Related papers: A discrete model of energy-conserved wavefunction …
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
In this letter, we have considered an electron in a coupled quantum dot system interacting with a detector represented by a point contact. We present a dynamical model for wave function collapse in the strong coupling to the detector limit.…
This brief article reviews stochastic processes as relevant to dynamical models of wave-function collapse, and is supplemental material for the review article arXiv:1204.4325
Wave function collapse models are considered as the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schr\"odinger equation, these models make predictions,…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…
In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…
The role of whitecapping losses of waves is investigated in a simple model based on conservation laws. It is shown that, for Airy waves, at least as much energy is lost in gradual reequilibration as is lost in the whitecapping events…
This is a review of formalisms and models (nonrelativistic and relativistic) which modify Schrodinger's equation so that it describes wavefunction collapse as a dynamical physical process.
Wave self-focusing in molecular systems subject to thermal effects, such as thin molecular films and long biomolecules, can be modeled by stochastic versions of the Discrete Self-Trapping equation of Eilbeck, Lomdahl and Scott, and this can…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
A stochastic model for nondemolition continuous measurement in a quantum system is given. It is shown that the posterior dynamics, including a continuous collapse of the wave function, is described by a nonlinear stochastic wave equation.…
A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent…
It is shown that within a quantum system, the wave field has a (potential) energy content that can be exchanged with quantum particles. Energy conservation in quantum systems holds if potential energy is correctly taken to be a field…
This paper aims to quantitatively relate the energy dissipated at a shock wave in a nonlinearly elastic bar to the energy in the oscillations in two related dissipationless, dispersive systems. In contrast to a phase boundary, there is no…
A novel discrete model (D-model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of…
We propose an effective non-relativistic framework in which wave-function collapse emerges as a deterministic dynamical instability induced by gravitational self-interaction and regulated by short-distance repulsion. The dynamics is…
A model of laminated wave turbulence is presented. This model consists of two co-existing layers - one with continuous waves' spectra, covered by KAM theory and Kolmogorov-like power spectra, and one with discrete waves' spectra, covered by…
We consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the water-air…
We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with…