aiming to show the applicability of the concept of very weak solutions. We consider a wave model with irregular position dependent mass and dissipation terms, in particular, allowing for…